An introduction to electromagnetism

Electromagnetism essentially describes the force between electrically charged particles conveyed by electromagnetic fields.

Electromagnetism is the fundamental force that governs the interactions between electrically charged particles.
Electromagnetism is apparent in the interplay between electric and magnetic fields.
Electromagnetism encompasses the observable effects we encounter in everyday life, including the transmission of light by electromagnetic waves.
The electromagnetic force is one of the four fundamental forces of nature, along with the strong nuclear force, the weak nuclear force, and gravity.

In terms of everyday experience, interactions between objects are often straightforward to visualise. We forcefully push open a jammed door or hammer a nail into wood. A strong gale can topple a tree, while a gentle summer breeze merely causes leaves to flutter. These interactions feel intuitive because we understand what it means when one thing pushes, pulls, or resists another. However, at an atomic level, most of these mechanical forces manifest the electromagnetic force. The interactions between atoms and molecules within objects are governed by electromagnetism, and it is this underlying reality that explains many of the mechanical forces that shape the world around us.

Electromagnetism also plays a key role in other kinds of everyday actions, such as observing the world around us, turning on a light, cooking with a microwave or induction hob, or changing channels with a TV remote.

Simply looking around involves light waves, a feature of electromagnetism, entering our eyes and triggering chemical reactions that produce signals transmitted to our brain.
Turning on a light passes an electric current—another phenomenon governed by electromagnetism—through a circuit containing an incandescent filament, a fluorescent gas, or an LED.
Microwaves and induction hobs both rely on electromagnetic waves. Microwaves use specific frequencies of electromagnetic radiation to heat food, while induction hobs use rapidly changing magnetic fields to induce currents in cookware, generating heat.
Most modern TV remotes use infrared light, part of the electromagnetic spectrum, to send signals to a TV.

FUNDAMENTAL FORCES

The electromagnetic force, one of nature’s four fundamental forces, influences both subatomic particles and large-scale objects. It is represented by electric and magnetic fields, with electric fields generated by stationary charges and magnetic fields by moving charges. This force is responsible for a range of phenomena, including light as electromagnetic radiation, electricity as charge flow, and magnetism. It also underlies electromagnetic induction, where changing magnetic fields produce electric currents. Additionally, the electromagnetic force plays a key role in certain mechanical forces, such as those binding atoms in molecules and generating friction and tension in everyday materials.

ELECTROMAGNETIC FORCE

The electromagnetic force is a fundamental interaction evident in phenomena such as magnetism, electromagnetic induction, light, electricity, and mechanical forces. It is studied in both classical electromagnetism and quantum electrodynamics, the latter being a branch of quantum mechanics. In classical electromagnetism, the electromagnetic force affects charged objects, such as positively charged hair and negatively charged balloons, while in quantum electrodynamics, it acts on charged particles, including positively charged protons and negatively charged electrons. Charged objects and particles generate electric and magnetic fields, which are integral to the behaviour and interactions governed by the electromagnetic force.

Electromagnetic Force is one of the four fundamental forces of nature. It governs the behaviour of electric and magnetic fields and is responsible for a wide range of phenomena, including light, electricity, magnetism, and electromagnetic induction. The interactions between charged particles take the form of exchanges of photons, which act as force carriers.

This article delves into the world of electromagnetism, aiming to establish a solid foundation for exploring matters such as how we perceive colour and interpret the world around us. These themes appear throughout the resources available on our website, lightcolourvision.org.

To better understand the role of electromagnetism in visual perception, we must first explore its function in shaping both the visible world and the invisible realm of electrically charged particles. Accordingly, our approach will examine phenomena on two distinct but inter-related scales:

Macro Scale: This includes phenomena such as reflection, refraction, and chromatic dispersion, and the afore mentioned mechanical effects of electromagnetic forces, which are best explained by classical electromagnetism.

Micro Scale: This involves interactions between subatomic charged particles, studied through Quantum Electrodynamics (QED), a theory grounded in the principles of quantum mechanics.

Understanding both scales begins with recognizing the connections between them and with the fact that charged particles and the objects they are a part of are the source of electromagnetic forces and the fields that convey them. The interactions between these particles are governed by their positive and negative electrical charges. Without charged particles, electromagnetism would not exist.

But there is more to it than that. Classical Electromagnetism describes charged particles and the systems they belong to as generating electric and magnetic fields which exert forces on other charged particles. These fields explain familiar phenomena, from the behaviour of distinct objects that push and pull to the generation and propagation of electromagnetic waves, including visible light. A hallmark of this perspective is the representation of the electromagnetism as continuous lines of force extending smoothly through space, interconnecting particles, fields, and forces while treating them as distinct components.

Quantum Electrodynamics (QED), in contrast, extends our understanding of these interactions by introducing a granular perspective. It portrays the electromagnetic field as quantized, comprising discrete energy units called photons. In QED, interactions between charged particles occur through the exchange of these photons, each carrying specific amounts of energy and momentum directly tied to their frequency. This concept of quantization redefines physical properties such as energy, charge, and angular momentum. It formulates a microscopic view of electromagnetic interactions, fundamentally reshaping how we understand forces and fields at the smallest scales.

While classical and quantum frameworks share the recognition of charged particles as sources of electromagnetic fields and forces, they diverge in their representations. In a nut shell, classical physics envisions smooth, continuous fields, whereas QED reveals a dynamic interplay of discrete photon exchanges. This distinction underscores the richness of electromagnetism as understood across different scales, bridging the macroscopic and quantum worlds.

While classical physics and quantum mechanics share this broad description, their interpretations and underlying principles differ significantly:

Classical Electromagnetism views charged particles and the systems they belong to as generating electric and magnetic fields. These fields exert forces on other charged particles, shaping the familiar world of distinct objects that push, pull, and interact with one another. Classical electromagnetism also explains phenomena such as the generation and propagation of electromagnetic waves, including those that produce visible light. A key feature of this perspective is that the electromagnetic force is represented as continuous lines of force extending smoothly through space between particles and the larger objects they compose. In this framework, particles, fields, and forces are interconnected but treated as distinct components.
Quantum Electrodynamics (QED) provides a contrasting view, where the interaction between charged particles is understood as the exchange of photons. Photons carry energy in discrete amounts directly related to their frequency. Unlike the smooth, continuous fields described in classical electromagnetism, QED portrays these interactions as discrete events, in which each photon transmits a specific quantity of energy and momentum.

ELECTROMAGNETIC FIELDS

The electromagnetic force is produced by positive and negative electrical charges and manifests as electromagnetic fields, which include both electric and magnetic components. From a classical perspective, electromagnetic fields are represented as electromagnetic waves with continuous and smooth oscillations in wavelength and frequency. In contrast, quantum physics describes electromagnetic fields as being composed of photons, which are discrete and quantized packets of energy and momentum. In quantum physics, quantization refers to the concept that certain physical properties, such as energy, charge, and angular momentum, are not continuous but exist in discrete units called quanta. These quanta represent the smallest possible, indivisible amounts of these properties, fundamentally changing our understanding of interactions at the microscopic scale.

Quantum Electrodynamics (QED) is the pivotal framework within quantum physics, that extends our understanding of electromagnetic interactions into new territory. Its hallmark contribution lies in treating electromagnetism as quantized units of energy, in such a way that the electromagnetic field is divided into discrete quanta. Within this framework, each photon is understood as a quantum of the electromagnetic field.

In quantum physics, quantization refers to the concept that certain physical properties—such as energy, charge, and angular momentum—are not continuous but exist in discrete units called quanta. These quanta represent the smallest possible indivisible amounts of these properties, which fundamentally reshapes our understanding of interactions at the microscopic scale.

While classical electromagnetism and QED fundamentally agree on the role of charged particles as sources of electromagnetic fields and as mediators of the forces governing particle interactions, the two frameworks diverge significantly in their approaches. Classical electromagnetism describes fields and forces as continuous, smooth phenomena, while QED introduces a granular perspective, portraying interactions as discrete exchanges of photons. This distinction underscores the complexities of understanding electromagnetism across different scales and highlights the interplay between classical and quantum perspectives.

A classical perspective of electromagnetism

Classical electromagnetism is a foundational part of classical field theory, which describes how physical fields, such as electric and magnetic fields, interact with matter and propagate through space and time. Classical field theory encompasses a broad range of phenomena, including electromagnetism, gravitation—explained by Newton’s law of universal gravitation and refined by Einstein’s General Relativity—and fluid dynamics, where fields describe properties like velocity and pressure.

A central focus of classical electromagnetism is the relationship between matter and energy. Charged objects generate electric and magnetic fields, which influence the motion and configuration of other charged objects, shaping the behaviour of matter.

In classical electromagnetism:

Electric fields store energy associated with the arrangement of charged particles and exert forces that cause attraction or repulsion between charges. These forces follow Coulomb’s law, decreasing in strength with distance.
Magnetic fields are generated by moving charges and currents, transferring energy and interacting with other magnetic materials or moving charges.
Electromagnetic waves, such as light, consist of oscillating electric and magnetic fields that carry energy through space and interact with matter via processes like absorption and reflection, transferring energy in the process.

This classical view presents energy as continuously distributed and transferred through fields, shaping the behaviour of matter in everyday phenomena. However, energy itself is not a physical substance but a property of systems that can be transferred or converted from one form to another. The interplay between matter and energy is evident across all scales, from the microscopic interactions of atoms to the vast structures of the universe.

While the classical perspective treats matter and energy as distinct entities, Einstein’s equation, $E=mc^2$ , later revealed their interchangeability under certain conditions, offering a more nuanced understanding of their relationship.

Electromagnetic force

In classical physics, the electromagnetic force manifests itself through electric and magnetic fields, which vary continuously and predictably. The strength of these fields depends on the amount of charge, the distance from a charged particle, and the momentum of moving charges. These fields make the force measurable, enabling the calculation of interactions between charges. This understanding underpins a wide range of phenomena, from light as electromagnetic waves to electric circuits and magnetic interactions.

James Clerk Maxwell (1831–1879) unified the behaviour of electric and magnetic fields through a set of four equations, known as Maxwell’s equations. These equations describe how fields interact with charges, currents, and each other, summarised as:

Electric charges produce electric fields.
Magnetic field lines form closed loops.
A changing magnetic field induces an electric field.
Electric currents and changing electric fields produce magnetic fields.

Electric & Magnetic Fields

Electric and magnetic fields are fundamental concepts in classical electromagnetism:

The electric field (E) describes the force experienced by a charged particle due to other nearby charges. It is generated by stationary electric charges, which can be positive or negative.
The magnetic field (B) describes the force experienced by moving charged particles (electric currents) or by magnetic materials. It is generated by moving charges and electric currents.

Classical waves

In the classical view, light is understood as electromagnetic waves propagating through empty space at the speed of light. These waves consist of oscillating electric and magnetic fields, oriented at right angles to each other and to the direction of propagation. This wave-like behaviour explains phenomena such as reflection, refraction, polarisation, and interference. Classical electromagnetism does not address photons, the quantum mechanical particle aspect of light.

Deterministic nature of interactions

In classical electromagnetism, interactions between charged particles and fields are deterministic. Maxwell’s equations allow precise predictions of how electric and magnetic fields behave and the forces they exert.

The term “deterministic” signifies that, given a system’s initial conditions, its future state can be accurately predicted. This implies that events unfold as inevitable consequences of preceding conditions, with no inherent randomness.

Continuous interaction

The electromagnetic force is conceived as a continuous interaction across space and time. Electric and magnetic fields are represented by continuous lines of force, which change smoothly and predictably over distance and time. These lines enable the uninterrupted transmission of electromagnetic effects, such as visible light and radio waves, without abrupt jumps.

In visualising fields, field lines depict the direction and strength of the force experienced by a positively charged particle. For electric fields, lines emanate from positive charges and terminate at negative charges, while magnetic field lines form closed loops, circulating from the north to the south pole of a magnet.

Classical laws of physics

The classical laws governing electromagnetic interactions are derived from Maxwell’s equations, which provide a comprehensive mathematical framework:

Gauss’s Law for Electricity: Electric charges produce electric fields.
Gauss’s Law for Magnetism: There are no isolated magnetic poles; magnetic field lines form closed loops.
Faraday’s Law of Induction: A changing magnetic field induces an electric field.
Ampère’s Law (with Maxwell’s correction): Oscillating electric fields and electric currents generate magnetic fields.

These equations not only unify electricity and magnetism but also reveal their connection to light, demonstrating that light itself is an electromagnetic wave. Maxwell’s unification marked a turning point in physics and laid the groundwork for quantum electrodynamics (QED), the modern theory describing electromagnetic interactions at the quantum level. Maxwell’s equations underpin technologies like wireless communication, imaging, and electric motors, showcasing their enduring relevance.

While Maxwell’s equations focus on the dynamics of fields, additional laws describe specific interactions between charges and fields:

Coulomb’s Law: Describes the electrostatic force between two charges, directly proportional to their magnitudes and inversely proportional to the square of their distance.
Lorentz Force Law: Explains the force exerted on a charged particle moving through electric and magnetic fields, essential for devices like motors and particle accelerators.

A quantum perspective on electromagnetism

Introduction

This section explores electromagnetism through the lens of quantum mechanics, particularly Quantum Electrodynamics (QED), which provides a deeper understanding of light, charged particles, and their interactions.

Quantum Mechanics

Quantum mechanics describes the behaviour of matter and energy at atomic and subatomic scales. It challenges classical notions by introducing key principles such as wave-particle duality, uncertainty, and quantization. Unlike deterministic classical theories, quantum mechanics embraces probabilistic interactions, offering insights into phenomena like electron orbitals and the photoelectric effect.

Quantum Field Theory

Quantum Field Theory (QFT) unites classical field theory, special relativity, and quantum mechanics, creating a framework for understanding fundamental forces. A key aspect of QFT is its field-centric approach: particles like electrons or photons are seen as excitations of their corresponding quantum fields. Quantum Electrodynamics (QED), a branch of QFT, focuses specifically on the electromagnetic field, providing a foundational theory for understanding light and charged-particle interactions.

Special relativity

Special relativity, developed by Albert Einstein, ensures that the laws of physics remain consistent for observers moving at constant speeds, even near the speed of light. This principle underpins QFT and QED, ensuring that descriptions of electromagnetic interactions—such as those involving photons and electrons—are valid for all observers.

Quantum fields

At the heart of QFT are quantum fields, which form the basis for all particles. Each particle corresponds to its own field: electrons arise from the electron field, photons from the electromagnetic field, and so on. These fields extend throughout space, and what we perceive as ’empty’ space is, in fact, their lowest energy state. Excitation within these fields manifest as particles (localized energy) or waves (distributed energy), explaining phenomena like interference, diffraction, and the photoelectric effect.

Quantum fields are the foundation of QFT. Each type of subatomic particle arises from a specific field: the electron field produces electrons, the quark field produces quarks, and the Higgs field produces Higgs bosons. The electromagnetic field gives rise to photons and electromagnetic waves, with their energy and momentum being manifestations of this field.

In this framework, empty space is not truly empty but represents the lowest energy state of any quantum field. Even in the absence of particles and waves, the electromagnetic field for example persists and can be excited to various energy levels. These excitations manifest as particle-like and wave-like properties of light. For example, photons behave as particles in the photoelectric effect and as waves in interference and diffraction patterns. Particles are localized excitations, while waves are more spread-out excitations.

The vacuum of space is a dynamic backdrop where particles like photons continuously emerge and disappear due to quantum fluctuations. These fluctuations produce measurable effects, such as the Casimir effect.

Electromagnetic field

In QED, the electromagnetic field is a fundamental, unified field that permeates all spacetime. Excitations of this field appear as photons, which serve as the force carriers for electromagnetic interactions. These interactions include the forces between charged particles, the propagation of light, and the behaviour of electromagnetic waves, all governed by the dynamics of this unified field.

Duality of matter and energy

Matter and energy are both excitations of quantum fields. QFT and QED provide a unified description of their relationship. Particles, in terms of their mass and the space they occupy, represent matter. However, particles also exhibit wave-like behaviour associated with energy. This wave-particle duality is a fundamental aspect of quantum physics.

Particles of light

The implications of the quantum perspective extend to the way we understand light. At the macro-scale, light reaching our eyes is composed of discrete, quantized particles, called photons, that make up the electromagnetic field. Each photon carries a specific amount of energy and momentum, which triggers biochemical responses in the retina’s photoreceptor cells, enabling vision.

QED also offers insights into these particle interactions at the subatomic scale. At this level, all interactions between particles are mediated by virtual particles. For example, electromagnetic interactions are facilitated by virtual photons. The strong nuclear force, which holds quarks together within protons and neutrons, is mediated by virtual gluons, while the weak nuclear force, responsible for processes like beta decay, is mediated by W and Z bosons.

Virtual particles

Virtual particles serve as transient intermediaries in interactions between real particles. They exist briefly and are described by mathematical models in quantum field theory to represent interactions over short timescales. Although virtual particles cannot be directly detected, their effects on stable particles and fields can be inferred and calculated. For instance, virtual photons facilitate the exchange of energy and momentum between charged particles, explaining imperceptible forces at play in electromagnetic interactions.

Their temporary existence is a consequence of quantum mechanics, particularly the uncertainty principle, which allows fluctuations in energy and momentum over extremely short timescales. These fluctuations enable virtual particles to exist fleetingly, playing a key role in mediating interactions that contribute to our understanding of particle dynamics.

Photons

In 1905, Albert Einstein introduced the concept of photons through his explanation of the photoelectric effect, which demonstrated that light is formed from discrete packets of energy. While Einstein’s work was foundational in the development of quantum theory, the specific term “photon” was later introduced by Gilbert N. Lewis in 1926. Einstein laid the groundwork for understanding photons, but Lewis coined the term to describe these quantum units of light that compose electromagnetic radiation.

In Quantum Electrodynamics (QED), the electromagnetic field is described as a quantized field, where photons are its quanta or individual excitations.

So, the term photon is used in physics in two distinct ways. Virtual and real photons are separate phenomena, despite the similarity in their names.

In 1905, Albert Einstein introduced the concept of photons to explain the photoelectric effect, demonstrating that light consists of discrete packets of energy. While Einstein’s work was foundational in the development of quantum theory, the term “photon” was later coined by Gilbert N. Lewis in 1926 to describe these quantum units of light.

In QED, the electromagnetic field is quantized, and photons are its quanta, or individual excitations. However, photons can refer to two different phenomena: real photons and virtual photons.

Real photons

Real photons are the observable particles that constitute electromagnetic radiation, including visible light. These massless particles travel at the speed of light in a vacuum and are emitted or absorbed when electrons transition between energy levels in atoms. Their energy, frequency, and wavelength determine the characteristics of electromagnetic radiation, from radio waves to gamma rays.

In QED, real photons are excitations of the electromagnetic field. Their energy is related to their frequency by the equation E=hf, where E is energy, h is Planck’s constant, and f is the frequency. Real photons can be emitted by various sources, such as stars or light bulbs, and can travel vast distances without losing energy. They can be reflected off surfaces of everyday objects or absorbed by particles, including electrons. For instance, the energy of photons absorbed by electrons in the leaves of plants play a crucial role in photosynthesis. Real photons also exhibit wave-particle duality, behaving as both waves and particles, and account for the entire electromagnetic spectrum.

Virtual photons

Unlike real photons, virtual photons are intermediate entities that mediate electromagnetic interactions between charged particles. In QED, they represent rapid fluctuations in energy and momentum at subatomic scales. Virtual photons are key to calculating and predicting the exchange of force, energy, and momentum between charged particles, although they do not produce light or constitute observable radiation.

Virtual photons serve a critical function in describing the underlying mechanisms of how electromagnetic fields operate. They model the quantum-scale interactions that give rise to the forces we experience in everyday life, such as the electromagnetic force.

Quantized units & probabilistic behaviour

Quantum mechanics reveals that at the smallest scales, nature is both quantized and probabilistic. Rather than being continuous, aspects of electromagnetism are reduced to discrete units or quanta.

Quantization means that electromagnetic fields are composed of discrete packets of energy, rather than being smooth, continuous lines. Each photon, for example, carries a specific amount of energy and momentum, allowing for precise interactions between charged particles at subatomic scales.

At the atomic level, quantization governs the energy levels of electrons orbiting the nucleus. Electrons can only occupy specific, quantized energy states, dictating their allowed orbital distances from the nucleus.

Probabilistic behaviour

Probabilistic behaviour in quantum mechanics is tied to the uncertainty principle, which states that certain properties, such as position and momentum, cannot both be precisely known at the same time. This principle introduces uncertainty into measurements of a particle’s properties, requiring them to be described in terms of probabilities.

This probabilistic nature applies to photons as well. While real photons are observable, their exact behaviour can only be predicted in terms of probabilities. The behaviour of photons is described by wave functions, which collapse upon measurement, yielding specific, measurable outcomes. In contrast, virtual photons remain probabilistic, existing only in the context of mathematical calculations.

More Quantum Electrodynamics (QED)

As outlined above, QED is the quantum mechanical theory that describes interactions between charged particles via the electromagnetic force that are absent from classical perspectives. These interactions are mediated by photons, the quantized units of light. QED unifies the concepts of particles, fields, and forces, revealing that light waves, electromagnetic fields, and photon interactions are different aspects of the same underlying reality. From a quantum perspective, our observations of the world around us can be understood as interactions with this underlying reality from which light is composed. For example, as light approaches the human eye the energy, momentum, and polarization of its constituent photons, as well as interactions with media it encounters during propagation determine what we see.

Developed in the mid-20th century by Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga, QED uses tools like Feynman diagrams to simplify the calculation of particle interactions. The theory also reveals the probabilistic nature of both virtual and real photons, providing insights into the particle dynamics that underlie the electromagnetic force.

Probabilistic Exchanges

Both virtual and real photons are described as probabilistic entities because they are not conceived as precisely defined point particles with fixed positions and energies, as in classical physics. Instead, they are understood as distributions of energy and momentum spread across space and time.

For virtual photons, their probabilistic nature involves the likelihood of their exchange during particle interactions. These virtual particles account for the probabilities of various interaction outcomes but do not produce observable effects themselves. The uncertainty surrounding virtual photons pertains to the intermediate states of interactions, rather than to measurable photon properties.

In contrast, the probabilistic nature of real photons relates to the likelihood of photon emission or absorption events and their specific properties when created or destroyed. While individual photon events are probabilistic, their distribution and statistical behaviour can be described with high accuracy. The probabilistic nature of both virtual and real photons is grounded in the Heisenberg uncertainty principle, which states that certain pairs of physical properties, such as position and momentum, cannot both be precisely known at the same time.

The behaviour and properties of photons are represented by wave functions, which express the probability of finding a photon in a particular state. These wave functions capture the inherent uncertainty of photons prior to measurement. When a measurement is made, the wave function collapses, resulting in specific, measurable values. For real photons, this collapse reveals discrete energy and momentum values, such as those observed when photons are emitted or absorbed by atoms. For virtual photons, the wave function collapse is theoretical; their interactions are described through calculated probabilities, as virtual photons cannot be directly observed.

Quantum theory

The probabilistic nature of quantum mechanics is supported by several key principles:

Wave-Particle Duality

Particles such as electrons and photons display both wave-like and particle-like behaviours. This duality implies that their exact positions and momenta cannot be precisely determined at the same time. Instead, their behaviours are described by probability distributions, with their nature depending on the type of measurement or experiment performed.

Uncertainty Principle

Heisenberg’s uncertainty principle establishes a fundamental limit to how precisely certain pairs of physical properties, like position and momentum, can be known simultaneously. This principle reflects a fundamental characteristic of the quantum world rather than a limitation of measurement tools.

Superposition Principle

A quantum system can exist in multiple states simultaneously until it is measured. Measurement causes the system to collapse into one of the possible states. This principle explains phenomena like interference patterns observed in the double-slit experiment.

Entanglement

When particles become entangled, the state of one particle instantaneously affects the state of the other, regardless of the distance separating them. This phenomenon challenges classical notions of locality.

Key concepts: Classical & QED views

The relationship between classical and quantum physics is both complementary and hierarchical. Classical physics remains highly effective for many practical applications at larger scales, but today it rests on the foundation of quantum physics, which offers a more fundamental description of nature, particularly at microscopic and subatomic levels. By integrating quantum mechanics with classical concepts, we extend our understanding of physical phenomena across different scales, from the microscopic to the macroscopic.

Classical Physics

Scope: Describes macroscopic phenomena and systems at everyday scales, including classical mechanics, electromagnetism, thermodynamics, and fluid dynamics.
Predictive Power: Offers accurate predictions and explanations for practical applications in fields such as engineering and astronomy.
Limitations: Does not account for phenomena at atomic and subatomic scales or under extreme conditions, such as near-light speeds or intense gravitational fields.
Tools for Light: Uses models like light rays and wave diagrams to describe how light propagates through different media. These models explain reflection, refraction, lens systems, and image formation, all crucial for designing optical instruments like microscopes and cameras.
Tools for Fields: Employs field lines to represent electric and magnetic fields, helping visualize how these fields interact with charged particles and influence their motion.

Quantum Mechanics

Scope: Describes phenomena at the microscopic scale, including the behaviour of atoms, subatomic particles, and quantum fields.
Principles: Introduces key concepts like wave-particle duality, quantization, superposition, and entanglement, which differ fundamentally from classical physics.
Framework: Provide an essential framework for understanding and predicting the behaviour of particles at very small scales, where classical theories do not apply.

Relationship

Classical Limit: Quantum physics includes classical physics as a special case. Under certain conditions, such as large numbers of particles or low energies, quantum predictions align with classical predictions—this is known as the classical limit.
Complementary: Classical physics remains a valuable approximation and practical tool in situations where quantum effects are negligible.
Hierarchy: Quantum mechanics underpins modern physics, with classical theories serving as approximations that emerge when quantum effects become insignificant.

Field Theory & Quantum Electrodynamics

Classical field theory predates quantum mechanics and describes how physical quantities, such as electric and magnetic fields, vary continuously across space and time. These fields mediate forces, such as the electromagnetic force, through interactions that occur at every point in space.

Quantum Electrodynamics (QED), a quantum field theory, advances this by describing how light (photons) and matter (charged particles like electrons) interact via the electromagnetic force. QED incorporates both the quantum nature of particles and the fields that mediate their interactions.

In QED, photons serve as both the mediators of electromagnetic interactions between charged particles and the quanta of the electromagnetic field itself. This view connects the exchange of virtual photons—responsible for mediating the force between particles—with the emission or absorption of real photons in processes such as radiation.

The QED framework resolves the long-standing ambiguity between the wave-like and particle-like properties of light. By treating photons as quanta of the electromagnetic field, QED explains how light behaves as both a wave and a particle. The theory provides a unified explanation for electromagnetic phenomena, encompassing classical wave behaviours such as wave interference and refraction, as well as particle-like interactions, including light scattering, atomic transitions, and interactions between charged particles.

QED extends our understanding of how fields operate at microscopic scales while remaining consistent with macroscopic observations. It not only refines theoretical models but also deepens our appreciation of the connections between electromagnetic forces, fields, and radiation (photon emission) across both classical and quantum domains.

Fields in Particle Descriptions

When describing fundamental particles such as electrons, protons, and neutrons, multiple fields operate within the framework of quantum field theory. Each field corresponds to a specific force that governs the interactions and behaviours of these particles:

Electromagnetic Field: Electrons, as negatively charged particles, interact directly with the electromagnetic field. This interaction governs their behaviour in both electric and magnetic fields, influencing their orbital dynamics around atomic nuclei and their interactions with photons.
Strong Nuclear Field: Protons, with a positive charge, and neutrons, which are neutral, primarily interact with the strong nuclear force within atomic nuclei. The strong nuclear force binds protons and neutrons together, ensuring nuclear stability. While protons also experience electromagnetic repulsion due to their positive charge, the strong nuclear force is significantly stronger and dominates inside the nucleus.
Weak Nuclear Field: The weak nuclear field governs processes such as beta decay, where particles change types. For example, a neutron can decay into a proton, an electron, and an electron antineutrino. Similarly, a proton can transform into a neutron, a positron, and an electron neutrino. This force is critical in nuclear reactions and particle interactions that involve changes in particle type and charge.

Let’s now summarize and compare the key concepts of particles, charges, forces, and fields in classical electromagnetism and Quantum Electrodynamics (QED).

Particles

Classical Perspective

In Classical Electromagnetism, particles like electrons and protons are considered point-like objects with no internal structure, possessing definite positions and trajectories. These particles carry electric charge and generate electric and magnetic fields, as described by Maxwell’s equations. Interactions between particles are deterministic, governed by well-defined laws such as Coulomb’s law (which describes the force between charged objects) and the Lorentz force law (which governs the motion of charged particles in electric and magnetic fields). Classical Electromagnetism accurately predicts phenomena such as the propagation of electromagnetic waves (including visible light) and the behaviour of charged particles, with interactions occurring in a smooth and continuous manner.

Quantum Perspective

In quantum physics, particles are not just tiny, point-like objects with charge. Instead, they are seen as excitations (disturbances or ripples) in the underlying fields that exist throughout space. For instance, an electron is a disturbance in the electron field, while a photon is a disturbance in the electromagnetic field. This idea is a key part of Quantum Electrodynamics (QED), which explains that particles come into existence and vanish based on how these fields interact with one another.

In Quantum Electrodynamics (QED), interactions between one particle and another are explained by the exchange of virtual photons. These virtual photons are not ‘real’ in the sense that the can be directly observed or measured like other everyday phenomena, but this doesn’t imply they are imaginary in a non-scientific sense. Instead, they are a theoretical construct used to describe how forces, such as the electromagnetic force, are transmitted between charged particles. Although we can’t directly detect virtual photons, they are crucial for accurately describing and predicting interactions in quantum physics. The appearance and disappearance of particles and the exchange of virtual photons are both understood as excitations in fields, demonstrating how these concepts are fundamentally related.

Unlike classical determinism, which treats the position and momentum of particles with certainty, Quantum Electrodynamics (QED) introduces a probabilistic approach. In QED, interactions are governed by inherent uncertainty, a fundamental aspect of quantum mechanics. This uncertainty, embodied in the Heisenberg uncertainty principle, reflects the experimental observations that virtual photons and other virtual particles cannot be directly resolved or observed. Despite this inherent uncertainty, the effects of virtual photons are crucial for accurately predicting and validating experimental results.

Charge

Classical Perspective

Electric charge is a fundamental property of matter, carried by particles such as electrons (with a negative charge) and protons (with a positive charge). These charges generate electric fields, which exert forces on other charges as described by Coulomb’s law.

Interactions between charged particles can be either attractive or repulsive. Particles with like charges repel each other, while those with opposite charges attract. This force is known as the electrostatic force. In classical electromagnetism, charges and their associated fields are treated as continuous, deterministic entities with well-defined properties, including magnitude and sign (+ or -). The behaviour of these fields is governed by Maxwell’s equations, which describe how electric charges and currents generate electric and magnetic fields that propagate through space. These equations explain various phenomena, from static electricity to the generation of electromagnetic waves.

According to Coulomb’s law, the strength and direction of the electrostatic force between two charged particles depend on:

The type of charge (positive or negative) carried by the particles,
The magnitude of each charge,
The distance separating the particles.

For example:

Every electron carries the same magnitude of charge as any other electron, and the same is true for protons. However, electrons and protons have opposite charges:

An electron has a charge of -1.602 x 10^-19 coulombs,
A proton has a charge of +1.602 x 10^-19 coulombs.

Neutrons, on the other hand, are electrically neutral. Although they are composed of quarks with fractional charges, these charges cancel each other out, resulting in a net charge of zero.
Electric charge plays a crucial role in explaining the formation of atoms, the structure of molecules, and the properties of all macroscopic matter. It also underpins the behaviour of electromagnetic radiation, including visible light, which interacts with charged particles to produce observable phenomena.

Quantum Perspective

In Quantum Electrodynamics (QED), charge is also understood to be a fundamental property of particles. Charges interact through the exchange of virtual photons. Virtual photons are conceptualized in both singular and plural forms, depending on the context of the interaction being described.

Singular Virtual Photon: In a single interaction or exchange process, a virtual photon can be thought of as a single, temporary mediator of force. For instance, if two particles interact through the exchange of a single virtual photon, this interaction can be depicted as a single virtual photon in a Feynman diagram.
Plural Virtual Photons: In more complex interactions or in scenarios involving multiple exchanges, multiple virtual photons may be involved. For example, in higher-order processes or in interactions over longer periods, there may be several virtual photons exchanged between particles. These multiple virtual photons collectively contribute to the total interaction between the particles thereby transmitting the electromagnetic force between them.

The quantization of charge and the quantization of the electromagnetic field are complementary aspects of the same quantum mechanical framework. Both are governed by principles that dictate that physical processes and interactions occur in discrete, quantized units.

Force

The electromagnetic force, while being a single unified force that permeates all of space, governs the local interactions between every microscopic particle that constitutes matter. It conforms to specific laws that describe how electrically charged particles interact, including the forces they exert on each other due to their relative motion and charge.

The concept of the electromagnetic force arises from classical electromagnetism, extends through quantum electrodynamics, and is integral to quantum field theory and the Standard Model of particle physics. The concept incorporates descriptions of how electrically charged particles interact via electric and magnetic fields, both at macroscopic and microscopic scales.

Classical Perspective

Electromagnetic Force as a Continuous Field: In Classical Electromagnetism, the electromagnetic force is viewed as a continuous force field arising from electric and magnetic interactions. This perspective is governed by Maxwell’s equations, which describe how electric charges and currents generate electric and magnetic fields. These fields interact with each other and with charged particles according to well-established laws.

Indirect Observation: The electromagnetic force itself is not directly observable. Its presence and magnitude are inferred indirectly from observable effects, such as the motion of charged particles and the presence of electric and magnetic fields, as well as their interactions.

Electric Forces: Electric forces arise from the interaction between static charges and are described by Coulomb’s law, which quantifies the force between charged particles based on measurements of their charge and the distance between them.

Magnetic Forces: Magnetic forces arise from moving charges (currents) and are described by the Lorentz force law. This law describes how magnetic fields exert forces on moving charges. The classical view of magnetic forces is particularly relevant at macroscopic scales, where currents and moving charges are observable and play a significant role in phenomena such as the behaviour of magnets, motors, and electromagnetic waves.

Quantum Perspective

Interlinked Concepts: In Quantum Electrodynamics (QED), the concepts of electromagnetic force, fields, charges, and both virtual and real photons are intricately interlinked within a quantized framework. This framework describes how these elements interact with reference to the principles and mathematical framework of quantum field theory (QFT). Virtual photons mediate forces, while real photons represent observable electromagnetic radiation.

In QED, electric and magnetic forces are communicated via the exchange of virtual photons, which mediate the electromagnetic force. This quantum mechanical framework replaces classical models in scenarios where classical physics is insufficient, such as at subatomic scales or when quantum effects dominate. Step in quantum mechanical calculations include:

Defining Quantum States: Specify the initial and final quantum states of the system (e.g., the states of charged particles involved).
Using Field Operators and the Lagrangian: Interactions are described through field operators and the Lagrangian formulation, which governs the dynamics of the system.
Feynman Diagrams: Draw and interpret Feynman diagrams to visually represent the interactions and exchanges of virtual photons between particles.
Applying Feynman Rules: Apply the rules associated with Feynman diagrams to derive mathematical expressions for the interactions, such as scattering amplitudes.
Calculating Observable Quantities: Compute observable quantities like scattering amplitudes, cross sections, or transition probabilities, which can be measured in experiments.
Incorporating Effects: Include additional quantum effects, such as magnetic moments, when calculating the influence of magnetic fields on particles.

The Lagrangian (or Lagrangian density in field theory) is a central function that encapsulates the dynamics of fields and particles. In classical mechanics, it is used to derive equations of motion via the principle of least action, so the shortest path between two states. In quantum field theory, the Lagrangian describes how fields (like the electromagnetic field) and particles (like photons and electrons) behave and interact.

Electrostatic Forces

Classical Perspective

Electrostatic forces deal specifically with static charges and the resulting electric fields. According to Coulomb’s law, the force between two static point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Electric fields in this context are described as continuous lines of force that emanate from positive charges and terminate on negative charges. These fields exert forces on other static charges, leading to attractions or repulsions depending on the sign of the charges involved.

The classical perspective does not account for the effects of motion or fields that change with time, focusing solely on the static distribution of charges and the forces they generate.

Examples of electrostatic forces are:

Rubbing a Balloon on Hair
Static Electricity in Clothes
Lightning
Photocopiers and Laser Printers
Walking on a Carpet
Dust on TV Screens and Monitor

Quantum Perspective

In the quantum perspective, electrostatic forces are also understood to result from static charges, but the interaction between these charges is described as being mediated by the exchange of virtual photons. Virtual photons are the carriers of the electromagnetic force in Quantum Electrodynamics (QED), and they facilitate the interaction between charged particles at the quantum level.

Even though the charges are static, the force is described as resulting from continuous exchanges of virtual photons, which introduces a probabilistic element into the interaction. This means that while the overall force appears static and deterministic at a macroscopic level, at the microscopic level, it is more accurately accounted for using quantum principles.

Magnetostatic Forces

Classical Perspective

Magnetostatic forces deal with the study of steady electric currents and the magnetic fields they create. It also looks at how these magnetic fields interact with other currents and magnetic materials. To understand this, we use laws like the Biot-Savart law and Ampère’s law, which explain how steady magnetic fields are produced and how they affect other currents and magnetic materials.

When a charged particle moves through a magnetic field, it experiences a force described by the Lorentz force law. This force depends on three things: the amount of charge, how fast the particle is moving, and the strength of the magnetic field. The force always acts at a right angle to both the direction of the particle’s motion and the magnetic field.

In classical physics, we think of magnetostatic forces as smooth and predictable. Steady electric currents create stable magnetic fields, which then interact with other currents and magnetic materials. This approach does not consider changes in magnetic fields or electromagnetic waves, focusing only on static or unchanging conditions.

Quantum Perspective

In quantum mechanics, magnetostatic forces involve the study of how quantum particles with charge, like electrons, interact with magnetic fields. Unlike in classical physics, where we deal with steady currents and static fields, quantum mechanics looks at how particles behave and interact with magnetic fields at the quantum level. This includes analysing how particles with magnetic moments (like electrons) respond to magnetic fields through quantum principles.

When quantum particles, such as electrons, move through a magnetic field, they experience a force according to quantum mechanics principles. This force is influenced by the particle’s charge, its velocity, and the strength of the magnetic field. However, instead of a fixed direction, this force is described probabilistically, reflecting the wave-like nature of particles and their interactions with the magnetic field.

From a quantum perspective, magnetostatic forces are understood through the behaviour of particles and fields at the quantum scale. The interaction between charged particles and magnetic fields is described using quantum field theory, which accounts for the probabilistic nature of particle behaviour and the effects of quantum fluctuations. This approach includes the concept of magnetic interactions mediated by virtual particles and the probabilistic nature of these interactions, as opposed to the deterministic view in classical physics.

Electric Field

An electric field is a component of the electromagnetic field created by stationary or moving electric charges. According to Maxwell’s equations, electric fields are continuous and deterministic in classical electromagnetism, influencing the behaviour of macroscopic objects by exerting forces on other charges. These fields are essential for understanding phenomena like electrostatic interactions and the propagation of electric currents in conductors.

Quantum Perspective

In Quantum Electrodynamics (QED), electric fields are quantized into discrete packets called photons. Photons are the quanta of the electromagnetic field, mediating interactions between charged particles through probabilistic exchanges. Electric fields in QED are associated with the emission and absorption of virtual photons, which dictate the probabilistic nature of interactions at microscopic scales. This framework explains phenomena such as atomic interactions and particularly the behaviour of electrons and photons.

Magnetic Field

Classical Perspective

Magnetic fields are produced by moving charges (currents) or magnetic materials, influencing other moving charges or magnetic dipoles. In classical electromagnetism, magnetic fields interact with moving charges to exert forces and influence macroscopic phenomena such as the motion of conductors in electromagnetic devices.

Quantum Perspective

In QED, magnetic fields are mediated by the exchange of virtual photons between charged particles. These virtual photons represent quantum fluctuations of the electromagnetic field. Magnetic interactions in QED are probabilistic and involve the exchange of virtual photons, impacting the behaviour of particles at microscopic scales.

Electromagnetic Field

Electromagnetic fields represent the influence of the electromagnetic force. They provide a framework for understanding and measuring the effects of electric, magnetic, and electromagnetic forces. Think of the electromagnetic field as a landscape where these forces manifest and interact. To understand the impact of these forces, measurements are made at various points within this field.

Unlike a static or uniform domain, the electromagnetic field is dynamic and constantly evolving. It responds to complex interactions between forces and matter across space, reflecting changes in both electric and magnetic components as they interact with each other and with charged particles. This can be explained as follows:

The presence and movement of charged particles determine the strength and direction of an electromagnetic field at any given point.
Imagine a charged particle as a pebble thrown into a pond. The impact creates ripples that are strongest at the point of contact and diminish with distance. Similarly, the movement of charged particles in an electromagnetic field generates “ripples” in the field, with interactions becoming more complex as more particles are involved.
The electromagnetic field responds dynamically to the presence and movement of charged particles, influencing both its electric and magnetic components. In regions with many charged particles—such as around stars or within clusters of atoms—the field’s effects are more pronounced and intricate. Conversely, in areas with fewer particles, such as deep space, the field’s effects are weaker and simpler to understand.
Electromagnetic fields act as the medium through which the electromagnetic force is transmitted. The continuous presence and movement of charged particles shape and modify this field, creating a dynamic environment throughout the universe.
It’s important to remember that the pond analogy has its limitations. Unlike a pond, the electromagnetic field is not composed of matter; it’s a fundamental concept in physics that cannot be fully captured by comparing it to a physical object. While the analogy helps with visualization, it doesn’t encompass the complete nature of the electromagnetic field.
Similarly, describing the electromagnetic field as a “carrier” can be challenging because it simplifies complex physical phenomena into conceptual terms. The abstract nature of fields and forces makes them difficult to convey precisely with everyday language

Classical Perspective

The classical perspective views the electromagnetic field as a continuous entity with both electric and magnetic components. This field is depicted using field lines, which illustrate the direction and strength of the field, and energy densities, which indicate the amount of energy stored within the field.

Maxwell’s equations describe how electric charges and currents give rise to electromagnetic waves—alternating oscillations of electric and magnetic fields that move through space. Electromagnetic waves, such as light, radio waves, and X-rays, are key manifestations of these fields and can be analysed and predicted using classical physics. This classical description is particularly relevant at macroscopic scales, where observable phenomena can be effectively studied.

Quantum Perspective

In QED, the electromagnetic field is quantized into discrete packets called photons. This produces a more advanced theory that builds on the classical electromagnetic field concept but describes the electromagnetic force as being mediated by the exchange of virtual photons, as well as the emission and absorption of real photons.

Virtual photons are a crucial part of this quantization, because of their ability to make accurate predictions about measurable quantities like the force between charged particles or the scattering of particles. They serve as the force carriers in these interactions. They exist in the context of an interaction (e.g., between two charged particles), where their role is to mediate the electromagnetic force. Their role is to ensure that the equations of QED work correctly and match experimental observations, but do not exist independently like real photons.

Richard Feynman was one of the pioneers of Quantum Electrodynamics (QED), which includes the concept of virtual particles. His Feynman diagrams provide a way to visualize particle interactions, including the role of virtual photons. Feynman was a practical physicist, known for stating that “if it works, it’s true,” emphasizing the importance of mathematical consistency and predictive power in theoretical constructs. He acknowledged that virtual particles were not directly observable but stressed that their effects could be measured and corresponded to reality.

Real photons, on the other hand, represent the quantized packets of energy that we can detect, such as visible light. Each photon carries specific energy and momentum, and they exhibit both particle and wave properties. The emission and absorption of these real photons explain phenomena like the behaviour of light and electromagnetic radiation.

QED describes how these real photons mediate interactions between charged particles, which affects how electromagnetic forces operate at microscopic scales. This quantum description is essential for understanding phenomena where quantum effects dominate, such as the behaviour of electrons in atoms and the interaction of light with matter.

Representing particles, forces, fields & waves

In this last section, let’s look at how to create and interpret diagrams dealing with electromagnetism.

Here are some suggestions of features that diagrams might cover:

Electromagnetic force

The electromagnetic force is most effectively visualized through the particles that generate it and the effects produced in the surrounding space by the fields that result from it. This force governs fundamental interactions like attraction and repulsion between charged particles and plays a crucial role in forming atoms, molecules, and matter. It directly influences many physical structures and processes, from atomic bonding to the behaviour of materials under electromagnetic influence.

Fields as Extensions of Force

Electric and magnetic fields can be shown as continuous lines extending through space. Electric field lines radiate from charges, while magnetic field lines form loops. These lines of force help visualize the range and intensity of the electromagnetic force, illustrating how charged objects interact even at a distance. Real-world examples include the effects of electric fields in capacitors or the magnetic fields around Earth that create phenomena like magnetic shielding.

Vector Representation

Use arrows (vectors) to show the direction and magnitude of force at different points in space. This helps clarify the strength and direction of electric and magnetic fields around particles. In real-world applications, understanding these vectors is key to predicting the behaviour of objects in fields, such as how electric forces shape current flow in circuits and how a compass aligns with Earth’s magnetic field.

Field Superposition

Diagrams can demonstrate the principle of superposition—how multiple fields (from different particles) interact and combine to create a resultant field. This is important in systems where multiple charges or fields are present, such as in electrical circuits, antennas, or even large-scale natural events like thunderstorms, where interacting fields can amplify or cancel each other out.

Charge Dynamics

Illustrate can show the behaviour of both stationary and moving charges, including how stationary charges create electric fields and how moving charges create both electric and magnetic fields. The movement of charges is at the foundation of electricity and magnetism. For instance, stationary charges lead to electrostatic phenomena, while moving charges create magnetic fields and drive electrical currents.

Moving Particles

Illustrations can demonstrate how the electromagnetic force acts on moving charges, particularly the influence of external magnetic fields (the Lorentz force) on their trajectory. This is evident in real-world examples like the behaviour of charged particles in Earth’s magnetic field, which creates phenomena like the aurora borealis, or in particle accelerators and electric motors, where the Lorentz force is harnessed to control particle motion or generate mechanical work.

Wave Propagation

In the case of electromagnetic radiation, diagrams can illustrate the oscillating electric and magnetic fields that are perpendicular to each other, showing how they propagate through space as a wave. These are relevant to wireless communication, light propagation, and energy transfer, so apply to radio transmission, optical fibres, and medical imaging.

Frequency and Wavelength

Frequencies and wavelengths can be shown to demonstrate different types of electromagnetic radiation (radio waves, visible light, X-rays, etc.). Different frequencies can be represented that correspond to different real-world phenomena and technologies, such as radio waves for broadcasting, microwaves for cooking, infrared for heat detection, visible light for vision, and X-rays for imaging.

Energy Flow

Diagrams can demonstrate how energy is transmitted via the electromagnetic field, especially in cases of radiation, so explain the concept of Poynting vectors, which describe the flow of energy. This is key to understanding energy transfer in systems like solar panels, wireless power transmission, and even in optical technologies like lasers or fibre optics, where energy is delivered through electromagnetic waves.

Relativistic Effects

If relevant, the way that electric and magnetic fields transform under relativistic motion (e.g., compression of field lines as charged particles approach the speed of light). These relativistic effects are critical in high-energy physics, particle accelerators, and certain astrophysical phenomena. They also impact practical technologies like GPS satellites, where relativistic corrections are necessary for accurate positioning.

Although the electromagnetic force is a unified interaction, diagrams can also reflect how its electric and magnetic components operate independently in certain situations. Key examples include:

Structure of Matter: The electric and magnetic components of electromagnetic fields play crucial roles in determining the structure and stability of matter, influencing phenomena such as chemical bonding, molecular geometry, and the behaviour of materials. For instance, the strength of the electric field between atoms is essential in holding molecules together.
Atoms: In atoms, the electric field generated by positively charged protons attracts negatively charged electrons, keeping them in orbit around the nucleus. The magnetic field produced by moving electrons can also affect their orbital paths, demonstrating how electric and magnetic forces can influence the stability of atomic structures.
The Lorentz Force: The interaction of moving charged particles, like electrons, with external magnetic fields can influence their trajectory. The Lorentz force shows how a charged particle moving through an electric or magnetic field experiences a force that can alter its speed and direction. This interaction is crucial in understanding how electromagnetic fields affect particle motion, such as in electric motors, generators, or magnetic confinement in fusion reactors.
Electromagnetic Radiation: Oscillating electric and magnetic fields propagate as electromagnetic waves, such as radio waves, microwaves, visible light, and X-rays. Diagrams can show how these oscillating fields are always perpendicular to each other, illustrating the dynamic interplay of the two components as they travel through space.

Visual devices

Field lines and loops

Field lines are key tools in the representation of forces and their fields in diagrams.

Radial Field Lines: These lines extend radially outward from positively charged particles and terminate on negatively charged particles or continue infinitely in the absence of opposing charges. Arrows are often added to diagrams to indicate the direction of the electromagnetic force along these lines.
Field Line Density: The density of radial field lines reflects the relative strength of the electromagnetic force. More concentrated lines indicate stronger forces, while sparser spacing of lines indicate weaker forces. The density of field lines is directly proportional to the magnitude of the electric field, representing the strength of the electromagnetic force at various points.
Closed Loops: Closed loops around irregularly shaped objects or circular patterns around charged particles represent areas of equal electric potential, known as equipotential lines.
Equipotential Lines: These lines mark regions where the force exerted by a charged particle is consistent. Voltage, which represents the potential energy difference between two points, remains constant along these lines. Importantly, equipotential lines are always perpendicular to electric field lines.
While radial and equipotential lines provide useful visualization tools, they are simplifications, not exact representations of reality. Nonetheless, they help illustrate core concepts of electromagnetism, such as how charged particles generate electromagnetic forces and how the fields they create have both direction and varying strengths.

Arrows and Vectors

Force Vectors: Use arrows to represent the direction and magnitude of forces acting on charged particles. The length of each arrow indicates the relative strength of the force at a particular location.
Field Vectors: Arrows are often used as vector representations to indicate the direction of the electric or magnetic field at various points in space. These vectors are especially useful for showing how the strength and orientation of the fields change depending on the particle’s location and motion.
Poynting Vector Arrows: Use arrows to indicate the flow of energy through the electromagnetic field. In diagrams representing radiation, such as light or radio waves, the Poynting vector illustrates the direction in which energy is being transmitted.

Applying tools in particular cases

Stationary Charged Particles

When illustrating stationary charged particles, the following factors need to be taken into account:

Electric Fields Only: Stationary charged particles generate only electric fields, which radiate symmetrically outward in all directions. The strength of these fields diminishes with distance, following the inverse-square law. This can be illustrated using radial field lines extending from the particle.
Dominance of the Electric Field: The electric field dominates in the case of stationary particles, governing their attraction or repulsion with other charged particles. This field plays a crucial role in atomic and molecular interactions, as it helps maintain the structure of matter by governing interactions between atoms and molecules.
Field Strength & Direction: The strength and direction of an electric field depend on the charge of the particle (positive or negative) and its magnitude. Field vectors can be used to indicate the force acting on nearby particles, with longer arrows indicating stronger forces.
No Magnetic Field: Stationary particles do not produce magnetic fields. Magnetic fields only arise when there is a movement of charge, so diagrams of stationary charges should avoid including magnetic field lines.
No Electromagnetic Radiation: Stationary particles do not emit electromagnetic radiation because such radiation requires both electric and magnetic fields. Only moving charges generate the oscillating fields necessary for radiation.

Moving Charged Particle

When illustrating moving charged particles, the following factors should be considered:
Generation of Electric and Magnetic Fields: Moving charged particles generate both electric and magnetic fields. This introduces a dynamic interaction between the two, as motion distorts the electric field. The field lines compress in the direction of travel and spread out behind the particle, representing this distortion visually.
Relativistic Effects on Field Lines: The distortion of electric field lines becomes more pronounced as the particle’s speed increases. At relativistic speeds, the compression of the field lines in the direction of motion aligns with the principles of special relativity. Diagrams should show this compression and elongation to reflect how the electric field changes with velocity.
Magnetic Field Orientation: The magnetic field arises from the motion of the charged particle and forms perpendicular to both its direction of motion and the electric field. This results in perpendicular orientation between the electric and magnetic components. Using field vectors, the distinct directions of these fields should be highlighted, demonstrating the interaction between the two.
Electromagnetic Radiation: When moving charged particles accelerate, they produce both electric and magnetic fields that oscillate and propagate as electromagnetic waves. Diagrams should visualize this by showing how these fields oscillate at a 90-degree angle to one another. The frequency of the oscillations determines the type of radiation (e.g., radio waves, visible light), which can be shown by varying the frequency and wavelength of the oscillations.
Wave Propagation: Illustrations should emphasize that the oscillating electric and magnetic fields are perpendicular to each other and to the direction of propagation. This can be visualized using wavefront diagrams that show how these fields propagate together as synchronized waves.

Electromagnetic waves

When illustrating electromagnetic waves, the following factors need to be taken into account:
Electromagnetic waves are produced whenever there is a combination of oscillating electric and magnetic fields. The key factor is their oscillation; these fields must be constantly changing to create a self-sustaining wave that can travel through space. The following situations lead to this phenomenon:
Accelerating Charged Particles: This is the most common cause of electromagnetic wave generation. When a charged particle, such as an electron, accelerates, it creates a disturbance in the surrounding electric and magnetic fields. This disturbance propagates outward as a wave, with the oscillating electric and magnetic fields traveling together. Diagrams illustrating this process could include:
Transitions of Electrons: Illustrate electrons moving between energy levels in atoms, which is responsible for the emission of light. Diagrams should show the energy levels and the associated electromagnetic radiation emitted during these transitions.
Charged Particles in a Magnetic Field: Show how charged particles moving in a magnetic field (as seen in radio and TV antennas) generate electromagnetic waves. Visuals could depict the motion of the charged particles alongside the emitted fields.
Thermal Vibrations: Represent the thermal vibrations of atoms in hot objects, which result in infrared radiation. This could include diagrams that demonstrate how thermal energy leads to oscillations in electric fields.
Vibrating Electric Currents: Rapidly changing electric currents can also generate electromagnetic waves. This principle underlies the operation of antennas used in radio, television, and other wireless communication technologies. Diagrams can illustrate the oscillating electric currents in an antenna, showing how these currents produce corresponding electromagnetic waves in the surrounding space.
Changing Magnetic Fields: Even changes in a magnetic field, without the presence of charged particles, can induce a corresponding change in the electric field and vice versa. This interaction creates a propagating electromagnetic wave. While this principle is less common, it has applications in specialized areas of physics. Diagrams could depict scenarios where a changing magnetic field induces an electric field, illustrating Faraday’s law of induction.

Additional Factors in Electromagnetic Wave Generation

In addition to the previously mentioned situations, several other factors can contribute to the generation of electromagnetic waves. These factors include:
Time-varying Electric Currents: Changes in the magnitude or direction of electric currents can create oscillating magnetic fields, which, in turn, induce electric fields. This principle is similar to how antennas operate, where varying currents produce radio waves.
Electromagnetic Induction: This phenomenon occurs when a conductor experiences a changing magnetic field, inducing an electric current within it. This principle is fundamental to the operation of many electrical generators and transformers. Diagrams could illustrate the relationship between the changing magnetic field and the induced current in the conductor.
Oscillating Dipoles: In molecules, oscillating electric dipoles (such as those found in polar molecules) can produce changing electric fields, which lead to corresponding magnetic fields. Visualizations can show how these dipoles oscillate, generating electromagnetic radiation.
Charged Particle Collisions: When charged particles collide, they can impart energy and momentum to each other, leading to changes in their velocities and the surrounding fields. Diagrams can depict the interactions during collisions and the resulting changes in electric and magnetic fields.
Plasma Dynamics: In plasmas (ionized gases), the collective motions of charged particles can create fluctuating electric and magnetic fields, which can propagate as waves. Diagrams could illustrate the chaotic behavior of charged particles in a plasma and how this leads to wave formation.

Electromagnetic radiation

Because they play such an important part in the topics covered here at lightcolourvision.org let’s look at the information that might be communicated through diagrams concerning electromagnetic radiation, particularly waves and photons.

Electromagnetic waves

Electromagnetic Force as the Driving Mechanism: The electromagnetic force is the primary influence on charged particles, determining their motion and acceleration and the fields generated around them. This motion and acceleration is critical to the production of electromagnetic radiation.
Acceleration of Charged Particles: Once the particle accelerates under the influence of the electromagnetic force, it disturbs its surrounding electric and magnetic fields. The motion causes these fields to change, which leads to the production of electromagnetic waves. For example, when electrons move between energy levels within atoms, they emit photons. Similarly, charged particles in a magnetic field, such as in a synchrotron, experience acceleration that produces synchrotron radiation.
Charged particles accelerate, they generate changing electric and magnetic fields around them. Newly generated fields interact with pre-existing fields in the surrounding space, creating a disturbance. The disturbance propagates outward as a new wavefront, consisting of oscillating electric and magnetic fields—this is the electromagnetic radiation produced by the acceleration.
Other examples include, when electrons move between energy levels within atoms, they emit photons. Similarly, charged particles in a magnetic field, such as in a synchrotron, experience acceleration that produces synchrotron radiation.
Disturbance in Pre-existing Fields:
Interaction of Fields: The disturbance in pre-existing electric and magnetic fields results from the fields generated by the acceleration of the charged particles. When charged particles accelerate, they create changing electric and magnetic fields that interact with and disturb the already present fields. This interaction involves:
- Superposition of Fields: The new fields combine with the existing fields, leading to changes in their strengths and configurations.
- Field Strength Alteration: The new electric and magnetic fields can either strengthen or weaken the existing fields, depending on their orientations.
- Propagation of Waves: This continuous interplay allows the electromagnetic wave to propagate through space, as the oscillating electric field generates a changing magnetic field, and vice versa.
The resulting electromagnetic waves come in a vast range of frequencies, forming the electromagnetic spectrum. This spectrum includes familiar forms of radiation like visible light, radio waves, and X-rays, each with unique properties determined by its frequency.
Now, the peculiar distinguishing factor of electromagnetic radiation is that the electric and magnetic fields within an electromagnetic wave or photon are perpendicular to each other, forming a right angle.

This can be summarised as follows:

Unified force, and oscillating Fields: As discussed already, electromagnetic radiation arises from the unified electromagnetic force. When charged particles accelerate, they create a disturbance propagating as a wave or as packets of energy called photons. Whether the carrier is a wave or a particle depends on the perspective being taken, but in both cases they consist of synchronized, oscillating electric and magnetic fields.
Perpendicular Fields: Now, the crucial point is that these oscillating electric and magnetic fields are always perpendicular to each other. This means they are at a 90-degree angle, forming a right angle.

Why is this perpendicular nature important?

Self-Propagating Wave: This configuration allows the wave to propagate through space without any need for a medium (unlike sound waves that require air or water). The oscillating electric field creates a changing magnetic field, and vice versa, in a self-perpetuating cycle that allows the wave to travel independently of other phenomena.
Distinguishing Feature: The perpendicular nature of the electric and magnetic fields is a defining characteristic of electromagnetic radiation. It is a defining characteristic and a necessity for electromagnetic radiation to propagate through space without a medium. It also allows for efficient energy transfer as the wave travels and enables various wave phenomena like reflection, refraction, and diffraction.
However, it remains an intriguing puzzle within classical electromagnetism. While Maxwell’s equations predict it as a necessity for wave propagation, the underlying cause of the perpendicular relationship of the electric and magnetic fields is a topic of ongoing exploration in physics. Similarly, Quantum Electrodynamics (QED) in describing electromagnetism at the quantum level doesn’t provide a simple explanation for perpendicularity.