# Coulomb’s law

Coulomb’s law describes the interaction between electrically charged particles. It tells us how strong the electrostatic force between them is, depending on their properties and their distance apart.

• Coulomb’s law states that the magnitude of the electrostatic force between two point charges, q1 and q2, is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. In simpler terms, the stronger the charges (either positive or negative), the closer they are and the stronger the force between them.
• The expressions in Coulomb’s law are:
• Force: It describes the electrostatic force, which can be either attractive or repulsive depending on the charges involved. Like charges repel each other, while opposite charges attract.
• Charge: The force is directly proportional to the product of the magnitudes of the two charges (q1 and q2). In simpler terms, the greater the charges, the stronger the force.
• Distance: The force is inversely proportional to the square of the distance (r) between the charges.
• So, as the distance between the charges increases, the force weakens rapidly, following an inverse-square relationship.
• Formula: This relationship can be expressed mathematically by the following equation:
• F = k * q1 * q2 / r^2
• F:  Represents the electrostatic force, measured in Newtons (N). It signifies the push or pull exerted between two charged particles due to their electrical interaction. The direction of the force depends on the signs of the charges: like charges repel each other, while opposite charges attract.
• k: This is Coulomb’s constant, a fundamental constant in electromagnetism. It has a value of approximately 8.99 x 10^9 N m^2/C^2 and serves as a proportionality constant relating the force to the charges and distance.
• q1 and q2: TRepresent the magnitudes of the two charges, measured in Coulombs (C). The force increases as the magnitude of either charge increases. Remember, charge can be positive or negative, and the signs matter for determining the attractive or repulsive nature of the force.
• r:  Represents the distance between the two charges, measured in meters (m). The force weakens with increasing distance, following an inverse-square relationship. As the distance doubles, the force decreases by a factor of four, and so on.
• r^2: This is the square of the distance. The force is inversely proportional to this value, emphasizing the rapid decrease in force with increasing distance.
##### Coulomb’s law and electric fields
• Coulomb’s law deals with electrically charged particles and the force they exert on other objects, whilst the electric field describes the resulting influence of that force on surrounding space.
• The strength and direction of the electric field produced by one or more charged particles can be calculated from Coulomb’s law using a mathematical calculation.
• The following information can be gathered:
• Magnitude: This refers to the strength of the electric field at a specific point in space. It reflects the intensity of the force experienced by a test charge placed at that point. The calculation typically results in a value with units of Newtons per Coulomb (N/C).
• Direction: The electric field is a vector field, meaning it has both magnitude and direction. The calculation based on Coulomb’s law allows you to determine the direction of the electric field at a specific point. This direction points away from a positive charge and towards a negative charge.
• Distribution: Depending on the complexity of the charge arrangement, you might be able to understand the spatial distribution of the electric field. For example, for a single-point charge, the field weakens with the inverse square of the distance from the charge. More complex configurations might require advanced calculations or numerical methods to visualize the field distribution.
• Force on other charges: Once you know the strength and direction of the electric field at a point, you can use that information to calculate the force that would be exerted on another charge placed at that point. This is achieved by simply multiplying the field strength by the magnitude of the other charge.
##### What is a test charge?
• A test charge is:
• Tiny and neutral: They have negligible mass and no inherent electric charge, minimizing their influence on the field.
• Respond easily: They are designed to easily react to the electric field, indicating its presence and characteristics.
• Examples: In reality, test charges can be extremely small charged particles like electrons or protons, but in the real world are more likely to be specialized instruments designed to detect electric fields, such as electroscopes.

Summary