Coulomb’s Law is one of essential formulae to identify forces occurring in a system of static charges.

Definition

It is used to determine the magnitude of the Electrostatic Force due to attraction/repulsion between two point charges A point charge is essentially a point (no length/area/volume) with an electric charge. These differ from Charge Distribution, which are more complex shapes.

Assume we have two point charges, labelled and . Coulomb's Law 2024-07-27 10.19.12.excalidraw

Formula

Coulomb's Law

\vec{F}{q{1} \ on \ q_{2}} = k_e\times\frac{|q_{1}||q_2|}{r^2} \hat{u}= \frac{1}{4\pi\epsilon_0}\times\frac{|q_1||q_2|}{r^2}\hat{u}

Terms
  • = Electrostatic force ()
  • = Coulomb’s constant ()
  • = Charge at points and (in Coulombs, )
  • = Distance between charges ()
  • = Permittivity in free space#tosee
  • = Unit vector representing the direction from to
Explanation

Coulomb's Law 2024-07-27 10.25.48.excalidraw

Essentially, we can now use the sign of the charges as well, to obtain the direction of force. The same principle rule of charges apply - opposites attract and like charges repel:

  • If is negative and is negative, is parallel to , showing the force is pushing away from the charges.
  • However, if is positive and negative (or vice versa), is now negative, i.e. is anti-parallel to , showing the charges are attracting Coulomb's Law 2024-07-27 10.40.23.excalidraw

Superposition of Point Charges

Essentially, if we have multiple point charges in a system, the total electrostatic force on a given charge is the sum of the forces from each individual charge. Pretty obvious. But this superposition is essential when using symmetry to derive forces on continuous charge distributions

Coulomb's Law 2024-07-27 10.44.36.excalidraw