Intro to the Electric Force

There are four fundamental forces in nature and they govern each and every interaction in the universe. Electromagnetic force is one of these four fundamental forces.

These fundamental forces are also known as fundamental interactions. Electric force is the one half of the electromagnetic interaction. It works among the charged particles.

The mathematical measurement of the electric force between any two point like static electric charges is described by Culomb's law.

''The magnitude of the electrostatic force of attraction between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. The force is along the straight line joining them.''

The mathematical form of his statement is $F=\frac{Cq_{1}q_{2}}{d^2}$ where c is $\frac{1}{4\pi\epsilon}$

Culomb's law only works for two point like charges. But if we have more than two, superposition principle takes this place to help. According to superposition principle the net force caused by more than two particles on a single one is the sum of the forces that would have been caused by each interaction individually.

Suppose, we have n particles. The electromagnetic interaction between i-th and j-th particles will be denoted by $F_{ij}$ So the total force on i-th particle due to the rest n-1 particles will be -

$\sum_{ }^{ }F=F_{i1}+F_{i2}+....+F_{in}=\sum_{j=1,j\ne i}^nF_{ij}=\sum_{j=1,j\ne i}^n\frac{Cq_iq_j}{r_{ij}^2}$