Force between Multiple Charges | Principle of Superposition

The electrostatic force between two charges can be calculated by Coulomb’s Law. This law makes it easy to find the electrostatic force between two charges.  To find electrostatic force between multiple charges, Coulomb’s Law is not enough so, by using the parallelogram law of vector addition the electrostatic force between multiple charges can be calculated easily.

Principle of Superposition

It states that force on any charge due to a number of other charges is the vector sum of all forces on that charge due to other charges, taken one at a time. The individual forces are unaffected by the presence of other charges.

Force on q₁ due to q₂ is denoted by F₁₂

Similarly, force on q₁ due to q₃ is denoted by F₁₃

Thus, the total force on q₁ due to other charges q₂ and q₃ is given as

F₁ = F₁₂ + F₁₃

The above calculation of force can be generalized to a system of more than three charges by using the superposition principle. Thus, the total force on q₁ due to the system of n charges.