Principle of Superposition:

It has been experimentally verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to other charges are taken at a time. The individual forces remain unaffected due to other charges presence. This method is called the principle of superposition.

The principal of superposition relies on Coulomb’s statement ‘like charges repel each other and unlike charges attract each other” and can be used to find the force on any charge in a system of multiple charges.

To better understand what principle of superposition is, consider a system having charges q1, q2, q3 and q4, and we have to find the force on q1, due to other remaining three charges.

Force due to system of multiple charges

Image 2: Force due to system of multiple charges

From the figure, we can see that charge q1 , faces three repulsive forces from q2 , q3 and q4 respectively. Let the force on charge q1, due to charge q2 be F12, the force on charge q1 due to charge q3 be F13 and force on charge q1 due to charge q4 be F14. And the distance between charge q1 and q2 is r12, the distance between charge q1 and q2, and the distance between charge q1 and q4 is r14.

The resultant force F will be the vector sum of F12 , F13 and F14. Mathematically

F = F12 + F13 + F14

where

Then total force on charge q1 due to other charges will be

Similarly, if there are ‘n’ charges in a system namely q1, q2 , q3 ……. qn then force q1 due to other charges will be given as: