Multiple Charges

Coulomb's law describes only the interaction of two point charges. Experiments show that when two charges exert forces simultaneously on a third charge, the total force acting on that charge is the vector sum of the forces that the two charges would exert individually. This important property is known as the superposition principle. This principle holds good for any number of charges.

Sub Topics

The Superposition Principle

The Superposition Principle

The principle states that when a number of charges are interacting , the resultant force on a particular charge is given by the vector sum of the forces produced by the individual charges.

If several point charges q₁_, q₂_, q₃.............. q_n simultaneously exert electric force on the charge q, then the net force on 'q' is obtained by taking the vector sum of the individual forces.

Mathematically, it can be stated as

This is the superposition principle of electric forces (also true for electric fields).

Considering a system of point charges q₁, q₂ …… q_n and if the position vectors are given by

then the forces experienced by any one charge due to the other charges can be written mathematically as follows:

where f₁ is the net force experienced by the q₁ charge and f₁₂, is the force experienced by q₁ due to q₂, f₁₃ is the force experienced by q₁ due to q₃ etc, then in general, it can be written as

Since a charge does not exert a force on itself combining Coulomb's law with supposition principle, the equation (1) can be written as

The vector sum are obtained by using parallelogram law of vectors. All of electrostatics is basically the consequence of Coulomb's law and the superposition principle.