Question

Derive an expression for electric field due to the system of point charges?

Answer 1

Electric field due to the system of point charges: 

Suppose a number of point charges are distributed in space. To find the electric field at some point P due to this collection of point charges, superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. This is called superposition of electric fields.

Consider a collection of point charges q₁, q₂, q₃,…., q_n located at various points in space. The ‘ total electric field at some point P due to all these n charges is given by

Here r_1p, r_2p, r_3p,…., r_np, are the distance of the charges q₁, q₂, q₃,…., q_n from the point respectively. Also \(\hat r\)_1p + \(\hat r\)_2p + \(\hat r\)_3p  ,….,  \(\hat r\)_np are the corresponding unit vectors directed from q_1, q_2, q₃, ....., q_n to point P.

Equation (2) can be re-written as,

For example in figure, the resultant electric field due to three point charges q₁, q₂, q₃ at point P is shown. Note that the relative lengths of the electric field vectors for the charges depend on relative distantes of the charges to the point P.