Potential due to a Group of Point Charges

Electric potential at a point describes the work done per unit positive charge in bringing it from infinity to that point, without any acceleration. Since potential is a scalar quantity, the total potential due to several charges is found by simple algebraic addition — unlike the electric field, which requires vector addition.

Discrete System of Charges

For charges +q₁, +q₂, −q₃, −q₄​ at distances r₁, r₂, r₃, r₄​ from point P, the resultant potential is:

For n point charges, generalized as:

When charge is spread continuously, the sum becomes an integral over infinitesimal charge elements dq:

V = \[\frac{1}{4\pi\varepsilon_0}\int\frac{dq}{r}\]

Types of Continuous Distributions

Here σ is surface charge density and ρ is volume charge density