Question

Can the potential of a non-uniformly charged sphere be the same as that of a point charge? Explain.

Short answer

Yes, a non-uniformly charged sphere's potential might be the same as a point charge.

Step-by-step solution

Definition of electric potential

At any distance from the charge, the electric potential owing to a point charge equals

$\mathbf{V}\mathbf{=}\mathbf{k}\frac{\mathbf{q}}{\mathbf{r}}$

Where k is a Coulomb's constant potential V at radius r .

potential on the charged sphere that is non-uniform charge distribution

At any point outside the volume of a sphere, the potential will be the same as the point charge because all the charges on the sphere can be assumed to be concentrated at one point.

Hence, outside the sphere, the electric field is the same as that of the point charge.