Question

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

Short answer

Both electric potential are similar for regions outside the sphere and differ within the sphere.

Step-by-step solution

Definition of electric potential

At any distance $\mathrm{r}$from the charge, the electric potential $\mathrm{V}$owing to a point charge $\mathrm{q}$is-

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

where is a coulomb's constant.

Final result and explanation.

At distances $\mathrm{r}$ outside the sphere, the electric potential of a uniformly charged sphere is similar to that of a point charge; that is, for $\mathrm{r}>\mathrm{R}$ ,where $\mathrm{R}$is the radius of the sphere.

Inside the charged sphere, the electric potential is zero; that is for $0<r<R$.

This is the point at which the charged sphere's electric potential differs from that of a point charge.