Question

A sphere of radius R has uniform volume charge density. The electric potential at a point situated at a distance r (r < R) is :

• A. due to the charge inside a sphere of radius r only
• B. due to the entire charge of the sphere
• C. due to the charge in the spherical shell of inner and outer radii r and R only
• D. independent of r

Answer 1

Answer: (A)

due to the charge inside a sphere of radius r only

By Gauss's law the electric field at a distance r is $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}$

or $E=\frac{Q_{en}}{4\pi {ϵ}_0{r}^2}$ where $Q_{en}=$ charge inside sphere of radius r.

As the potential $V=-\int Edr$ so the electric potential at r due to charge inside a sphere of radius r only.