Question

A non-conducting sphere has a total charge Q uniformly distributed throughout its volume. the centre of the sphere is at origin and its radius is R. let $U_1$be the electrostatic potential energy in the region inside the sphere and $U_2$ be the electrostatic potential energy in another imaginary spherical shell, having inner radius R and outer radius infinity, centred at origin. select the correct alternative(s)

• A. $U_1=\frac{Q^2}{8\pi {\epsilon }_{0}R}$
• B. $U_2=\frac{Q^2}{8\pi {\epsilon }_{0}R}$
• C. $U_1+U_2=\frac{3}{5}\times \frac{Q^2}{4\pi {\epsilon }_{0}R}$
• D. $U_1=\frac{3Q^2}{20\pi {\epsilon }_{0}R}$

Answer 1

The correct option is A $U_1=\frac{Q^2}{8\pi {\epsilon }_{0}R}$

Non-conducting sphere has a total charge $=Q$

the centre of the sphere is at origin and its radius $=R$

$U_1=$ Electrostatic potential energy in the region inside the sphere

$U_2=$ the electrostatic potential energy in another spherical shell.

having inner radius $=R$

outer radius infinity

$U_1=\frac{Q^2}{\delta \pi {ϵ}_{0}R}$ because, the potential will be

$U_1=\frac{1}{2}Q\times U$ (This is the working formula of potential energy)

$U_1=\frac{1}{2}\times Q\times \frac{Q}{4\pi {ϵ}_{0}R}$

or, $U_1=\frac{1}{2}\times \frac{Q^2}{4\pi {ϵ}_{0}R}=\frac{Q^2}{8\pi {ϵ}_{0}R}$

Since, $U_2$ be the electrostatic potential energy then, $U_2=0$.