Question

A solid sphere of radius $R$ has a charge $+2Q$. A hollow spherical shell of radius $3R$ placed concentric with the first sphere has net charge $-Q$. Calculate the potential difference between the spheres :

• A. $\frac{Q}{3\pi {\epsilon }_{0}R}$
• B. $\frac{2Q}{3\pi {\epsilon }_{0}R}$
• C. $\frac{3Q}{\pi {\epsilon }_{0}R}$
• D. $\frac{4Q}{3\pi {\epsilon }_{0}R}$

Answer 1

The correct option is A $\frac{Q}{3\pi {\epsilon }_{0}R}$

$V_{AB}$ = Potential at $3R$ due to both the spheres $-$ Potential at $R$ due to both the spheres

$=\frac{1}{4\pi {ϵ}_0}\frac{-Q}{3R}+\frac{1}{4\pi {ϵ}_0}\frac{2Q}{3R}-[\frac{1}{4\pi {ϵ}_0}\frac{-Q}{3R}+\frac{1}{4\pi {ϵ}_0}\frac{2Q}{R}]$

$=\frac{1}{4\pi {ϵ}_0}\frac{2Q}{R}(\frac{1}{3}-1)$

$=-\frac{1}{4\pi {ϵ}_0}\frac{2Q}{R}\frac{2}{3}$

$=-\frac{Q}{3\pi {ϵ}_{0}R}$