Question

Two isolated, concentric, conducting spherical shells have radii $R$ and $2R$ and uniform charges $q$ and $2q$ respectively. If $V_1$ and $V_2$ are potentials at points located at distances $3R$ and $\frac{R}{2}$, respectively, from the centre of shells. Then the ratio of $\left(\frac{V_2}{V_1}\right)$ will be

• A. 2
• B. 1
• C. $\frac{1}{2}$
• D. 0

Answer 1

Answer: (A)

For point, $r=\frac{R}{2}$
$V_1=$ Potential of surface radius $R+$ Potential of surface radius $2R$
$=\frac{kq}{R}+\frac{k2q}{2R}=\frac{2kq}{R}$
For point $r=3R$
$V_2=$ Potential due to charges $q$ and $2q$ assumed to be concentrated at centre $=\frac{k(3q)}{3R}=\frac{kq}{R}$
So, ratio $\frac{V_1}{V_2}=2$