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 $2R$
$=\frac{k q}{R}+\frac{k 2 q}{2 R}=\frac{2 k q}{R}$
For point $r=3 R$
$V_{2}=$ Potential due to charges $q$ and $2 q$ assumed to be concentrated at centre $=\frac{k(3 q)}{3 R}=\frac{k q}{R}$
So, ratio $ \frac{V_{1}}{V_{2}}=2$