Question

Two concentric, thin, metallic spheres of radii $R_1$ and $R_2(R_1 > R_2)$ bear charges and $Q_1$ respectively. Then the potential at radius $r$ between $R_1$ and $R_2$ will be $1 / 4\pi\, \varepsilon_{0}$ times

• A. $\frac{Q_{1}+Q_{2}}{r}$
• B. $\frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{r}$
• C. $\frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{R_2}$
• D. $\frac{Q_{1}}{R_{2}}+\frac{Q_{2}}{R_1}$

Answer 1

Answer: (B)

Potential at radius, $r$,
$V_{r}=$ potential at $P$ due to $Q_{1}+$ potential at $P$ due to $Q_{2}$
$V_{r} =V_{1}+V_{2}$
$=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{r}\right]$