Q. Three concentric spherical shells have radii $a,b$ and $c(a < b < c)$ and have surface charge densities $\sigma, - \sigma$ and $\sigma$ respectively. If $V_{A},\ V_{B}$ and $V_{C}$ denote the potentials of the three shells, then, for $c = a + b,$ we have
A) $V_{C} = V_{A} \neq V_{B}$
B) $V_{C} = V_{B} \neq V_{A}$
C) $V_{C} \neq V_{B} \neq V_{A}$
D) $V_{C} = V_{B} = V_{A}$
Explanation
(a) $V_{A} = \frac{\sigma}{\in_{0}}(a - b + c)$
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$V_{B} = \frac{\sigma}{\in_{0}}\left( \frac{a^{2}}{b} - b + c \right)$
$V_{C} = \frac{\sigma}{\in_{0}}\left( \frac{a^{2}}{c} - \frac{b^{2}}{c} + c \right)$
On putting $c = a + b \Rightarrow V_{A} = V_{C} \neq V_{B}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.