Q.
Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure $(a < b < c).$ Their surface charge densities are $\sigma, - \sigma\ and\ \sigma$ respectively. Calculate the electric potential on the surface of shell A
A) $\frac{\sigma}{\varepsilon_{0}}(a - b + c)$
B) $\frac{\sigma}{\varepsilon_{0}}(a - b - c)$
C) $\frac{\sigma}{\varepsilon_{0}}\left( a^{2} + b^{2} + c^{2} \right)$
D) $\frac{\sigma}{\varepsilon_{0}}(a + b - c)$
Explanation
(a) The electric potential on the surface of shell $A$
[image:2_image129.emf]
$V_{A} = V_{a} + V_{b} + V_{c}$
$V_{A} = \frac{1}{4\pi\varepsilon_{0}}.\frac{q_{a}}{a} + \frac{1}{4\pi\varepsilon_{0}} + \frac{q_{b}}{b} + \frac{1}{4\pi\varepsilon_{0}}.\frac{q_{c}}{c}$
Or
$V_{A} = \frac{1}{4\pi\varepsilon_{0}}.\frac{4\pi a^{2}\sigma}{a} + \frac{1}{4\pi\varepsilon_{0}}.\frac{4\pi b^{2}( - \sigma)}{b} + \frac{1}{4\pi\varepsilon_{0}}.\frac{4\pi c^{2}\sigma}{c}$
$\left( \because q = 4\pi r^{2}\sigma \right)$
$or\ \ V_{A} = \frac{\sigma}{\varepsilon_{0}}(a - b + c)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.