Question

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. $\frac{\sigma }{{\epsilon }_0}\cdot (a-b+c)$
• B. $\frac{\sigma }{{\epsilon }_0}\cdot (a-b-c)$
• C. $\frac{\sigma }{{\epsilon }_0}\cdot (a^2+b^2+c^2)$
• D. $\frac{\sigma }{{\epsilon }_0}\cdot (a+b-c)$

Answer 1

The correct option is A $\frac{\sigma }{{\epsilon }_0}\cdot (a-b+c)$

The electric potential on the surface of shell A
$V_A=V_a+V_b+V_c$
$V_A=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_a}{a}+\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_b}{b}+\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_c}{c}$
$V_A=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{4\pi a^2\sigma }{a}+\frac{1}{4\pi {\epsilon }_0}\cdot \frac{4\pi b^2(-\sigma )}{b}+\frac{1}{4\pi {\epsilon }_0}\cdot \frac{4\pi c^2\sigma }{c}$ $[\because q=4\pi r^2\sigma ]$
or $V_A=\frac{\sigma }{{\epsilon }_0}(a-b+c)$