Question

Some charge Q is to be distributed on 3 concentric shell such that surface charge density on each shell is same as shown. Find the electric potential at r(<a) from point O.

• A. $\frac{Q(a+b-c)}{4\pi {\epsilon }_0(a^2+b^2+c^2)}$
• B. $\frac{Q(a+b+c)}{4\pi {\epsilon }_0(a^2+b^2+c^2)}$
• C. $\frac{Q(a+b+c)}{4\pi {\epsilon }_0(a^2-b^2+c^2)}$
• D. $\frac{Q(a+b-c)}{4\pi {\epsilon }_0(a^2+b^2-c^2)}$

Answer 1

Answer: (B)

$\frac{Q(a+b+c)}{4\pi {\epsilon }_0(a^2+b^2+c^2)}$

$r<a$

from point $0$.

$\oint \overline{E}.d\overline{A}=\frac{Q_{inside}}{{ϵ}_0}$

${ϵ}_0=8.854\times {10}^{-12}\frac{e^2}{{Nm}^2}$

Now, $E\times 4\pi R_1^2=\frac{-5\mu C}{{ϵ}_0}=\frac{Q_{inside}}{{ϵ}_0}$

$E=\frac{Q_{inside}}{4\pi {ϵ}_0{R}_1^2}$

$E_1=\frac{K{Q}_{incide}}{R_1^2}$

$E_{2}A=\frac{Q_{inside}}{{ϵ}_0}$

$F_{y}4\pi R_z^2=\frac{Q}{{ϵ}_0}$

Now, $\frac{Q(a+b+c)}{4\pi {ϵ}_0(a^2+b^2+c^2)}$