Question

A small conducting spherical shell with inner radius $a$ and outer radius $b$ is concentric with a larger conducting spherical shell with inner radius $c$ and outer radius $d$ (as shown in Fig). The inner shell has total charge $+2q$ and the outer shell has charge $+4q$. Calculate the electric field in terms of $q$ and the distance $r$ from the common centre of the two shells for:
$c<r<d$

• A. Zero
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{r^2}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{6q}{r^2}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$

Answer 1

Answer: (A)

Zero

i. $r<a.E=0$, since $Q=0$. (Fig.)

ii. $a<r<b.E=0$, since $Q=0$.

iii. $b<r<c$. Since $Q=+2q,E=\frac{1}{4\pi {ϵ}_0}\frac{2q}{r^2}$,

iv. $c<r<d.E=0$, since $Q=0$.

v. $r>d.\frac{1}{4\pi {ϵ}_0}\frac{6q}{r^2}$, since $Q=+6q$.