Question

A positive charge $Q$ is placed on a conducting spherical shell with inner radius $R_1$ and outer radius $R_2$ . A particle with charge $q$ is placed at the center of the spherical cavity. The magnitude of the electric filed at a point in the cavity, a distance $r$ from center is

• A. zero
• B. $\frac{Q}{4\pi {\epsilon }_0{R}^2}$
• C. $\frac{q}{4\pi {\epsilon }_0{r}^2}$
• D. $\frac{(q+Q)}{4\pi {\epsilon }_0{r}^2}$

Answer 1

Answer: (B)

Total charge on shell $=+Q$
Here, total charge on shell is $+Q$. So, the $(-Q)$
is on the inner surface of shell.
Hence, electric field inside the conductor $=0$
According the Gauss's law,
$\rho Eds=\frac{Q}{{\epsilon }_0}$
$E\oint ds=\frac{Q}{{\epsilon }_0}$
$E\left(4\pi r^2\right)=\frac{Q}{{\epsilon }_0}$
Electric field, $E=\frac{Q}{4\pi r^2{\epsilon }_0}$