Question

A point charge $q_1$ is placed inside cavity. If $q_1$ is at center of cavity , then $\overrightarrow{E}$ at a point which is at a distance $r$ from the center of cavity $(r>r_1)$ , due to the induced charge on the surface of cavity is

• A. $\frac{q_1}{4\pi {\epsilon }_0{r}^2}$ away from the center of cavity.
• B. $\frac{q_1}{4\pi {\epsilon }_0{r}_1^2}$ away from the center of cavity.
• C. $\frac{q_1}{4\pi {\epsilon }_0{r}^2}$ towards the center of cavity.
• D. Zero.

Answer 1

The correct option is C $\frac{q_1}{4\pi {\epsilon }_0{r}^2}$ towards the center of cavity.

Given,

$q_1$ is at center of cavity.

Let us consider a point $S$ which is at a distance $r$ from the center of cavity.

$\because r>r_1$ , the point $S$ lies inside the conductor.

Since the electric field intensity outside the cavity due to $q_1$ and $-q_1$ would be zero.

We can say that, ${\overrightarrow{E}}_{-q_1}+{\overrightarrow{E}}_{q_1}=0$

$\Rightarrow {\overrightarrow{E}}_{-q_1}=-{\overrightarrow{E}}_{q_1}=\frac{q_1}{4\pi {\epsilon }_0{r}^2}$ (towards the center of cavity)

Hence, option (c) is the correct answer.