Question

The magnitude of the electric field $\overline{E}$ in the annular region of a charged cylindrical capacitor,

• A. is same throughout
• B. is higher near the outer cylinder then near the inner cylinder
• C. varies as $1/r$ where $r$ is the distance from the axis
• D. varies as $1/r^2$ where $r$ is the distance from the axis

Answer 1

The correct option is C varies as $1/r$ where $r$ is the distance from the axis

Let us assume a cylinder of radius $r$ in the annular region.

On applying Gauss law for this cylinder.

$\Rightarrow \int \overrightarrow{E}.\overrightarrow{dA}=\frac{Qenc}{E_0}$

$\Rightarrow E\left(2\pi re\right)=\frac{q}{E_0}$ [ $l=$ length of cylinder ]

$\Rightarrow E=\frac{q}{2\pi E_{0}re}$

$\Rightarrow E\alpha \frac{1}{r}.$

Hence, the answer is varies as $\frac{1}{r}$ where $r$ is the distance from the axis.