Question

The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor

• A. is the same throughout.
• B. is higher near the outer cylinder than near to it.
• C. varies as $\frac{1}{r}$, where $r$ is the distance from the axis.
• D. varies as $\frac{1}{r^2}$, where $r$ is the distance from the axis.

Answer 1

The correct option is C varies as $\frac{1}{r}$, where $r$ is the distance from the axis.

We know this pretty well that the Electric field in the annular region of a charged cylindrical capacitor is given by,

$E=\frac{2k\lambda }{r}$

Where,
$k=\frac{1}{4\pi {ϵ}_0}$
$\lambda =$ Change per unit length
$r=$ Distance from the axis of cylinder

Hence, $E\propto \frac{1}{r}$

Hence, option $\left(c\right)$ is correct.