Question

How does the electric field $\left(E\right)$ between the plates of a charged cylindrical capacitor vary with the distance $r$ from the axis of the cylinder?

• A. $E\propto \frac{1}{r^2}$
• B. $E\propto \frac{1}{r}$
• C. $E\propto r^2$
• D. $E\propto r$

Answer 1

Answer: (B)

Let the length of the cylinder is $l$ and linear mass density $\lambda$ .
Applying Gauss's theorem,
$E\times 2\pi rl=\frac{\lambda l}{{ϵ}_0}\Rightarrow E=\frac{\lambda }{2\pi r{ϵ}_0}\Rightarrow E\propto \frac{1}{r}$
So, the electric field between the plates of charged cylindrical capacitor vary as $E\propto \frac{1}{r}$ .