Question

How does the electric field (E) between the plates of a charged thin cylindrical capacitor varies 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)

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

we assume a cylinder of radii $r$ and length $l$ as a Gaussian surface .

using Gauss' law , $E.2\pi rl=\frac{\lambda l}{{ϵ}_0}$

so the expression of electric field in between the cylinders is $E=\frac{\lambda }{2\pi {ϵ}_{0}r}$

$\therefore E\propto \frac{1}{r}$