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  4. How does the electric field (E) between the plates of a charged cylindrical capacitor vary with the distance r from the axis of the cylinder?

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Q. 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?

NTA AbhyasNTA Abhyas 2022

Solution:

Let the length of the cylinder is $l$ and linear mass density $\lambda $ .
Applying Gauss's theorem,
$E\times 2\pi rl=\frac{\lambda l}{\epsilon _{0}}\Rightarrow E=\frac{\lambda }{2 \pi r \epsilon _{0}}\Rightarrow E \propto \frac{1}{r}$
So, the electric field between the plates of charged cylindrical capacitor vary as $E \propto \frac{1}{r}$ .