The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance $r(r R)$ from its axis is inversely proportional to $r^{n}$, where $n$ is a positive integer. Find $n$.

Question

The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance $r(r > R)$ from its axis is inversely proportional to $r^{n}$, where $n$ is a positive integer. Find $n$.

Aicharya · Accepted Answer

According to Gauss law $\int E \cdot d s=\frac{q l}{\varepsilon_{0}}$ $\int E \cdot d s=2 \pi r l ;$ (E is constant) $E \cdot 2 \pi r l=\frac{q l}{\varepsilon_{0}} \Rightarrow E=\frac{q}{2 \pi \varepsilon_{0} r}$ i.e. $E \propto \frac{1}{r}$

The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a…

Solution