An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} / \mathrm{m}^2$ is placed on $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to…

Question

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} / \mathrm{m}^2$ is placed on $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}: 1$. The value of $n$ is_______.

Aicharya · Accepted Answer

$\begin{aligned} & \frac{\mathrm{E}_{\mathrm{S}}}{\mathrm{E}_{\ell}}=\frac{\sigma}{2 \epsilon_0} \times \frac{2 \pi \epsilon_0 \mathrm{r}}{\lambda} \\ & =\frac{\pi \times \sigma \mathrm{r}}{\lambda} \\ & =\frac{\pi \times 2 \lambda \times 2}{\lambda}=\frac{4 \pi}{1} \\ & \therefore \mathrm{n}=16\end{aligned}$

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} /…

Solution