An infinite plane sheet of charge having uniform surface charge density +σs C/m^ 2 is placed ​

Question

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^{2}\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_{\mathrm{e}} \mathrm{C} / \mathrm{m}\) is placed at \(\mathrm{z}=4 \mathrm{m}\) plane and parallel to \(\mathrm{y}\)-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 \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is ________.

Answer 1

Correct answer is : 16

\(\frac{\mathrm{E}_{\mathrm{S}}}{\mathrm{E}_{\ell}}=\frac{\sigma}{2 \epsilon_{0}} \times \frac{2 \pi \epsilon_{0} \mathrm{r}}{\lambda}\)

\(=\frac{\pi \times \sigma r}{\lambda}\)

\(=\frac{\pi \times 2 \lambda \times 2}{\lambda}=\frac{4 \pi}{1}\)

\(\therefore \mathrm{n}=16\)