Question 715: Electrostats & Capacitance

Question

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$$ 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 _________.

Accepted Answer

Given $$\sigma_s=2 \lambda_e$$
At point $$P, E_S=\frac{\sigma_S}{2 \varepsilon_0}$$
$$\begin{aligned}
& E_I=\frac{\lambda_e}{2 \pi r \varepsilon_0} \
& \frac{E_S}{E_I}=4 \pi: 1=\pi \sqrt{n}: 1
\end{aligned}$$
For value of $$n=16$$

Electrostats & Capacitance

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