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Q.

A charge of $2 μC$ starts moving (with negligible velocity) from infinity towards a large conducting plate. The kinetic energy of the charge is $m$ milli Joule and force acting on it is $n$ micro Newton, when it is at a distance of $30 m$ from the plate.

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Detailed Solution

Using the method of images
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$\begin{array}{ll} U_{\infty} = 0 U_{d} = \frac{1}{2} [\frac{- q^{2}}{4 {πϵ}_{0} \times 2 d}] \\ W = \frac{{kq}^{2}}{4 d} K = 9 \times 10^{9} {Nm}^{2} / e^{2} \\ \begin{array}{l} So K . E . = \frac{9 \times 10^{9} {Nm}^{2} / e^{2}}{4 \times 30} \\ K . E . = 300 μJ \\ f = \frac{{kq}^{2}}{4 d^{2}} = 10 μN \end{array} \end{array}$

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