Three point charges 1C, 2C and 3C are placed at the corners of an equilateral triangle of side 1 m. Calculate the work required to move these charges to the corners of a small equilateral triangle of side 0.5 m.

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$199 \times 10^{9} J$

$29 \times 10^{9} J$

$99 \times 10^{9} J$

$19 \times 10^{9} J$

answer is C.

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Detailed Solution

Initial electrostatic potential energy
$\begin{array}{l} U_{i} = 9 \times 10^{9} [\frac{1 \times 2}{1} + \frac{2 \times 3}{1} + \frac{1 \times 3}{1}] = 99 \times 10^{9} \\ U_{f} = 9 \times 10^{9} [\frac{1 \times 2}{0 .5} + \frac{2 \times 3}{0 .5} + \frac{1 \times 3}{0 .5}] \\ = 22 \times 9 \times 10^{9} = 198 \times 10^{9} \end{array}$
Amount of work done = U_f – U_i
$= 99 \times 10^{9} J$