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Two equal point charges are fixed at x = - a and x = + a on the axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of system, when Q is displaced by a small distance x along the X-axis is approximately proportional to

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$x$

$x^{2}$

$x^{3}$

$1 / x$

answer is B.

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Detailed Solution

$P E_{i} = \frac{1}{4 π \in_{0}} [\frac{q Q}{a} + \frac{q Q}{a} + \frac{q^{2}}{2 a}] P E_{f} = \frac{1}{4 π \in_{0}} [\frac{q Q}{a + x} + \frac{q Q}{a - x} + \frac{q^{2}}{2 a}]$

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