Q.

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

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a

X

b

X2

c

X3

d

1/X

answer is B.

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Detailed Solution

When Q is at position x, thenU=qQ4πε01(a+x)+1(a−x)or   U=2qQa4πε0a2−x2∴ dUdx=2aqQ4πε02xa2−x22                =2aqQ4πε0×2xa4 ∵a2−x2≈a2Now   dU∝dx  or  U∝x2.
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Two equal point charges are fixed at x = -α and x = +α on the X-axis . Another point charge Q is placed at the origin. The change in electrical potential energy of Q when it is displaced by a small distance x along the X-axis, is approximately proportional to