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

Options

A. x
B. `x^(2)`
C. `x^(3)`
D. `1//x`

Answer

B

Explanation

`U_(i)=(2KQq)/a` and `U_(f)=KQq[1/(a+x)+1/(a-x)]`
`rArr |DeltaU|=(2KQqx^(2))/a^(3)` for `x lt lt a :. DeltaU prop x^(2)`