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 disatnce 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_(1)`(Potential energy of system when charge Q is at Q)
`= (qQ)/a + (qQ)/a = (2qQ)/a `
Therefore , when Q is hsifted from O to O .

Then `U_(2) = (qQ)/(a+x) +(qQ)/((a-x)) approx (2qQ)/a (1+(x^(2))/(a^(2)))`
` :. DeltaU = U_(2)-U_(1) approx (2qQ)/(a^(3)) (x^(2))`
` :. DeltaU prop x^(2)`