For the situation shown in the figure below, find the force experienced by the dipole:

Options

A. `(|P|Q)/(2pi epsi_(0) r^(3))`
B. `(pQ)/(2 pi epsi_(0) r^(3))`
C. `(3Q_(p))/(2 pi epsi_(0) r^(3))`
D. None of these

Answer

A

Explanation

Force experienced by dipole in non-uniform electric field, is given by
`F=p (2E)/(2r)`, Here `E=Q/(4 pi e r^2)`
We have to take derivative of E along dipole length, i.e., along `overline r`
So `(2E)/(2R)=- (2Q)/(4 pi e_0 r^3)`, So required force (magnitude) `= (| vec p| Q)/(2 pi e_0 r^3)`
Alternative : Force on Q due to P = Force on P due to Q
`Q overline E=Q 1/(4 pi e_0) (2|vecp|)/r^3=(pQ)/(2 pi e_0 r^3)`