A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force `F` If the distance of the charge is doubled, the force acting on the charge will be

Options

A. `2F`
B. `F/2`
C. `F/4`
D. `F/8`

Answer

D

Explanation

The electric field at a point distance r from electric dipole is
`R=1/( 4 pi epsilon_(0)) . (2p)/(r^(3))` (axial line)
Where p is dipole moment and r is the distance of charge from centre of dipole.
or `E prop 1/(r^(3))`
Force on charge is
`F=QE` or `F prop 1/(r^(3))`
`(F_(2))/(F_(1))=((r_(1))/(r_(2)))^(2)`
Given `r_(1)=r_(2)=2r,F_(1)=F`
`(F_(2))/F=(r/(2r))^(3)=1/8` or `F_(2)=F/8`