As shown in the figure an electric dipole lies at a distance `x` from the centrr of a chargerd ring of radius `R` with charge `Q` uniformly distributed over it .The net force acting on the dipole is

Options

A. `(aQq)/(4piepsilon_(0))(R^(2)-2x^(2))/(2piepsilon_(0)(R^(2)+x^(2))^(5//2))`
B. `(aQq)/(2piepsilon_(0))(R^(2)+2x^(2))/(2piepsilon_(0)(R^(2)+x^(2))^(5//2))`
C. `(aQq)/(4piepsilon_(0))(R^(2)+2x^(2))/(2piepsilon_(0)(R^(2)+x^(2))^(5//2))`
D. `(aQq)/(2piepsilon_(0))(R^(2)-2x^(2))/(2piepsilon_(0)(R^(2)+x^(2))^(5//2))`

Answer

D

Explanation

Field due to ring is given by
`E=(Qx)/(4piepsilon_(0)(R^(2)+x^(2))^(3//2))`
`rArr` Force on dipole is given by `F=p((dE)/(dx))`
`f=2axxq(d)/(dx)[(Qx)/(4piepsilon_(0)(R^(2)+r^(2))^(3//2))]`
`=(2aqxxQ)/(4piepsilon_(0))[x xx((-3)/(2))(R^(2)+r^(2))^(-3//2)(2x)+(R^(2)+x^(2))^(-3//2)]`
`=(2aqxxQ)/(4piepsilon_(0))(R^(2)+r^(2))^(-5//2)[-3x^(2)+(R^(2)+r^(2))]`
`F=(aqQ)/(2piepsilon_(0))[(R^(2)-2x^(2))/((R^(2)+r^(2))^(5//2))]`