A dipole of dipole moment `P` is kept at the centre of a ring of radius `R` and charge `Q` the dipole moment has direction along the ring due to the dipole is :

Options

A. zero
B. `(kpQ)/(R^(3))`
C. `(2kpQ)/(R^(3))`
D. `(kpQ)/(R^(3))` only if the change is uniformly distributed on the ring .

Answer

B

Explanation

Electric field at each point on the surface of ring due to the dipole is `E=(kp)/(R^(3))` in direction opposite to the dipole moments .(figure below)
Hence net force on ring is `F=QE=(kpQ)/(R^(3))`
Alternate solution
Electric field due to ring at point`P` on its axis at a distance `x` from the centre `O` of the ring is
`E=k.(Qx)/((x^(2)+R^(2))^(3//2)),(dE)/(dx)]_(at x=0)=(kQ)/(R^(3))`
Force on dipole =`(dE)/(dx)=(kQp)/(R^(3))`