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 axis of the ring. The resultant force on the ring due to the dipole is

$\frac{kpQ}{R^3}$

$ F = p \frac{dE}{dx} $

$ E = \frac{kQ}{2{R^2+x^2}^{3/2}}$ 

$\frac{dE}{dx} _{ x= 0 }= \frac{kQ}{R^3}$

$\Rightarrow F =  p \frac{dE}{dx} = \frac{kpQ}{R^3}$