A small electric dipole is kept on the axis of a uniformly charged ring at distance $\sqrt{2} R$ cm from the center of the ring. The direction of the dipole moment is along the axis. The dipole moment is P , charge of the ring is Q and radius of the ring is R. The force on the dipole is $\frac{k P Q}{n \sqrt{3} R}$ . Find value of n

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answer is C.

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Detailed Solution

$F = \frac{d U}{d x} = \frac{P d E}{d x} = \frac{P d \frac{k Q x}{{(x^{2} + R^{2})}^{\frac{3}{2}}}}{d x} = P k Q \sqrt{x^{2} + R^{2}} (\frac{R^{2} - 2 x^{2}}{{(x^{2} + R^{2})}^{3}}) A t x = \sqrt{2} R w e g e t F = \frac{k P Q}{3 \sqrt{3} R}$

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