Charges –q and +q located at A and B ,respectively constitute an electric dipole.
Distance AB =2a,O is the mid point of the dipole and OP is perpendicular to AB A charge Q is placed at P where OP =y and y>>2a .The charge Q experiences an electrostatic force F . if Q is now moved along the equatorial line to $P^{'}$ such that $O P^{'} = (\frac{y}{3})$ . The force on Q will be $n \times F$ .
Find n

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answer is 27.

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Detailed Solution

Electric field of equatorial plane of dipole $= - \frac{K P}{r^{3}}$
$∴$ At point p, $F = + \frac{K P}{y^{3}} Q$
At point $p^{1}$
$F^{1} = + \frac{K P Q}{{(y / 3)}^{3}}$
=27F

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