Two ideal electric dipoles A and B, having their dipole moment p1 and… | JEE Main 2021 (25 Jul, Shift 2)

Q55JEE Main 2021 · 25 JUL · SHIFT 2Medium

Electric Dipole

Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37 $^\circ$ with the axis. The ratio of the dipole moment of A and B, $\frac{p_1}{p_2}$ is: (take $\sin 37^\circ = \frac{3}{5}$ )

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Answer: (c)

C is on the axis of A: $E_A = \frac{2kp_1}{r^3}$ along the axis.
C is on the equatorial line of B: $E_B = \frac{kp_2}{r^3}$ perpendicular to the axis.
$\tan37^\circ = \frac{E_B}{E_A} = \frac{p_2}{2p_1} = \frac{3}{4}$
$\frac{p_1}{p_2} = \frac{2}{3}$ , so the answer is (c).

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