Two ideal electric dipoles A and B, having their dipole moment $P_{1} and P_{2}$ 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 $37^{0}$ with the axis. The ratio of the dipole moment of A and B, $\frac{P_{1}}{P_{2}}$ is: (take sin $37^{0}$ = 3/5)

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$\frac{2}{3}$

$\frac{3}{8}$

$\frac{4}{3}$

$\frac{3}{2}$

answer is C.

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Detailed Solution

$E_{1} = \frac{2 K P_{1}}{r^{3}}$ , $E_{2} = \frac{K P_{2}}{r^{3}}$

$\tan 37^{0} = \frac{E_{2}}{E_{1}} = \frac{P_{2}}{2 P_{1}}$

$\frac{3}{4} = \frac{P_{2}}{2 P_{1}} \Rightarrow \frac{P_{1}}{P_{2}} = \frac{2}{3}$

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