Question 255 of 311

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 $37^{\circ}$ with the axis. The ratio of the dipole moment of $A$ and $B,\dfrac{{p}_{1}}{{p}_{2}}$ is$:($ take $\left.\sin 37^{\circ}=\dfrac{3}{5}\right)$

A$\dfrac{3}{8}$B$\dfrac{3}{2}$C$\dfrac{2}{3}$D$\dfrac{4}{3}$

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Answer: (C) $\dfrac{2}{3}$

$\tan 37^{\circ}=\dfrac{3}{4}=\dfrac{\dfrac{k{P}_{2}}{{r}^{3}}}{\dfrac{2k{P}_{1}}{{r}^{3}}}=\dfrac{{P}_{2}}{2{P}_{1}}=\dfrac{3}{4}$
$\dfrac{{P}_{2}}{{P}_{1}}=\dfrac{3}{2}$
$\dfrac{{P}_{1}}{{P}_{2}}=\dfrac{2}{3}$