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 $(37^{0}) = \frac{3}{5}$ )

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$\frac{2}{3}$

$\frac{3}{8}$

$\frac{4}{3}$

$\frac{3}{2}$

answer is A.

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Detailed Solution

point C is on the axial line of electric dipole A. so electric field due to electric dipole B. so electric field due to electric dipole B at point C is , $E_{2} = \frac{p_{2}}{4 π ε_{0} r^{3}} \hat{j}$
Net electric field at point C is ${\vec{E}}_{C} = \vec{E_{1}} + \vec{E_{2}}$
An net electric field is making $37^{o}$ with the axis ,