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 \(B, \frac{P_{1}}{P_{2}}\) is \(....\) (take \(\left.\sin 37^{\circ}=\frac{3}{5}\right)\)

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{3}\)

Detailed explanation

\(\tan 37^{\circ}=\frac{3}{4}=\frac{\frac{ kP _{2}}{ r ^{3}}}{\frac{2 kP _{1}}{ r ^{3}}}=\frac{ P _{2}}{2 P _{1}}=\frac{3}{4}\)

\(\frac{ P _{2}}{ P _{1}}=\frac{3}{2}\)

\(\frac{ P _{1}}{ P _{2}}=\frac{2}{3}\)

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