Two short electric dipoles \(A\) and \(B\) having dipole moment \(p_1\) and \(p_2\) respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point \(x\) is making an angle of \(60°\) with the line joining points \(O\) and \(x\). The ratio of the dipole moments \(p_2/p_1\) is _______.

Let the distance of point \(x\) from the origin \(O\) be \(r\).

Point \(x\) lies on the axial line of dipole A. The electric field at \(x\) due to dipole A is directed along the horizontal axis and its magnitude is given by:
\(E_A = \dfrac{1}{4\pi\epsilon_0} \dfrac{2p_1}{r^3}\)

Point \(x\) lies on the equatorial line of dipole B. The electric field at \(x\) due to dipole B is directed perpendicular to the horizontal axis and its magnitude is given by:
\(E_B = \dfrac{1}{4\pi\epsilon_0} \dfrac{p_2}{r^3}\)

The resultant electric field makes an angle of \(60^{\circ}\) with the line \(Ox\) (the horizontal axis). Therefore, the tangent of this angle is the ratio of the perpendicular component of the electric field to the parallel component:
\(\tan 60^{\circ} = \dfrac{E_B}{E_A}\)

Substituting the expressions for \(E_A\) and \(E_B\):
\(\sqrt{3} = \dfrac{\dfrac{1}{4\pi\epsilon_0} \dfrac{p_2}{r^3}}{\dfrac{1}{4\pi\epsilon_0} \dfrac{2p_1}{r^3}}\)

\(\sqrt{3} = \dfrac{p_2}{2p_1}\)

\(\dfrac{p_2}{p_1} = 2\sqrt{3}\)

Answer: \(2\sqrt{3}\)