Two short electric dipoles $A$ and $B$ having dipole moments $p_1$ and $p_2$ respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ makes an angle of $60^{\circ}$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is . . . . . . .

An electric dipole of moment $p$ is placed at the origin along the $x$-axis. The electric field at a point $P$,whose position vector makes an angle $\theta$ with the $x$-axis,will make an angle $\phi$ with the $x$-axis. If $\tan \alpha = \frac{1}{2} \tan \theta$,where $\alpha$ is the angle between the electric field vector and the position vector,then the angle $\phi$ that the electric field makes with the $x$-axis is:

The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2r$ on the equatorial line from the mid-point of the dipole. Then,the value of $x$ is

At any point on the perpendicular bisector of the line joining two equal and opposite charges,which of the following is true?

Two charges $\pm 10\; \mu C$ are placed $5.0\; mm$ apart. Determine the electric field at $(a)$ a point $P$ on the axis of the dipole $15\; cm$ away from its centre $O$ on the side of the positive charge,as shown in Figure $(a),$ and $(b)$ a point $Q, 15\; cm$ away from $O$ on a line passing through $O$ and normal to the axis of the dipole,as shown in Figure.

For an electric dipole with charge $q = 2 \times 10^{-6} \ C$ and separation distance $d = 0.01 \ m$,if the external electric field is $E = 5 \times 10^{5} \ N/C$,calculate the maximum torque acting on the dipole.