An electric dipole is placed along the $x$-axis at the origin $O$. $A$ point $P$ is at a distance of $20 \, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$-axis. If the electric field at $P$ makes an angle $\theta$ with the $x$-axis,the value of $\theta$ would be

An electric dipole is situated in an electric field as shown in the figure. The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to the paper at point $A$ in an anti-clockwise direction. If the angle of rotation is measured with respect to the direction of the electric field,then the torque for different values of the angle of rotation $\theta$ is correctly represented by which graph among $a, b, c, d$ given in the figure?

Write the equation for the electric field produced by an electric dipole at a point on its axial line,given the condition $r >> a$.

The electric dipole moment of a short electric dipole is $p$. The electric potential at a point at a distance $r$ from its center and making an angle $\theta$ with the axis of the dipole is .......

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 . . . . . . .

Two point dipoles of dipole moments $\vec{p}_1$ and $\vec{p}_2$ are at a distance $x$ from each other,and $\vec{p}_1 \parallel \vec{p}_2$. The force between the dipoles is: