An electric dipole of length $20 \ cm$ having $\pm 3 \times 10^{-3} \ C$ charge is placed at $60^{\circ}$ with respect to a uniform electric field and experiences a torque of magnitude $6 \ N-m$. The potential energy of the dipole is:

Obtain the expression for the electric field due to an electric dipole at a point on its axial line.

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:

$A$ dipole with an electric moment $\vec{p}$ is located at a distance $r$ from a long thread charged uniformly with a linear charge density $\lambda$. Find the force $F$ acting on the dipole if the vector $\vec{p}$ is oriented along the thread.

An electric dipole consists of two opposite charges each of magnitude $1 \,\mu C$ separated by a distance of $2 \,cm$. The dipole is placed in an external field of $10^5 \,N/C$. The maximum torque on the dipole is ......... $Nm$.

$A$ wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a vertical electric field $E$. Then the value of $E$ is