$A$ point electric dipole placed at the origin has a potential given by $V(r, \theta) = \frac{p \cos \theta}{4 \pi \varepsilon_0 r^2}$,where $\theta$ is the angle made by the position vector with the direction of the dipole. Then,

$A$ 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.

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance,the new force will be

An electric dipole with dipole moment $4 \times 10^{-9} \text{ Cm}$ is aligned at $60^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \text{ NC}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

Choose the incorrect statement from the following.

$A$ point charge $q$ of mass $m$ is suspended vertically by a string of length $l$. $A$ point dipole of dipole moment $\overrightarrow{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole,the angles and distances is shown in the figure. If the work done in bringing the dipole to this position is $N \times (mgh)$,where $g$ is the acceleration due to gravity,then the value of $N$ is. . . . . . (Note that for three coplanar forces keeping a point mass in equilibrium,$\frac{F}{\sin \theta}$ is the same for all forces,where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)