An electric dipole with dipole moment $p$ is placed with its axis at $30^{\circ}$ to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is

Two charges of $+25 \times 10^{-9} \, C$ and $-25 \times 10^{-9} \, C$ are placed $6 \, m$ apart. Find the ratio of the electric field intensity at a point $4 \, m$ from the center of the electric dipole on the $(i)$ axial line and $(ii)$ equatorial line.

An electric dipole with dipole moment $5 \times 10^{-7} \text{ C m}$ is placed in an electric field of $2 \times 10^4 \text{ N C}^{-1}$ at an angle of $60^{\circ}$ with the direction of the electric field. The torque acting on the dipole is:

Obtain the expression for the torque acting on an electric dipole in a uniform external electric field.

Two charges $+q$ and $-q$ are placed at a distance $b$ apart as shown in the figure. The electric field at a point $P$ on the perpendicular bisector as shown is

For a short dipole placed at origin $O$,the dipole moment $P$ is along the $x$-axis,as shown in the figure. If the electric potential and electric field at point $A$ (at distance $r$ on the $x$-axis) are $V_0$ and $E_0$,respectively,then the correct combination of the electric potential and electric field,respectively,at point $B$ (at distance $2r$ on the $y$-axis) is given by