An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole through $\frac{\pi}{3}$ radians is:

If the electric field intensity at a distance $x$ on the axis of a dipole is equal to the electric field intensity at a distance $y$ on its equatorial line,then the ratio $x:y$ is:

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:

An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^5\,N C^{-1}$. It experiences a torque equal to $4\,N m$. Calculate the magnitude of charge on the dipole,if the dipole length is $2\,cm$. (in $,mC$)

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 $2 \times 10^{-10} \text{ C m}$ is aligned at an angle $30^{\circ}$ with the direction of a uniform electric field of $10^4 \text{ N C}^{-1}$. The magnitude of the torque acting on the dipole is: