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 .......

An electrical dipole coincides on the $z$-axis and its midpoint is at the origin of the coordinate system. The electric field at an axial point at a distance $z$ from the origin is $\vec{E}(z)$ and the electric field at an equatorial point at a distance $y$ from the origin is $\vec{E}(y)$. Here $z = y \gg a$,so $\left| \frac{\vec{E}(z)}{\vec{E}(y)} \right| = . . . . . . . .$.

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 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 $,mC$)

The potential at a point $P$ due to an electric dipole is $1.8 \times 10^5 \, V$. If $P$ is at a distance of $50 \, cm$ from the centre $O$ of the dipole and the line $OP$ makes an angle of $60^{\circ}$ with the positive side of the axial line of the dipole,what is the dipole moment?

The electric field at a point due to an electric dipole,on an axis inclined at an angle $\theta$ $(< 90^{\circ})$ to the dipole axis,is perpendicular to the dipole axis,if the angle $\theta$ is