Potential Due to a Electric Dipole

The electric potential at the equatorial position due to the dipole is zero.

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

A molecule of a substance has a permanent electric dipole moment of magnitude ${10}^{-30} \mathrm{C} \mathrm{m}$. A mole of this substance is polarized by applying a strong electrostatic field of magnitude ${10}^7 \mathrm{V}\mathrm{ }{\mathrm{m}}^{-1}$. The direction of field is changed by an angle $60°$. The heat released by the substance in aligning it's dipole along the new direction of the field is:

Which of the following is not true?

Two charges $+20\mathrm{ }\mathrm{\mu }\mathrm{C}$ and $-20 \mathrm{\mu }\mathrm{C}$ are placed $10 \mathrm{mm}$ apart. The electric field at point $\mathrm{P}$, on the axis of the dipole $10 \mathrm{cm}$ away from its centre $\mathrm{O}$ on the side of the positive charge is

Two electric dipoles $\overrightarrow{P_1}=-4Qa\widehat{i}$ and $\overrightarrow{P_2}=-2Qa\widehat{\mathrm{i}}$ are at points $A$ and $B$ separate by distance $r.$ Find the distance from point $A$ where net electric potential is zero.

In the given dipole, for $r>>2l$ , the electric potential at $A$ will be

An electric dipole is fixed at the origin of coordinates. Its moment is directed in the positive $\mathrm{x}$ -direction. A positive charge is moved from the point $\left(\mathrm{r},\mathrm{ }0\right)$ to the point $\left(-\mathrm{r},\mathrm{ }0\right)$ by an external agent. In this process, the work done by the agent is

A short dipole is placed along $X$-axis with centre at origin. The electric field at a point $P$, which is at a distance $r$ from origin such that, $\overrightarrow{OP}=\overrightarrow{r}$ makes an angle of $45°$ with $X$-axis, is directed along a direction making -

Two charges $+q$ and $-q$ are kept apart. Then at any point on the right bisector of line joining the two charges,

The ratio of electric field and potential ($\mathrm{E}/\mathrm{V}$) at mid-point of electric dipole of length $l$, for which separation is