A dipole of dipole moment $\overrightarrow{p}=(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}) \mathrm{cm}$ is kept at a point $A$ whose coordinates are $(1,-1,3)$. If an external electric field $\overrightarrow{E}=(5\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}) \mathrm{V} {\mathrm{m}}^{-1}$ is applied then the potential energy of the dipole be,

An electric dipole is placed in a uniform electric field $\overrightarrow{E}$ of magnitude $40 \mathrm{N} {\mathrm{C}}^{-1}$. The graph below shows the magnitude of the torque on the dipole versus the angle $\mathrm{\theta }$ between the field $\overrightarrow{E}$ and the dipole moment $\overrightarrow{p}$. The magnitude of dipole moment $\overrightarrow{p}$ is equal to

Two small electric dipoles, each of the dipole moment $p\hat{\mathrm{i}}$ are situated at $(0, 0, 0)$ and $(r, 0, 0)$. The electric potential at a point $\left(\frac{r}{2}, \frac{\sqrt{3}r}{2}, 0\right)$ is

An electron is projected, as shown in the figure, with kinetic energy $K$ and at an angle $\text{θ}=45°$ between the two charged plates. What should be the magnitude of the electric field between the plates so that the electron just fails to strike the upper charged plate?

$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \mathrm{cm}$ placed in air. The magnitude of the electric field (in $\mathrm{N} {\mathrm{C}}^{-1}$ ) at a distance of $20 \mathrm{cm}$ from its centre is

The figure below shows field lines of an electric field. The spacing between the lines parallel to the page is same everywhere. If the magnitude of the field at $A$ is $40 \mathrm{N} {\mathrm{C}}^{-1}$, then the magnitude of the field at $B$ is approximately,

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)