Due to polarisation of a dielectric slab filling the gap between capacitor plates, the charge induced is $80\%$ that of the charge appearing on the capacitor plate. The dielectric constant of the slab material is

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