The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $\sigma$ is ( $\varepsilon_0=$ permittivity of free space)

The electric charges ' $+2 q$ ', ' $+2 q$ ', ' $-2 q$ ' and ' $-2 q$ ' are placed at the corners of square of side ' 2 L ' as shown in figure. The electric potential at point 'A', midway between the two charges ' $+2 q$ ' and ' $+2 q$ ' is

( $\varepsilon_0=$ permittivity of free space)

An electric dipole having each charge of magnitude $2 \mu \mathrm{C}$ is placed in an electric field of intensity $8 \times 10^{+4} \mathrm{~N} / \mathrm{C}$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \mathrm{~N}-\mathrm{m}$, the length of the dipole is