Two spherical hollow spheres of radii '$R_1$' and '$R_2$' are charged with same charge. Let '$\sigma_1$' and '$\sigma_2$' are their respective charge densities, then the ratio $\sigma_1$ to $\sigma_2$ is

An electric dipole of length $0.5\ \mu\text{m}$ is placed with its axis making an angle of $30^\circ$ with uniform electric field $10^4\ \text{V/m}$. If it experiences a torque of $5 \times 10^{-9}\ \text{Nm}$, the magnitude of the charge on the dipole is ($\sin 30^\circ = 0.5$)

Two charges $q_1$ and $q_2$ are separated by a distance of 30cm. A third charge $q_3$ initially at point C is shown in figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from C to D is $q_3 k/4\pi\varepsilon_0$, the value of K is ($\varepsilon_0$ = permittivity of free space)

The electric field in the region is $\vec{E} = a\hat{i} + b\hat{j}$ where 'a' and 'b' are constants. The net electric flux passing through a square area of side 'l' parallel to Y-Z plane is