A charge of $5 \mu \mathrm{C}$ is placed at the centre of a spherical shell $S_1$ of radius 10 cm . Now this system is enclosed inside another spherical shell $S_2$ of radius 20 cm . The ratio of the electrical flux through the surface $S_2$ to $S_1$ is :

Two point charges $P=+25 \mu C$ and $Q=-16 \mu C$ are placed 5 cm apart. Find the position of the point at which the resultant electric field is zero:

Bodies $P, Q, R, S$ are labelled as having charges $Q_P=0.5 \times 10^{-19} C, Q_Q=0.7 \times 10^{-19} C$, $Q_R=2.1 \times 10^{-19} C, Q_S=4.8 \times 10^{-19} C$ respectively.

Select the body having the correct charge.

[Given electronic charge $=e=1.6 \times 10^{-19} \mathrm{C}$ ]

In a uniform electric field $10^6 N C^{-1}$ an electric dipole of length 4 cm is placed with its axis making an angle $60^{\circ}$ with the electric field. If the dipole experiences a torque of $8 \sqrt{3} \mathrm{~N} \mathrm{~m}$.

Find the potential energy of the dipole.