What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

A particle having a charge of 2.0 × 10^–4 C is placed directly below and at a separation of 10 cm from the bob of a simple pendulum at rest. The mass of the bob is 100g. What charge should the bob be given so that the string becomes loose?

(a) Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.

(b) A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.

OR

(a) Derive an expression for the electric field at any point on the equatorial line of an electric dipole.

(b) Two identical point charges, q each, are kept 2m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.

Repeat the previous problem if the particle is displaced through a distance x along the line AB.

Two charges 2.0 × 10^–6 C and 1.0 × 10^–6 C are placed at a separation of 10 cm. Where should a third charge be placed such that it experiences no net force due to these charges?