Electrostatic Potential and Capacitance

Two charges $5 \times 10$–8 C and –$3 \times 10$–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.

Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart.

A spherical conductor of radius 12 cm has a charge of $1.6 \times 10$–7C distributed uniformly on its surface. What is the electric field

A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

Three capacitors each of capacitance 9 pF are connected in series.

Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.

In a parallel plate capacitor with air between the plates, each plate has an area of $6 \times 10$–3 m2 and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

Explain what would happen if in the capacitor given in Exercise 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,

A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

A 600pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?