Chapter 2 Solutions — Electrostatic Potential and Capacitance

Exercises

1. 1.
   Two charges 5 × 10^-8 C and –3 × 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.
2. 2.
   A regular hexagon of side 10 cm has a charge 5 μC at each of its vertices. Calculate the potential at the centre of the hexagon.
3. 3.
   Two charges 2 μC and –2 μC are placed at points A and B 6 cm apart.

   • (a) Identify an equipotential surface of the system.
   • (b) What is the direction of the electric field at every point on this surface?
4. 4.
   A spherical conductor of radius 12 cm has a charge of 1.6 × 10^-7 C distributed uniformly on its surface. What is the electric field

   • (a) inside the sphere,
   • (b) just outside the sphere,
   • (c) at a point 18 cm from the centre of the sphere?
5. 5.
   A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1 pF = 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?
6. 6.
   Three capacitors each of capacitance 9 pF are connected in series.

   • (a) What is the total capacitance of the combination?
   • (b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
7. 7.
   Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.

   • (a) What is the total capacitance of the combination?
   • (b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.
8. 8.
   In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10^-3 m^2 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?
9. 9.
   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) while the voltage supply remained connected,
   • (b) after the supply was disconnected.
10. 10.
    A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
11. 11.
    A 600 pF capacitor is charged by a 200 V 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?