2.18 EXERCISES

Q2.1: 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.

A2.1: 10 cm, 40 cm away from the positive charge on the side of the negative charge.

Q2.2: 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.

A2.2: 2.7 × 10^6 V

Q2.3: Two charges 2 μ C and −2 μ C 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?

A2.3:


(a) The plane normal to AB and passing through its mid-point has zero potential everywhere.


(b) Normal to the plane in the direction AB.

Q2.4: A spherical conductor of radius 12 cm has a charge of 1.6 × 10^−7C, 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?

A2.4:


(a) Zero


(b) 10^5 N C^−1


(c) 4.4 × 10^4 N C^−1

Q2.5: 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?

A2.5: 96 pF

Q2.6: 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?

A2.6:


(a) 3 pF


(b) 40 V

Q2.7: 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.

A2.7:


(a) 9 pF


(b) 2 × 10^−10 C, 3 × 10^−10 C, 4 × 10^−10 C

Q2.8: 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?

A2.8: 18 pF, 1.8 × 10^−9 C

Q2.9: Explain what would happen if in the capacitor given in Exercise 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) was inserted between the plates,


(a) while the voltage supply remained connected.


(b) after the supply was disconnected.

A2.9:


(a) V = 100 V, C = 108 pF, Q = 1.08 × 10^−8 C


(b) Q = 1.8 × 10^−9 C, C = 108 pF, V = 16.6 V

Q2.10: A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

A2.10: 1.5 × 10^−8 J

Q2.11: 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?

A2.11: 6 × 10^−6 J