# NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance

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The class 12th chapter of Physics “Electrostatic Potential and Capacitance” explains electrostatic potential, problems based on the effective capacitance of capacitors, energy stored in a capacitor, important derivations and formulas, development of electrostatic potential, etc.

##### Question 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.

Given
q1 = 5×10–8 C, r = 16 cm= 0.16 m
q2 = –3 × 10–8 C
Let potential be zero at a distance x metre from
positive charge q1
$\therefore$ r1 = x metre
r2 = (0.16 – x) metre  ##### Question 2:

A regular hexagon of side 10 cm has a charge 5 $\mathrm{\mu }$C at each of its vertices. Calculate the potential at the centre of the hexagon.

From the figure TBQ 2.2 we have OP = OQ = OR = OS = OT = OU = r = 10 cm = 0.1 m And given q = 5 $\mathrm{\mu }$C = 5 × 10–6 C
$\therefore$ Potential at O due to all the charges ##### Question 3:

Two charges 2 $\mathrm{\mu }$C and –2 $\mathrm{\mu }$C are placed at points A and B 6 cm apart. Identify an equipotential surface of the system.
What is the direction of the electric field at every point on this surface ?

The plane normal to AB and passing through its mid-point has zero potential everywhere hence the plane is equipotential.

Normal to the plane is the direction AB.

##### Question 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

1. inside the sphere
2. just outside the sphere
3. at point 18 cm from the centre of the sphere ?

(a) Zero  ##### Question 5:

A parallel plate capacitor with air between the plates has a capacitance of 8pF (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 ?

The capacitance of capacitor with air as dielectric is given by ##### Question 6:

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

What is the total capacitance of the combination ?

What is the potential difference across each capacitor, if the combination is connected to a 120 volt supply ?

Given C 1= C 2= C 3 = 9 pF = 9 × 10 –12 F; V = 120 volt.
Total capacitance of the series combination is given by Let q be charge on each capacitor. Then, sum of the potential differences across their plates must be equal to 120 V ##### Question 7:

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

What is the total capacitance of the combination ?

Determine the charge on each capacitor, if the combination is connected to a 100 V supply. Here C1 = 2pF; C2 = 3pF; C3 = 4pF ; V = 100 volt
Total capacitance of the parallel combination is given by
C = C1 + C2 + C3 = 2 + 3 + 4 = 9 pF.
Let q1, q2 and q 3 be the charges on C1, C2 and C3 respectively. In the parallel combination, the potential difference across each capacitor will be equal to the supply voltage i.e. 100 V.
Therefore, q1 = C1 V = 2 × 1012 × 100
= 2 × 10–10 C,
q2 = C2 V=3×10–12×100 =3×10–10 C and q 3 = C 3 V = 4×10–12×100=4×10 –12 C.

##### Question 8:

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

Given
A = 6 × 10–3 m2, d = 3 mm = 3 × 10–3 m C0 = ?
V0 = 100 V, q = ? ##### Question 9:

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

1. While the voltage supply remained connected.
2. After the supply was disconnected.

(a) When supply voltage remains connected
V = 100 volt (voltage remains constant) Capacitance C = KC 0 = 6 × 18 = 108 pF Charge q =1.8 × 10 –9 C (remains constant)

(b) After the supply is disconnected ##### Question 10:

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

Given C = 12 pF = 12 × 10–12 C
V = 50 volt ##### Question 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 ?  