Electrostatic Potential and Capacitance: Class 12 Important Questions with Answers

Practice set: test yourself

Try every question before looking at the answers below. 64 or more out of 80 means you are ready for the board.

C. Very short answer (1 mark each)

1. Define 1 electron volt.
2. What is the potential at the centre of a charged conducting sphere of radius R with charge q?
3. Write the relation between E and V.
4. Name the device that stores electrical energy in its field.
5. Why is the potential inside a conductor constant?
6. Equivalent of two 4 μF capacitors in series?
7. What happens to C if the plate separation is doubled?
8. Give one example each of polar and non-polar molecules.
9. What is the dielectric constant of a metal?
10. Energy stored in a 2 μF capacitor charged to 100 V?

D. Short answer I (2 marks each)

1. Derive the potential at a distance r from a point charge Q.
2. Draw equipotential surfaces for (a) a point charge, (b) a uniform field.
3. Show that the work done in moving a charge between two points is path independent.
4. Derive the equivalent capacitance of three capacitors in series.
5. Find the PE of charges 2 μC, −3 μC and 4 μC at the corners of an equilateral triangle of side 10 cm.
6. What is electrostatic shielding? Give one use.
7. A capacitor of 5 μF is charged to 200 V. Find its charge and energy.
8. Show that the energy density of a parallel plate capacitor's field is $\frac{1}{2}{\epsilon }_0{E}^2$.

E. Short answer II (3 marks each)

1. Derive the potential of a short dipole at a point making angle θ with its axis.
2. Derive the PE of a dipole in a uniform field. Find the work to rotate a dipole of $4\times 10^{-9}$ C m from 0° to 90° in $5\times 10^4$ N/C.
3. A parallel plate capacitor (A = 0.02 m², d = 2 mm) has a dielectric slab of K = 4 and thickness 1 mm. Find C.
4. Explain polarisation of a dielectric and show that $E=E_0/K$ inside it.
5. A 4 μF capacitor charged to 50 V is joined to an uncharged 2 μF capacitor. Find the common potential and the energy lost.
6. In $\vec{E}=30x^2\hat{i}$ N/C, find the p.d. $V_A-V_B$ for A at x = 1 m and B at x = 2 m.

F. Long answer (5 marks each)

1. Derive C for a parallel plate capacitor with a dielectric slab of thickness t. What is C when the slab is metallic?
2. Derive the energy stored in a capacitor. A 10 μF capacitor at 100 V is disconnected and a slab of K = 5 fills it. Find the new V and U, and explain the change.
3. Derive the PE of a system of three point charges. Four charges +q, +q, −q, −q (like charges adjacent) are at the corners of a square of side a: find U.
4. State six results of electrostatics of conductors with reasons. Two far-apart spheres of radii 2 cm and 4 cm each carry 6 μC. They are joined by a thin wire: how much charge flows, and which way?

G. HOTS (higher-order thinking)

1. A dipole is on the x-axis. Is any work needed to move a charge from infinity to a point on the y-axis? Why?
2. Why does a capacitor block dc but allow ac (charging and discharging)? What happens to the charge if the dielectric breaks down?
3. Can there be a point where V = 0 but E ≠ 0? And where E = 0 but V ≠ 0? Give one example each.
4. When a slab is pulled out of an isolated charged capacitor, its energy rises. Where does the extra energy come from?

Rough work

20 MCQs

1. The SI unit of potential is
   (a) J (b) N/C (c) volt (d) C/V
2. Potential at distance r from charge q is
   (a) $kq/r$ (b) $kq/r^2$ (c) $k{q}^2/r$ (d) $kqr$
3. Potential on the equatorial line of a dipole
   (a) $kp/r^2$ (b) $2kp/r^2$ (c) infinite (d) zero
4. The angle between E and an equipotential surface is
   (a) 0° (b) 90° (c) 45° (d) 180°
5. Work done in moving 2 C through 10 V is
   (a) 5 J (b) 20 J (c) 0.2 J (d) 12 J
6. PE of a dipole is minimum when θ is
   (a) 90° (b) 45° (c) 180° (d) 0°
7. Capacitance of a parallel plate capacitor is
   (a) ${\epsilon }_{0}A/d$ (b) ${\epsilon }_{0}d/A$ (c) $A/{\epsilon }_{0}d$ (d) ${\epsilon }_{0}Ad$
8. Filling with K multiplies C by
   (a) 1/K (b) K² (c) K (d) √K
9. Two 6 μF in series give
   (a) 12 μF (b) 6 μF (c) 2 μF (d) 3 μF
10. Energy stored in a capacitor is
    (a) $C{V}^2$ (b) $\frac{1}{2}C{V}^2$ (c) $\frac{1}{2}Q{V}^2$ (d) $\frac{1}{2}CV$
11. Energy density of an electric field is
    (a) ${\epsilon }_0{E}^2$ (b) $\frac{1}{2}{\epsilon }_{0}E$ (c) $\frac{1}{2}{\epsilon }_0{E}^2$ (d) ${\epsilon }_{0}E/2$
12. Inside a charged conductor
    (a) E = 0, V constant (b) E = 0, V = 0 (c) E constant (d) V = 0
13. If $V=4x^2$ V, E at x = 1 m is
    (a) 4 V/m (b) −8 V/m (c) 8 V/m (d) 2 V/m
14. 1 eV equals
    (a) $10^{-19}$ J (b) $1.6\times 10^{-19}$ C (c) $1.6\times 10^{-19}$ J (d) 1 J
15. An isolated charged capacitor: plates pulled apart. Its energy
    (a) decreases (b) stays the same (c) becomes zero (d) increases
16. Polar molecule among these
    (a) H₂O (b) O₂ (c) CO₂ (d) CH₄
17. Metal slab of thickness d/2 in a capacitor $C_0$: new C
    (a) $2C_0$ (b) $C_0$ (c) $4C_0$ (d) $C_0/2$
18. PE of two charges $q$ and $-q$ at distance r
    (a) $-k{q}^2/r^2$ (b) $k{q}^2/r$ (c) zero (d) $-k{q}^2/r$
19. Work to turn a dipole from 0° to 180° in E
    (a) pE (b) 2pE (c) 0 (d) −2pE
20. C₁ = 2 μF and C₂ = 3 μF in parallel at 10 V: total charge
    (a) 25 μC (b) 12 μC (c) 50 μC (d) 60 μC

1 (c) · 2 (a) · 3 (d) · 4 (b) · 5 (b) · 6 (d) · 7 (a) · 8 (c) · 9 (d) · 10 (b) · 11 (c) · 12 (a) · 13 (b) · 14 (c) · 15 (d) · 16 (a) · 17 (a) · 18 (d) · 19 (b) · 20 (c)

Assertion–Reason (6)

(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

1. A: No work is done in moving a charge on an equipotential surface. R: The field is perpendicular to the equipotential surface.
2. A: The potential inside a charged hollow sphere is zero. R: The field inside it is zero.
3. A: A dielectric slab increases the capacitance. R: It reduces the field and hence the p.d. for the same charge.
4. A: Capacitors in series have the same charge. R: The equivalent capacitance in series is the sum of the capacitances.
5. A: The PE of a system of two like charges is positive. R: Work has to be done against repulsion to bring them together.
6. A: Electric field is the negative gradient of potential. R: The field points in the direction of decreasing potential.

Key: 1 (a) · 2 (d) · 3 (a) · 4 (c) · 5 (a) · 6 (b)

Answers to the practice set