Electromagnetic Induction: 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. State Faraday's law.
2. What is magnetic flux? Is it a scalar?
3. Dimensional formula of L?
4. On what factors does M depend?
5. What is a back emf?
6. Write the emf of a rod rotating about one end.
7. Name the parts of an ac generator.
8. Why is the induced current zero when a loop moves inside a uniform field?
9. 1 H in terms of V, s and A?
10. Write ε for N turns.

D. Short answer I (2 marks each)

1. State Lenz's law and explain how it follows from energy conservation.
2. Derive ε = Blv for a rod moving on rails.
3. Derive the emf of a rod rotating about one end in B.
4. Derive the energy stored in an inductor.
5. A coil of 100 turns, area 0.01 m², in 0.2 T is turned from ⊥ to ∥ in 0.1 s. Find the average emf.
6. Define mutual inductance and give its unit.
7. Find L if the current changes at 50 A/s and the emf is 10 V.
8. Draw Φ–t and ε–t for a coil rotating at ω starting with its plane ⊥ B.

Rough work

E. Short answer II (3 marks each)

1. Derive the mutual inductance of two long coaxial solenoids. Show that M₁₂ = M₂₁.
2. Derive the self-inductance of a long solenoid and the magnetic energy density.
3. Explain the principle and working of an ac generator and derive ε = NBAω sin ωt.
4. A 2 m rod rotates about its centre at 20 rev/s in 0.5 T ⊥ its plane. Find the emf between the centre and an end, and between the ends.
5. A square loop of side 10 cm, resistance 1 Ω, is pulled out of 0.5 T at 2 cm/s. Find the current, its duration and the heat produced.
6. Show the directions of induced current when (a) the N pole approaches a coil, (b) the S pole moves away from it.

F. Long answer (5 marks each)

1. State Faraday's and Lenz's laws. A rod of length l slides at v on rails in B, the circuit having resistance R: derive the current, the force and the power, and show energy is conserved.
2. Define self- and mutual inductance. Derive L of a solenoid and M of coaxial solenoids. A 0.5 m solenoid of 1000 turns, area 5 cm², has a 50-turn coil wound on its middle: find M.
3. Describe an ac generator with a labelled diagram. A coil of 100 turns, area 200 cm², turns at 50 rev/s in 0.1 T: find the peak emf. What is the emf when its plane makes 30° with B?

G. HOTS (higher-order thinking)

1. A copper ring is held horizontally and a magnet is dropped through it. Does the ring feel a force? Which way?
2. Why are the two wires of a non-inductive coil wound in opposite directions?
3. An aeroplane flies horizontally over India. Is any emf induced between its wing tips? Which field component matters?
4. Why does a spark appear at a switch when a circuit containing a large coil is broken?

20 MCQs

1. The SI unit of flux
   (a) tesla (b) henry (c) weber (d) gauss
2. Induced emf equals
   (a) −dΦ/dt (b) Φ (c) Φ/t² (d) dB/dA
3. Lenz's law follows from conservation of
   (a) charge (b) momentum (c) mass (d) energy
4. Emf of a rod of length l moving at v ⊥ B
   (a) Bl/v (b) Blv (c) Bv/l (d) B²lv
5. Rod rotating about one end
   (a) BωL² (b) ½BωL² (c) ½BωL (d) 2BωL²
6. Self-inductance of a solenoid
   (a) μ₀nAl (b) μ₀N/A (c) μ₀n²A/l (d) μ₀n²Al
7. Energy stored in an inductor
   (a) ½LI² (b) LI (c) L²I (d) ½L²I
8. SI unit of inductance
   (a) weber (b) tesla (c) henry (d) farad
9. Peak emf of a generator
   (a) NBA (b) NBω (c) BAω (d) NBAω
10. A magnet falls through a cut ring: acceleration
    (a) zero (b) g (c) < g (d) > g
11. Flux through a coil whose plane is ∥ B
    (a) BA (b) BA/2 (c) zero (d) maximum
12. M for coaxial solenoids
    (a) μ₀n₁n₂πr₁²l (b) μ₀n₁n₂πr₂²l (c) μ₀n₁²πr₁²l (d) μ₀n₁n₂l
13. Magnetic energy density
    (a) μ₀B²/2 (b) B²/2μ₀ (c) B/2μ₀ (d) ½ε₀E²
14. Φ = 3t² + 2t; emf at t = 1 s
    (a) 5 V (b) 6 V (c) 8 V (d) 2 V
15. Dimension of L
    (a) [ML²T⁻¹A⁻²] (b) [MLT⁻²A⁻¹] (c) [ML²T⁻³A⁻¹] (d) [ML²T⁻²A⁻²]
16. For fixed N, L of a solenoid increases when
    (a) l decreases, A increases (b) l and A both increase (c) l increases, A decreases (d) both decrease
17. Induced charge q in a coil depends on
    (a) ΔΦ and R (b) time taken (c) rate only (d) speed
18. The emf of a generator is maximum when the coil's plane is
    (a) ⊥ B (b) at 45° (c) at 60° (d) ∥ B
19. Flux 0.2 Wb falls to zero in 0.1 s through 10 turns: emf
    (a) 2 V (b) 20 V (c) 0.2 V (d) 200 V
20. Back emf in an inductor
    (a) aids the current (b) is always zero (c) opposes changes in current (d) depends on R only

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: A magnet falls slower through a copper tube than through a glass tube. R: Induced currents in copper oppose the motion.
2. A: Induced emf is larger when the flux is larger. R: Emf is proportional to the flux.
3. A: M is maximum when two coils are wound on each other. R: Flux linkage is then maximum.
4. A: Lenz's law obeys energy conservation. R: The induced current always flows clockwise.
5. A: An inductor opposes changes in current. R: It stores energy ½LI².
6. A: A loop moving inside a uniform field without rotating has no induced current. R: The flux through it does not change.

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

Answers to the practice set