Electromagnetic Induction Class 12 Physics Notes

• The motional EMF can be understood as the magnetic force on the free charges inside the moving conductor.
• Rotating a rod of length l about one end in a field B induces
• $\epsilon =\frac{1}{2}B\omega l^2$
• .

• AC generator: a coil rotating in a magnetic field produces a sinusoidally varying EMF
• $\epsilon =NBA\omega \sin \omega t$
• .
• Transformer: mutual inductance transfers energy between windings.
• $\frac{V_s}{V_p}=\frac{N_s}{N_p}$
• .
• Step-up transformers have more secondary turns; step-down have fewer.
• Ideal transformer:
• $V_p{I}_p=V_s{I}_s$
• (power conserved).

Example: A $0.5\text{m}$ conductor moves at $4\text{m/s}$ perpendicular to a $0.2\text{T}$ field. Find the motional EMF.

Solution: $\epsilon =Blv=0.2\times 0.5\times 4=0.4\text{V}$.

Exercises (NCERT Q6.1–Q6.8)

• 6.1) Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f): (a) a bar magnet (S–N) moved toward a coil pqr; (b) a bar magnet (S–N) moving along the common axis of two coaxial coils pqr and xyz; (c) the tapping key of the first of two backed coils just being closed; (d) the rheostat of the first of two backed coils being adjusted; (e) two adjacent coils, the tapping key of one just being released, with a loop xyz coupled; (f) a straight wire carrying current I with a circular loop in the same plane.
• 6.2) Use Lenz's law to determine the direction of induced current in the situations described by Fig. 6.16: (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire. (Field lines are directed into the plane of the loop.)
• 6.3) A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
• 6.4) A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s⁻¹ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?
• 6.5) A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
• 6.6) A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s⁻¹, at right angles to the horizontal component of the earth's magnetic field, 0.30 × 10⁻⁴ Wb m⁻². (a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of the emf? (c) Which end of the wire is at the higher electrical potential?
• 6.7) Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V is induced, give an estimate of the self-inductance of the circuit.
• 6.8) A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

Answers at a glance

1. 1
   Q6.1 → (a) qrpq; (b) prq in pqr and yzx in xyz; (c) yzxy; (d) zyxz (reverses if the primary current falls); (e) xryx; (f) no induced current (zero flux).
2. 2
   Q6.2 → (a) Anticlockwise (adcb) — flux increases. (b) Clockwise (abcd) — flux decreases.
3. 3
   Q6.3 → ε ≈ 7.5 × 10⁻⁶ V.
4. 4
   Q6.4 → (a) ε = 2.4 × 10⁻⁴ V, lasts 2 s. (b) ε = 6 × 10⁻⁵ V, lasts 8 s.
5. 5
   Q6.5 → ε = 100 V between the centre and the ring.
6. 6
   Q6.6 → (a) ε = 1.5 × 10⁻³ V. (b) Direction west → east. (c) The eastern end is at higher potential.
7. 7
   Q6.7 → L = 4 H.
8. 8
   Q6.8 → Change of flux linkage = 30 Wb.

MCQ Questions

1 Mark Questions

1. 1
   State Faraday's law of electromagnetic induction.
2. 2
   State Lenz's law. Which conservation principle does it follow?
3. 3
   Define the self-inductance of a coil and give its SI unit.
4. 4
   What are eddy currents, and how are they minimized in transformers?

2 Mark Questions

1. 1
   A rod of length 0.5 m moves with a speed of 10 m/s perpendicular to a magnetic field of 0.2 T. Find the motional emf induced across it. (Ans: ε = Bvl = 1.0 V)
2. 2
   The magnetic flux through a coil changes from 2 × 10⁻³ to 6 × 10⁻³ Wb in 0.01 s. Find the average induced emf. (Ans: ε = Δφ/Δt = 0.4 V)
3. 3
   State the expression for the mutual inductance between two long coaxial solenoids and define the henry in terms of it. (Ans: M = μ₀n₁n₂πr₁²l)

3 Mark Questions

1. 1
   Derive the motional emf induced across a conductor of length l moving with velocity v perpendicular to a uniform magnetic field B, using both the Lorentz force and Faraday's law. (Ans: ε = Bvl)
2. 2
   Derive the expression for the self-inductance of a long air-cored solenoid in terms of its geometry. (Ans: L = μ₀n²Al)
3. 3
   Explain how eddy currents are produced, give two applications (induction furnace and electromagnetic damping), and state how they are minimized in transformer cores.

5 Mark Questions

1. 1
   Explain Lenz's law with the help of examples and show that it follows from the conservation of energy.
2. 2
   Describe the principle and working of an AC generator (dynamo). Derive the expression for the induced emf, ε = NBAω sin ωt, and sketch the emf–time graph.