NCERT Solutions for Class 12 Physics Chapter 6 Electromagnetic Induction
NCERT Solutions for Class 12 Physics Chapter 6 Electromagnetic Induction provides complete conceptual notes, key equations, derivations, and step-by-step textbook solutions covering Faraday's laws, Lenz's law, motional emf, eddy currents, self and mutual inductance, and AC generator working principles.
Overview of Topics & Subtopics (Click to Jump)
1. Magnetic Flux & Faraday's Law of EMI
Short Note:
• Magnetic Flux (Φ_B): The total number of magnetic field lines passing normally through a surface area A in magnetic field B: Φ_B = B · A = B A cos θ. SI Unit: Weber (Wb) or Tesla-meter² (T·m²).
• Faraday's First Law: Whenever the magnetic flux linked with a closed circuit changes, an electromotive force (emf) is induced in the circuit, which lasts as long as the change in flux continues.
• Faraday's Second Law: The magnitude of induced emf in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit:
- Formula: ε = -N (dΦ_B / dt), where N is the number of turns in the coil.
2. Lenz's Law & Conservation of Energy
Short Note:
• Lenz's Law: The direction of the induced current is always such that it opposes the change in magnetic flux that produces it. This opposition is represented by the negative sign in Faraday's law: ε = - (dΦ_B / dt).
• Lenz's Law and Conservation of Energy:
- When a bar magnet is moved towards a coil, mechanical work is done against the repulsive magnetic force produced by the induced current.
- This mechanical work done is converted into electrical energy, which subsequently dissipates as heat (Joule heating). If there were no opposition, electrical energy would be created without expending mechanical work, violating the Law of Conservation of Energy.
3. Motional Electromotive Force & Eddy Currents
Short Note:
• Motional EMF (Translational): EMF induced across the ends of a conductor of length l moving with velocity v perpendicular to a uniform magnetic field B: ε = B l v.
• Motional EMF (Rotational): EMF induced in a metallic rod of length l rotating with angular speed ω about one end in uniform magnetic field B: ε = (1/2) B ω l² = B A f.
• Eddy Currents (Foucault Currents): Circulating loops of electrical current induced within solid metallic blocks when subjected to a changing magnetic field.
- Disadvantages: Cause heat loss and overheating in transformers and electric motors.
- Minimization: Reduced by using laminated metal cores insulated from each other.
- Applications: Electromagnetic damping in galvanometers, induction furnaces, electric brakes in trains.
4. Inductance (Self & Mutual) & AC Generator
Short Note:
• Self-Inductance (L): Phenomenon in which an induced emf is produced in a coil due to change in current in the same coil. Φ = L I => ε = -L (dI / dt). SI Unit: Henry (H).
- Solenoid Self-Inductance: L = (μ₀ N² A) / l = μ₀ n² A l.
- Energy Stored in Inductor: U = (1/2) L I².
• Mutual Inductance (M): Phenomenon in which changing current in a primary coil induces emf in a nearby secondary coil. Φ₂ = M I₁ => ε₂ = -M (dI₁ / dt).
- Mutual Inductance of Coaxial Solenoids: M = (μ₀ N₁ N₂ A) / l = μ₀ n₁ n₂ A l.
• AC Generator: Converts mechanical energy into alternating electrical energy based on EMI.
- Induced EMF Formula: ε = ε₀ sin(ω t) = N A B ω sin(ω t), where ε₀ = N A B ω is the peak voltage.
Intext & Conceptual Questions
• Statement: Lenz's law states that the polarity of induced electromotive force is such that it produces a current whose magnetic field opposes the change in magnetic flux that produced it.
• Compliance with Energy Conservation:
1. Consider a bar magnet approaching a coil with its North pole facing the coil. The induced current flows in a direction such that the coil face becomes a North pole, resisting the approach of the magnet.
2. An external mechanical agent must do work against this repulsive force to move the magnet closer.
3. This mechanical work done is transferred to the system and converted into electrical energy in the coil. Thus, Lenz's law is a direct consequence of the Law of Conservation of Energy.
| Feature | Self-Inductance (L) | Mutual Inductance (M) |
|---|---|---|
| Coils Involved | Involves a single coil. | Involves two neighboring coils (Primary & Secondary). |
| Working Concept | EMF is induced in the coil due to variation of current in the same coil. | EMF is induced in the secondary coil due to variation of current in primary. |
| Governing Equation | ε = -L (dI / dt) | ε₂ = -M (dI₁ / dt) |
| Main Application | Choke coils, inductors in tuning circuits. | Transformers and induction coils. |
Textbook Chapter End Exercise Questions
Given:
• Length of metallic rod (l) = 1.0 m
• Angular frequency (ω) = 400 rad/s
• Magnetic field (B) = 0.5 T
Formula:
The induced rotational motional emf is given by:
ε = (1 / 2) × B × ω × l²
Calculation:
ε = 0.5 × 0.5 × 400 × (1.0)²
ε = 0.25 × 400 × 1
ε = 100 V
The emf developed between the centre and the ring is 100 V.
Given:
• Side of square loop (a) = 10 cm = 0.1 m => Area (A) = 0.1 × 0.1 = 0.01 m²
• Resistance (R) = 0.5 Ω
• Initial Magnetic Field (B₁) = 0.10 T, Final Magnetic Field (B₂) = 0 T
• Angle θ between magnetic field (North-East) and normal to loop (North) = 45°
• Time interval (Δt) = 0.70 s
Step 1: Calculate Initial Magnetic Flux (Φ₁)
Φ₁ = B₁ A cos θ = 0.10 × 0.01 × cos(45°) = 10⁻³ × (1 / √2) ≈ 0.000707 Wb
Φ₂ = 0 Wb
Change in flux (ΔΦ) = |Φ₂ - Φ₁| = 0.000707 Wb
Step 2: Calculate Induced EMF (ε)
ε = ΔΦ / Δt = 0.000707 / 0.70 ≈ 0.00101 V = 1.01 mV
Step 3: Calculate Induced Current (I)
I = ε / R = 0.00101 / 0.5 = 0.00202 A = 2.02 mA
The magnitude of the induced current during this time interval is 2.02 mA.
Read More & Chapter Resources
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