Electromagnetic Induction — Class 12 Physics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 12 Physics chapter "Electromagnetic Induction" — 7 important questions with detailed answers for CBSE board exam preparation.

✓ 100% Free ✓ No Login Needed ✓ NCERT / CBSE Aligned ✓ Download as PDF

TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Electromagnetic Induction" — 7 important questions with detailed answers for CBSE boar…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

🤖 Stuck on any question? Ask Syllab's free AI Tutor for a step-by-step explanation — instant, unlimited, no login.

Key Questions Covered:

State Faraday's law of electromagnetic induction. Write mathematical expression.
A square loop of side 10 cm is placed in magnetic field 0.5 T. If field decre…
Define self-inductance (L). Derive expression for self-inductance of solenoid.
What is mutual inductance (M)? Explain with two coils.
Define AC generator. Derive expression for induced emf in rotating rectangula…
A rectangular coil of 100 turns, area 0.05 m², rotates in magnetic field of 0…
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
State Faraday's law of electromagnetic induction. Write m…	✓ Solved
A square loop of side 10 cm is placed in magnetic field 0…	✓ Solved
Define self-inductance (L). Derive expression for self-in…	✓ Solved
What is mutual inductance (M)? Explain with two coils.	✓ Solved
Define AC generator. Derive expression for induced emf in…	✓ Solved
A rectangular coil of 100 turns, area 0.05 m², rotates in…	✓ Solved

Showing 6 of 7 questions

Q1: State Faraday's law of electromagnetic induction. Write mathematical expression.

Faraday's Law of Electromagnetic Induction: Rate of change of magnetic flux through a circuit induces emf in the circuit. Mathematical Expression: ε = -dΦ_B/dt where ε = induced emf (volts) Φ_B = magnetic flux (Weber, Wb) t = time (seconds) Alternatively, for N turns: ε = -N(dΦ_B/dt) Integral form over time interval t₁ to t₂: ε = -N × (Φ₂ - Φ₁)/(t₂ - t₁) Magnetic Flux: Φ_B = ∫B⋅dA = BA cos θ (for uniform field) where B = magnetic flux density A = area of loop θ = angle between B and normal...

Q2: A square loop of side 10 cm is placed in magnetic field 0.5 T. If field decreases to 0.2 T in 0.1 s, find induced emf.

Given: Side of square loop = 10 cm = 0.1 m Initial magnetic field B₁ = 0.5 T Final magnetic field B₂ = 0.2 T Time interval Δt = 0.1 s Field perpendicular to loop (θ = 0°) Area of loop: A = side² = (0.1)² = 0.01 m² Initial flux: Φ₁ = B₁A cos 0° = 0.5 × 0.01 = 0.005 Wb Final flux: Φ₂ = B₂A cos 0° = 0.2 × 0.01 = 0.002 Wb Change in flux: ΔΦ = Φ₂ - Φ₁ = 0.002 - 0.005 = -0.003 Wb Rate of change of flux: dΦ/dt = ΔΦ/Δt = -0.003 / 0.1 = -0.03 Wb/s Induced emf (using Faraday's law): ε = -dΦ/dt = -(-...

Q3: Define self-inductance (L). Derive expression for self-inductance of solenoid.

Self-Inductance (L): Property of coil to oppose change in its own current. Definition: L = |ε|/|dI/dt| = Φ_B/I where ε = induced emf dI/dt = rate of change of current Φ_B = magnetic flux through coil I = current in coil SI Unit: Henry (H) = Wb/A = V⋅s/A Smaller units: mH (millihenry), μH (microhenry) For Solenoid: Consider solenoid with N turns, length L, cross-sectional area A. Magnetic field inside solenoid: B = μ₀nI = μ₀(N/L)I Magnetic flux through each turn: Φ = BA = μ₀(N/L) × I × A ...

Q4: What is mutual inductance (M)? Explain with two coils.

Mutual Inductance (M): Property describing how change in current in one coil induces emf in nearby coil. Definition: M₁₂ = Φ₂₁/I₁ = |ε₂|/|dI₁/dt| where Φ₂₁ = flux through coil 2 due to current I₁ in coil 1 ε₂ = induced emf in coil 2 I₁ = current in coil 1 SI Unit: Henry (H) For two coils: Coil 1 (primary): Current I₁, N₁ turns, area A₁ Coil 2 (secondary): N₂ turns, area A₂, separation d Mutual inductance: M₁₂ = M₂₁ = M (reciprocal property) Expression (ideal case, coils wound on same core)...

Q5: Define AC generator. Derive expression for induced emf in rotating rectangular coil.

AC Generator: Device that converts mechanical energy into electrical energy using electromagnetic induction. Principle: Rotating coil in uniform magnetic field generates alternating emf. Derivation for Rectangular Coil: Setup: - Rectangular coil with N turns, area A - Rotates in uniform magnetic field B - Angular velocity ω (rad/s) - At t = 0, coil plane parallel to field (flux = 0) Step 1: Angle θ between normal and field at time t θ = ωt (starting from θ = 0) Step 2: Magnetic flux through...

Q6: A rectangular coil of 100 turns, area 0.05 m², rotates in magnetic field of 0.2 T at 50 Hz. Find peak and RMS values of induced emf.

Given: N = 100 turns A = 0.05 m² B = 0.2 T f = 50 Hz (frequency) Angular velocity: ω = 2πf = 2π × 50 = 100π rad/s Peak (Maximum) EMF: ε₀ = NBAω Step 1: ε₀ = 100 × 0.2 × 0.05 × 100π Step 2: ε₀ = 100 × 0.2 × 0.05 × 100π Step 3: ε₀ = 100 × 1 × π = 100π V Step 4: ε₀ = 314.16 V ≈ 314 V RMS Value: ε_rms = ε₀/√2 Step 1: ε_rms = 100π/√2 Step 2: ε_rms = 100π/1.414 Step 3: ε_rms = 314.16/1.414 Step 4: ε_rms = 222.14 V ≈ 222 V Alternatively: ε_rms = 2πfNBA/√2 = (2π × 50 × 100 × 0.2 × 0.05)/√2 ε_rms =...

Showing 6 of 7 questions. Visit the full page for complete solutions.