Is it correct to say: Forgetting the negative sign in Faraday's law?

ε = −dΦ/dt. The minus sign is Lenz's law — do not drop it in derivations.

Is it correct to say: Using Φ = BA even when B and A are at an angle?

Include cos θ: Φ = BA cos θ. If loop plane is parallel to B, Φ = 0.

Is it correct to say: Assuming self-inductance depends on current?

L is a geometric constant. It never depends on the instantaneous current.

Is it correct to say: Confusing motional EMF ε = Bvl with self-induced EMF ε = −L dI/dt?

First is due to physical motion, second due to changing current. Different scenarios.

Is it correct to say: Writing coefficient of coupling as k = M/(L₁L₂) instead of M/√(L₁L₂)?

Denominator is the geometric mean √(L₁L₂), not the product.

Is it correct to say: Forgetting the AC generator peak EMF has factor ω?

ε₀ = NBAω. Missing ω is a common HSC slip.

Electromagnetic Induction

Faraday's laws, Lenz's law, self and mutual induction, AC generator, LC oscillations — Maharashtra HSC Physics Ch 12

📐 12 formulas✏️ 3 examples🎯 5 practice⚖️ 5 marks🏫 Maharashtra State Board📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Faraday's laws of electromagnetic induction (statement + expression ε = −dΦ/dt) is asked every year for 2 marks. Learn to state both laws explicitly.
→Derivation of self-inductance of a solenoid (L = μ₀n²lA) and mutual inductance of two coaxial solenoids are Maharashtra HSC favourites.
→AC generator — principle, construction, working with labelled diagram and expression ε = ε₀sin(ωt) is a common 4-mark question.
→For LC oscillations, learn the analogy with SHM (charge ↔ displacement, current ↔ velocity) — Balbharati devotes a full section to this.
→Always state Lenz's law when explaining direction of induced current — it is the mark-scoring keyword.

📐 Formulas(12)

Magnetic Flux

Φ_{B} = B \cdot A = B A cos θ

Faraday's Law of Induction★ Board fav

ε = - \frac{d Φ _{B}}{d t}

Motional EMF★ Board fav

ε = B v l

Self-Inductance

ε = - L \frac{d I}{d t} Φ = L I

Symbol	Meaning
$L$	Self-inductance (H)

Self-Inductance of a Solenoid★ Board fav

L = μ_{0} n^{2} A l

Mutual Inductance

ε_{2} = - M \frac{d I _{1}}{d t}

Mutual Inductance of Coaxial Solenoids★ Board fav

M = μ_{0} n_{1} n_{2} A l

Energy Stored in an Inductor

U_{L} = \frac{1}{2} L I^{2}

AC Generator EMF★ Board fav

ε = ε_{0} sin (ω t), ε_{0} = N B A ω

LC Oscillation Angular Frequency

ω = \frac{1}{L C}

Charge in LC Circuit

q (t) = q_{0} cos (ω t)

Coefficient of Coupling

k = \frac{M}{L _{1} L _{2}}

✏️ Solved Examples

1Solved Exampleeasy3 steps

A coil of 200 turns has an area of 100 cm² and is placed in a magnetic field of 0.5 T. Find the change in flux linkage when the coil is rotated from 0° to 60°.

Initial flux (θ = 0°):

Φ_{1} = N B A cos 0° = 200 \times 0.5 \times 1 0^{- 2} \times 1 = 1 Wb

2Solved Exampleboard4 steps

A solenoid 40 cm long has 800 turns and cross-sectional area 4 cm². Calculate its self-inductance and the energy stored in it when a current of 3 A flows.

Turns per unit length.

n = \frac{N}{l} = \frac{800}{0.4} = 2000 /m

3Solved ExampleHOTS4 steps

An LC circuit has L = 20 mH and C = 50 µF. Initially the capacitor holds Q₀ = 6×10⁻⁴ C. (i) Find the frequency of oscillation. (ii) Find the maximum current in the inductor.

Angular frequency.

ω = \frac{1}{L C} = \frac{1}{20 \times 1 0 ^{- 3} \times 50 \times 1 0 ^{- 6}} = 1 0^{3} rad/s

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Forgetting the negative sign in Faraday's law
✓ε = −dΦ/dt. The minus sign is Lenz's law — do not drop it in derivations.
2
Using Φ = BA even when B and A are at an angle
✓Include cos θ: Φ = BA cos θ. If loop plane is parallel to B, Φ = 0.
3
Assuming self-inductance depends on current
✓L is a geometric constant. It never depends on the instantaneous current.
4
Confusing motional EMF ε = Bvl with self-induced EMF ε = −L dI/dt
✓First is due to physical motion, second due to changing current. Different scenarios.
5
Writing coefficient of coupling as k = M/(L₁L₂) instead of M/√(L₁L₂)
✓Denominator is the geometric mean √(L₁L₂), not the product.
6
Forgetting the AC generator peak EMF has factor ω
✓ε₀ = NBAω. Missing ω is a common HSC slip.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
A rod of length 0.5 m moves at 4 m/s perpendicular to a magnetic field of 0.2 T. Find the induced EMF.
Q2
A 100-turn coil has area 200 cm². Field changes uniformly from 0.1 T to 0.6 T in 0.2 s. Find the induced EMF.
Q3
Two coils have mutual inductance 0.5 H. Current in the primary changes at 4 A/s. Find EMF in the secondary.
Q4
An inductor of 40 mH stores 0.2 J. Find the current through it.
Q5
State Lenz's law and describe its consistency with the law of conservation of energy.

📝 Notes

Electromagnetic Induction — Maharashtra HSC Overview

Chapter 12 of the Balbharati Class 12 Physics textbook covers EM induction, self and mutual inductance, AC generator and LC oscillations.

Maharashtra syllabus specifics

LC oscillations and the SHM analogy (q ↔ x, I ↔ v, 1/C ↔ k, L ↔ m) are treated more formally in the Maharashtra syllabus than in NCERT. Expect a 3-mark theoretical question.
Derivation of self-inductance of a solenoid and mutual inductance of two coaxial solenoids are both listed explicitly in the Board syllabus. Practise both.
The AC generator treatment in Balbharati includes labelled construction diagram, principle, working and expression for EMF — often asked together as a 4-mark question.
Maharashtra Board sometimes uses the term coefficient of coupling k — CBSE uses it too but rarely asks numericals on it. HSC does.

Strategy

Learn to state Faraday's law in both differential (ε = −dΦ/dt) and integral (∮E·dl = −dΦ/dt) forms — the latter appears at the end of the chapter.
Distinguish clearly between motional EMF and induced EMF from changing B. Both are cases of Faraday's law but the source of dΦ/dt is different.
The negative sign in ε = −dΦ/dt is Lenz's law — never omit it in derivations, or you will lose a mark.