Is it correct to say: Confusing 'flux' with 'rate of change of flux' — the flux itself need not induce an EMF?

EMF appears only when \Phi *changes* with time. A steady flux gives zero EMF.

Is it correct to say: Ignoring Lenz's law sign and getting wrong current direction?

Induced current opposes the change in flux. If flux is increasing, induced B inside loop opposes it — use right-hand rule to fix current direction.

Is it correct to say: Confusing self-inductance L with mutual inductance M?

L relates EMF in a coil to its *own* current change. M relates EMF in coil 2 to current change in *coil 1*.

Is it correct to say: Forgetting that inductance depends only on geometry (and medium), not on I?

L and M are constants for a fixed coil. They do NOT change when I changes — the *EMF* does.

Is it correct to say: Not converting cm² to m² in flux/inductance calculations?

1 cm² = 10⁻⁴ m². Missing this factor gives an answer off by 10⁴.

Is it correct to say: Applying \varepsilon = BLv when v is parallel to L or B?

\varepsilon = BLv only when B, L, v are mutually perpendicular. Otherwise use \varepsilon = (\vec{v}\times\vec{B})\cdot\vec{L}.

Electromagnetic Induction

Faraday's law, Lenz's law, motional EMF, self and mutual inductance, AC generator — NCERT Class 12 Physics Ch 6

📐 12 formulas✏️ 3 examples🎯 6 practice⚖️ 5 marks🏫 CBSE📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Faraday's law + Lenz's law (statement + direction of induced current) is nearly guaranteed as a 2–3 mark question.
→Motional EMF derivation (\varepsilon = BLv) is a repeat 3-mark board favourite — memorise the force/work chain.
→Self-inductance of a solenoid (L = \mu_0 n²Al) derivation appears in ~40% of past papers.
→Never drop the minus sign in \varepsilon = -d\Phi/dt without stating you're finding magnitude.
→For AC generator, know peak EMF \varepsilon_0 = NBA\omega and its instantaneous form.

📊 Diagram

Coil with changing magnetic flux inducing EMF in a closed loop

📐 Formulas(12)

Magnetic Flux

Φ = B \cdot A = B A cos θ

Symbol	Meaning
$Φ$	Magnetic flux (Wb = T·m²)
$θ$	Angle between B and area vector

Faraday's Law of Induction★ Board fav

ε = - N \frac{d Φ}{d t}

Symbol	Meaning
$ε$	Induced EMF (V)
$N$	Number of turns
$d Φ/ d t$	Rate of change of flux (Wb/s)

Lenz's Law★ Board fav

ε = - \frac{d Φ}{d t}

Motional EMF★ Board fav

ε = B Lv

Self-Induced EMF

ε = - L \frac{d I}{d t}

Symbol	Meaning
$L$	Self-inductance (H = Wb/A)
$d I / d t$	Rate of change of current (A/s)

Self-Inductance of a Solenoid★ Board fav

L = μ_{0} n^{2} A l = \frac{μ _{0} N ^{2} A}{l}

Mutual Inductance

ε_{2} = - M \frac{d I _{1}}{d t}

Symbol	Meaning
$M$	Mutual inductance (H)
$I_{1}$	Current in primary coil (A)

Mutual Inductance of Two Coaxial Solenoids

M = μ_{0} n_{1} n_{2} A l

Energy Stored in an Inductor

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

Magnetic Energy Density

u_{B} = \frac{B ^{2}}{2 μ _{0}}

AC Generator EMF

ε = ε_{0} sin (ω t), ε_{0} = N B A ω

Series/Parallel Inductors (no mutual coupling)

L_{ser i es} = L_{1} + L_{2}, \frac{1}{L _{p a r a l l e l}} = \frac{1}{L _{1}} + \frac{1}{L _{2}}

✏️ Solved Examples

1Solved Exampleeasy4 steps

A rectangular coil of 100 turns and area 200 cm² is placed with its plane perpendicular to a magnetic field that changes uniformly from 0.2 T to 0.6 T in 0.5 s. Find the induced EMF.

Convert area to SI, note field ⊥ plane means cos\theta = 1

A = 200 cm^{2} = 200 \times 1 0^{- 4} m^{2} = 2 \times 1 0^{- 2} m^{2}

2Solved Exampleboard5 steps

A metal rod of length 50 cm slides on horizontal rails at 4 m/s in a vertical uniform field of 0.5 T. The rails and a resistor of 2 \Omega form a closed loop. Find (a) motional EMF, (b) current in the loop, (c) mechanical power supplied by the external agent.

Motional EMF

ε = B Lv = 0.5 \times 0.5 \times 4 = 1.0 V

3Solved ExampleHOTS6 steps

A long solenoid of length 60 cm and radius 2 cm has 1200 turns. A small coil of 40 turns and area 4 cm² is placed at its centre, with axis parallel. If the current in the solenoid changes from 0 to 3 A in 0.2 s, find the mutual inductance and the EMF induced in the small coil.

Turns per metre of solenoid

n_{1} = \frac{1200}{0.6} = 2000 turns/m

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Confusing 'flux' with 'rate of change of flux' — the flux itself need not induce an EMF
✓EMF appears only when \Phi *changes* with time. A steady flux gives zero EMF.
2
Ignoring Lenz's law sign and getting wrong current direction
✓Induced current opposes the change in flux. If flux is increasing, induced B inside loop opposes it — use right-hand rule to fix current direction.
3
Confusing self-inductance L with mutual inductance M
✓L relates EMF in a coil to its *own* current change. M relates EMF in coil 2 to current change in *coil 1*.
4
Forgetting that inductance depends only on geometry (and medium), not on I
✓L and M are constants for a fixed coil. They do NOT change when I changes — the *EMF* does.
5
Not converting cm² to m² in flux/inductance calculations
✓1 cm² = 10⁻⁴ m². Missing this factor gives an answer off by 10⁴.
6
Applying \varepsilon = BLv when v is parallel to L or B
✓\varepsilon = BLv only when B, L, v are mutually perpendicular. Otherwise use \varepsilon = (\vec{v}\times\vec{B})\cdot\vec{L}.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
A coil of 500 turns and area 10 cm² is in a field 0.4 T. It is pulled out completely in 0.1 s. Average induced EMF?
Q2
A solenoid of length 1 m has 2000 turns and radius 2 cm. Compute its self-inductance.
Q3
Current in an inductor of 0.5 H changes at 20 A/s. Self-induced EMF?
Q4
Energy stored when 4 A flows through a 2 H inductor?
Q5
An AC generator has 200 turns, coil area 100 cm², rotates at 50 Hz in field 0.5 T. Peak EMF?
Q6
A rod 40 cm long moves at 5 m/s perpendicular to a 0.2 T field. Motional EMF?

📝 Notes

Electromagnetic Induction — key concepts

The single phenomenon: a changing magnetic flux through a circuit induces an EMF around that circuit. This is the basis of the electric generator, transformer, and induction motor.

Faraday, in three sentences

Whenever the magnetic flux \Phi through a closed loop changes, an EMF \varepsilon = −d\Phi/dt is induced.
The change can come from a changing B, a moving area (motional EMF), or a rotating coil (generator).
With N turns, replace \Phi with N\Phi (flux linkage).

Lenz's law — the "why" of the minus sign

The induced current always flows in a direction that opposes the change producing it. If flux is increasing, the induced B opposes it; if decreasing, the induced B supports it. This is a statement of energy conservation: an induced current cannot make its own source of energy.

Motional EMF — two equivalent derivations

Force picture: free electrons in the moving rod feel qv × B, get pushed along the rod, produce EMF = BLv.
Flux picture: area swept per second = Lv, so d\Phi/dt = BLv. Same answer.

Self and mutual inductance

Self-inductance L (Henry) — property of a coil. \varepsilon_{self} = −L(dI/dt). Opposes changes in its own current — "electrical inertia".
Mutual inductance M — property of a pair of coils. \varepsilon_2 = −M(dI_1/dt). Basis of the transformer.

Quick sanity checks

If flux is not changing, EMF is zero — full stop.
Magnetic energy density B²/(2\mu_0) and electric energy density \tfrac{1}{2}\varepsilon_0 E² look alike — remember which \mu goes where.
L is measured in henry (H) = V·s/A = Wb/A.
Doubling turns quadruples L (since L ∝ N²) but only doubles M for coupled coils (M ∝ N_1 N_2).
Any solution must satisfy energy conservation: mechanical work done = electrical energy dissipated (motional EMF problems).