Induced emf in a closed circuit equals the negative rate of change of magnetic flux: ε = -dΦ/dt. Flux Φ = ∫ B · dA.
-- NCERT Class 12 Physics, Ch. 6, p. 157Faraday's Law
8 MCQs2 revision cards9-step worked example
Source: NCERT Electromagnetic Induction and Alternating CurrentsPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 25 Sep 2026
Faraday's Law, explained for NEET
The frequent error on this topic is reading Faraday's law as "a magnetic field induces an EMF." It does not. A coil sitting still inside the strongest uniform field in the lab has zero induced EMF. What the law says is that EMF is proportional to the rate of change of flux — the derivative, not the value.
NCERT Class 12 Physics Chapter 6, page 157, states it as ε = −dΦ_B/dt, where Φ_B = BA cos θ is the flux through the loop. Three things can change flux: B, the area A enclosed, or the orientation θ. Change any one and you get an EMF; hold all three fixed and you get nothing, however large B is.
For an N-turn coil the flux links each turn, so ε = −N dΦ_B/dt. Dropping N is a routine loss of marks in numerical questions.
Two consequences worth holding separately. First, a large flux with small rate of change gives a small EMF; a small flux collapsing fast gives a large one. Only the slope matters. Second, EMF depends on how fast the change happens, so halving the time over which the same flux change occurs doubles the EMF — this is the basis of most NEET numerical items on this topic.
The minus sign carries the direction information (Lenz's law, covered separately in this unit — here treat it as the sign convention only, and work with magnitudes when computing).
In NEET, this topic appears as a two-step item: extract ΔΦ from given B, A and θ data, then divide by Δt. The distractors are built from the ways that extraction goes wrong — using B instead of BA, forgetting cos θ, forgetting N, or dividing by the wrong interval.
Watch out: when a question gives you flux at two instants, you need the difference, not either value on its own — and the sign of that difference tells you direction, not magnitude.
Can you answer these Faraday's Law MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
According to Faraday's law of electromagnetic induction, the EMF induced in a closed loop is proportional to
Show answer and why every option is right or wrong
Answer: C. C is correct. NCERT Class 12 Physics Chapter 6, page 157, states the law as ε = −dΦ_B/dt: the induced EMF equals the negative rate of change of flux, not the flux itself.
Why A is wrong: A is wrong because a constant flux, however large, gives zero EMF — only the derivative of flux matters.
Why B is wrong: B is wrong because a loop at rest in a strong but steady field has no induced EMF; the field magnitude alone is not the source term.
Why D is wrong: D is wrong because area enters only through the flux product Φ_B = BA cos θ, and a fixed area with fixed B and θ produces no EMF.
MCQ 2Easy RecallPractice
The SI unit of magnetic flux, as used in the statement of Faraday's law, is the
Show answer and why every option is right or wrong
Answer: B. B is correct. Flux Φ_B is measured in webers; NCERT Class 12 Physics Chapter 6, page 157, gives EMF in volts as the rate of change of flux in webers per second.
Why A is wrong: A is wrong because the tesla is the unit of magnetic field B, not of flux; flux is B times area.
Why C is wrong: C is wrong because the henry is the unit of inductance, which relates flux linkage to current rather than measuring flux itself.
Why D is wrong: D is wrong because one weber does equal one volt-second, but dividing by metre gives a different quantity altogether.
MCQ 3Easy RecallPractice
For a coil of N turns linked by a changing flux Φ_B, the magnitude of the induced EMF is given by
Show answer and why every option is right or wrong
Answer: D. D is correct. The flux links each of the N turns, so the EMFs add in series: ε = N dΦ_B/dt, as set out in NCERT Class 12 Physics Chapter 6, page 157.
Why A is wrong: A is wrong because it is the single-turn result; each additional turn contributes its own EMF in series.
Why B is wrong: B is wrong because it divides by the turn count, which would make a multi-turn coil worse than a single loop.
Why C is wrong: C is wrong because the turn dependence is linear, not quadratic — the square appears in inductance expressions, not in Faraday's law.
MCQ 4Direct ApplicationPractice
The magnetic flux through a single-turn loop changes uniformly from 6.0 × 10⁻² Wb to 2.0 × 10⁻² Wb in 0.20 s. The magnitude of the induced EMF is
Show answer and why every option is right or wrong
Answer: A. A is correct. ΔΦ = 4.0 × 10⁻² Wb, so ε = ΔΦ/Δt = (4.0 × 10⁻²)/(0.20) = 0.20 V, applying ε = dΦ_B/dt from NCERT Class 12 Physics Chapter 6, page 157.
Why B is wrong: B is wrong because it multiplies the flux change by the time instead of dividing by it.
Why C is wrong: C is wrong because 0.30 V is 6.0 × 10⁻²/0.20: it uses the initial flux as the change, ignoring that the flux falls only to 2.0 × 10⁻² Wb.
Why D is wrong: D is wrong because 0.40 V is (6.0 + 2.0) × 10⁻²/0.20: it adds the two flux values instead of subtracting them. The change is 4.0 × 10⁻² Wb, so ε = 4.0 × 10⁻²/0.20 = 0.20 V.
MCQ 5Direct ApplicationPractice
A coil of 50 turns encloses an area of 2.0 × 10⁻² m². The magnetic field perpendicular to its plane falls uniformly from 0.40 T to zero in 0.50 s. The magnitude of the induced EMF is
Show answer and why every option is right or wrong
Answer: C. C is correct. ΔΦ per turn = ΔB × A = 0.40 × 2.0 × 10⁻² = 8.0 × 10⁻³ Wb; ε = N ΔΦ/Δt = 50 × (8.0 × 10⁻³)/(0.50) = 0.80 V, per NCERT Class 12 Physics Chapter 6, page 157.
Why A is wrong: A is wrong because 0.40 V is the change in field, 0.40 T, reported as the EMF: it skips the rate, the area and the 50 turns. ε = N·A·ΔB/Δt = 50 × 2.0 × 10⁻² × 0.40/0.50 = 0.80 V.
Why B is wrong: B is wrong because it omits the turn count N, giving only the single-loop EMF.
Why D is wrong: D is wrong because 16 V does not follow from ε = N·A·ΔB/Δt with one factor dropped (dropping the area gives 40 V, dropping the turns 1.6 × 10⁻² V). The correct value is 50 × 2.0 × 10⁻² × 0.80 = 0.80 V.
MCQ 6Direct ApplicationPractice
A flat loop of area 4.0 × 10⁻² m² sits in a uniform field of 0.50 T with its normal making an angle of 60° with the field. The flux through the loop is
Show answer and why every option is right or wrong
Answer: A. A is correct. Φ_B = BA cos θ = 0.50 × 4.0 × 10⁻² × cos 60° = 0.50 × 4.0 × 10⁻² × 0.50 = 1.0 × 10⁻² Wb, using the flux definition underlying Faraday's law in NCERT Class 12 Physics Chapter 6, page 157. The angle 60° is exact and does not limit the significant figures.
Why B is wrong: B is wrong because it omits cos θ entirely, treating the normal as parallel to the field.
Why C is wrong: C is wrong because it uses sin 60° instead of cos 60°; the angle given is between the normal and the field, so the cosine applies.
Why D is wrong: D is wrong because 8.0 × 10⁻² Wb is eight times the correct flux; even dividing by cos 60° instead of multiplying gives only BA/cos 60° = 4.0 × 10⁻² Wb. Φ = BA cos 60° = 0.50 × 4.0 × 10⁻² × 0.50 = 1.0 × 10⁻² Wb.
MCQ 7CalculationPractice
A square loop of side 0.20 m lies with its plane perpendicular to a uniform field of 0.30 T. The loop is pulled fully out of the field region in 0.10 s. If instead the same loop is pulled out in 0.050 s, the induced EMF becomes
Show answer and why every option is right or wrong
Answer: D. D is correct. The flux change ΔΦ = BA is identical in both cases, but ε = ΔΦ/Δt, so halving Δt doubles the EMF — the rate dependence stated in NCERT Class 12 Physics Chapter 6, page 157.
Why A is wrong: A is wrong because EMF varies inversely with the first power of the time interval, not its square.
Why B is wrong: B is wrong because it inverts the relationship: a shorter interval gives a larger, not smaller, EMF.
Why C is wrong: C is wrong because it confuses the flux change with the EMF — the same ΔΦ over different Δt gives different EMFs, which is the core of Faraday's law.
MCQ 8CalculationPractice
A circular coil of 100 turns and radius 0.10 m lies in a field of 0.20 T directed along its axis. The coil is rotated through 90° about a diameter in 0.10 s, so that its plane becomes parallel to the field. Taking π² ≈ 10, the average induced EMF is closest to
Show answer and why every option is right or wrong
Answer: A. A is correct. Initial flux per turn = BA = 0.20 × π(0.10)² = 6.28 × 10⁻³ Wb; final flux is zero (normal now perpendicular to B, cos 90° = 0). ε = N ΔΦ/Δt = 100 × 6.28 × 10⁻³/0.10 = 6.3 V, applying ε = N dΦ_B/dt from NCERT Class 12 Physics Chapter 6, page 157. The turn count 100 and the angle 90° are exact.
Why B is wrong: B is wrong because it is ten times too small, as if the rotation took 1.0 s instead of 0.10 s.
Why C is wrong: C is wrong because it treats the flux as reversing from +BA to −BA; a 90° rotation brings the flux to zero, not to the opposite sign.
Why D is wrong: D is wrong because it halves the flux change, using the average flux BA/2 in place of the change from BA to zero.
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Faraday's Law: quick recall before you leave
How do you solve a Faraday's Law question? A worked example
Pattern: EMF induced in a coil by changing flux (the highest-frequency in-scope pattern for this topic; observed 2022 and 2024).
- 1
Given
• Number of turns, N = 200 (exact, counting number)• Area of coil, A = 5.0 × 10⁻² m²• Magnetic field perpendicular to the coil's plane falls from B₁ = 0.60 T to B₂ = 0.10 T• Time for the change, Δt = 0.25 s
- 2
Required
Magnitude of the average induced EMF.
- 3
Concept
Flux through each turn is Φ_B = BA cos θ. Here the field is perpendicular to the plane of the coil, so it is along the normal and θ = 0, giving cos θ = 1 and Φ_B = BA. Only B changes; N, A and θ are fixed. The EMF follows from the rate of change of flux linkage, N Φ_B.
- 4
Formula
ε = N |ΔΦ_B| / Δt, where ΔΦ_B = A ΔB for fixed area and orientation.
- 5
Substitution
ΔB = B₁ − B₂ = 0.60 − 0.10 = 0.50 T
ΔΦ_B = A ΔB = (5.0 × 10⁻²)(0.50)
ε = 200 × (5.0 × 10⁻²)(0.50) / 0.25 - 6
Calculation
ΔΦ_B = 2.5 × 10⁻² Wb
N ΔΦ_B = 200 × 2.5 × 10⁻² = 5.0 Wb
ε = 5.0 / 0.25 = 20 V
The turn count N = 200 is a counting number and cos 0° = 1 is exact; neither limits the significant-figure count. The measured quantities (5.0 × 10⁻² m², 0.50 T, 0.25 s) each carry two significant figures. - 7
Final answer
ε = 2.0 × 10¹ V.
(Written in scientific notation because "20 V" leaves the trailing zero ambiguous — the answer carries two significant figures, matching the two-figure data.) - 8
Common trap
The two failure modes here are dropping N — which gives 0.10 V, a hundredfold error that still looks like a plausible small EMF — and using B₁ alone rather than ΔB, which gives 24 V and sits close enough to the correct value to survive a quick sanity check. Write ΔB explicitly on its own line before substituting. Note also that the field falling to 0.10 T rather than to zero is the whole point of the item: a question that ends at zero is testing arithmetic, and one that does not is testing whether you take the difference.
- 9
Similar NEET-style question
A coil of 500 turns and area 2.0 × 10⁻² m² has its plane perpendicular to a field that increases uniformly from 0.20 T to 0.45 T in 0.50 s. Find the magnitude of the average induced EMF. *(Answer: 5.0 V.)*
What to remember before solving Faraday's Law questions
Formula
Motional emf
Rod of length L moving with velocity v in field B perpendicular to both: ε = B L v. Induced by the magnetic Lorentz force on charge carriers.
-- NCERT Class 12 Physics, Ch. 6, p. 163Which Faraday's Law formulas do you need for NEET?
1 formula — click to collapse
Faraday's law of induction
Induced EMF in circuit equals negative rate of change of magnetic flux. Lenz's law in the sign.
| Symbol | Quantity | SI Unit |
|---|---|---|
| epsilon | induced EMF | V |
| Phi_B | magnetic flux | Wb |
Valid when
- Closed loop
- Flux change real (motion or B change)
More in Electromagnetic Induction and Alternating Currents: 4 exam traps and mistakes · 10 formulas · 5 question patterns from its other lessons.
Faraday's Law questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
1Zero weber
22 weber
30.5 weber
41 weber
NTA Answer: Option 3(final)
All 20 past-paper questions from Electromagnetic Induction and Alternating Currents →
How does NEET ask about Faraday's Law?
1 recurring pattern from past papers — click to collapse
EMF induced in coil by changing flux. Lenz's law sign: opposes change.
InterpretationMedium
Common distractors
wrong sign direction
Picks induced current in wrong direction
Sources
NCERT refs: Class 12 Physics Chapter 6, p.157
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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