Thirty multiple choice questions on flux, Faraday’s and Lenz’s laws, motional emf and inductance. No question from this chapter appeared in the papers I could extract, so every question here is built to the AAI pattern and to the difficulty the domain section has shown elsewhere.
30questions
35 minsuggested time
2verified PYQs
MCQformat throughout
Score0 correct · 0 of 30 attempted
Before you begin
Formulas you will need
Key formulas
Magnetic flux: Φ = BA cosθ · unit weber (Wb) = T m²
Faraday: ε = −N dΦ ∕ dt · Motional emf: ε = Bvl · Induced charge: q = NΔΦ ∕ R
Self induction: ε = −L dI ∕ dt · Energy stored: U = ½LI² · Solenoid: L = μ0n²Al
Mutual induction: ε2 = −M dI1 ∕ dt · μ0 = 4π × 10−7 T m A−1
How to use this worksheet. Only a changing flux induces an emf — a large steady flux induces nothing. And in Φ = BA cosθ, the angle is measured from the normal to the surface, not from the plane, which is the reverse of what most students assume.
Section A · Level 1
Flux, Faraday and Lenz
Ten questions. None should take more than twenty seconds.
Q1
The SI unit of magnetic flux is the:
Magnetic flux is measured in weber, which is one tesla times one square metre.
Q2
Magnetic flux through a plane surface of area A in a uniform field B is given by:
Φ = BA cosθ, where θ is the angle between the field and the normal to the surface. The flux is greatest when the field is perpendicular to the plane.
Q3
Faraday's law states that the induced emf is proportional to the:
It is the rate of change of flux that matters, not the flux itself. A large but steady flux induces nothing at all.
Q4
The negative sign in Faraday's law is a statement of:
The minus sign expresses Lenz's law: the induced effect always opposes the change that produced it.
Q5
Lenz's law is a direct consequence of the conservation of:
If the induced effect assisted the change instead of opposing it, energy would be created from nothing. Lenz's law is energy conservation applied to induction.
Q6
The SI unit of inductance is the:
Inductance is measured in henry, defined as one volt-second per ampere.
Q7
An emf is induced in a coil when:
Only a changing flux induces an emf. Extra turns increase the emf but cannot create one on their own.
Q8
Eddy currents are induced in:
A changing flux drives circulating currents within any solid conductor. They dissipate energy as heat, which is useful in braking but wasteful in transformer cores.
Q9
The energy stored in an inductor carrying current I is:
U = ½LI², the magnetic analogue of the ½CV² stored in a capacitor.
Q10
An AC generator converts:
Rotating a coil in a magnetic field changes the flux through it and induces an emf, so mechanical work is converted into electrical energy. A motor does the reverse.
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Section B · Level 2
Induced emf, current and stored energy
Ten questions. Check whether the question wants emf, current or charge.
Q11
A coil of area 0.2 m² lies perpendicular to a uniform field of 0.5 T. The flux through it is:
With the field perpendicular to the plane, the angle to the normal is zero and cosθ = 1, so Φ = 0.5 × 0.2 = 0.1 Wb.
Q12
The flux through a coil changes by 0.02 Wb in 0.1 s. If the coil has 100 turns, the induced emf is:
ε = NΔΦ ∕ Δt = 100 × 0.02 ∕ 0.1 = 20 V. Forgetting to multiply by the number of turns gives option 3.
Q13
A rod of length 0.5 m moves at 5 m/s perpendicular to a field of 0.4 T. The motional emf is:
ε = Bvl = 0.4 × 5 × 0.5 = 1 V. All three quantities must be mutually perpendicular for this simple form to apply.
Q14
An inductor of 2 H carries a current of 3 A. The energy stored is:
U = ½LI² = 0.5 × 2 × 9 = 9 J. Option 1 omits the square, option 3 omits the half.
Q15
The current through a 0.5 H inductor changes by 4 A in 0.2 s. The induced emf is:
ε = L dI ∕ dt = 0.5 × 4 ∕ 0.2 = 10 V.
Q16
Two coils have a mutual inductance of 0.2 H. The current in the first changes at 5 A/s. The emf induced in the second is:
ε2 = M dI1 ∕ dt = 0.2 × 5 = 1 V.
Q17
A coil is rotated so that its plane becomes parallel to the magnetic field. The flux through it is then:
With the plane parallel to the field, the normal is perpendicular to it, so cos 90° = 0 and the flux vanishes. This is the instant when the induced emf in a generator is greatest.
Q18
A coil of resistance 2 Ω has an emf of 4 V induced in it. The induced current is:
The induced emf drives a current according to Ohm's law: I = 4 ∕ 2 = 2 A.
Q19
When the north pole of a magnet is pushed towards a coil, the near face of the coil behaves as a:
By Lenz's law the coil opposes the approach, so it presents a north pole to repel the incoming north pole. Withdrawing the magnet would reverse this.
Q20
A total charge q flows through a coil of resistance R when the flux changes by ΔΦ. The charge is given by:
Integrating the induced current over time gives q = NΔΦ ∕ R. Notice that the charge depends on the total flux change but not on how quickly it happens.
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Section C · Level 3
Self and mutual inductance, eddy currents
Ten questions. Each needs a formula plus a piece of reasoning.
Q23
The self inductance of a long solenoid of n turns per unit length, cross-sectional area A and length l is:
L = μ0n²Al. The dependence on the square of the turn density is why inductance rises sharply as a coil is wound more tightly.
Q24
A solenoid has 1000 turns per metre, cross-sectional area 10−4 m² and length 0.5 m. Its self inductance is closest to:
L = μ0n²Al = 4π × 10−7 × 106 × 10−4 × 0.5 = 6.3 × 10−5 H.
Q25
If the number of turns of a coil is doubled, its self inductance becomes:
Inductance depends on the square of the number of turns, so doubling the turns quadruples L.
Q26
Eddy current losses in a transformer core are reduced by:
Thin insulated laminations break the circulating current paths, cutting the heat loss sharply while leaving the magnetic circuit intact.
Q27
A metal plate swinging between the poles of a magnet comes to rest quickly because of:
The changing flux induces eddy currents in the plate, and by Lenz's law they oppose the motion. This is the principle behind electromagnetic braking.
Q28
In a coil rotating uniformly in a magnetic field, the induced emf is maximum when the plane of the coil is:
The emf follows the rate of change of flux, which peaks when the flux itself is momentarily zero — that is, when the coil's plane lies along the field.
Q29
Two coils are placed so that no flux from one links the other. Their mutual inductance is:
Mutual inductance measures the flux linkage between coils. With no shared flux, M is zero — which is why sensitive circuits are mounted with their coils at right angles.
Q30
The induced charge in a circuit depends on:
Since q = NΔΦ ∕ R, only the total flux change and the resistance matter. Changing the flux quickly gives a larger current for a shorter time, and the charge comes out the same.
Q31
A current-carrying inductor is suddenly disconnected from its supply. A large spark often appears at the switch because:
A rapid drop in current means a very large dI ∕ dt, and the induced emf L dI ∕ dt can far exceed the supply voltage. That is why inductive circuits need protective diodes.
Q32
Which of the following does not induce an emf in a stationary coil placed in a magnetic field?
Any of the first three changes the flux and so induces an emf. A constant flux, however strong, induces nothing.
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Section D · Previous year questions
Straight from the AAI ATC papers
Two questions from the 2023 papers, recovered by optical character recognition of the scanned answer sheets and independently re-solved.
Q21PYQ 2023 · Morning
A constant current I is maintained in a coil of pure inductance L. The energy stored in the coil is:
The energy stored in an inductor is ½LI², the magnetic counterpart of ½CV² for a capacitor. Options 3 and 4 both omit the factor of one half, and option 1 halves it twice.
Q22PYQ 2023 · Morning
Two coils are arranged close to each other. When the current in one coil changes from 0 A to 10 A in 0.5 s, the flux linked with the other coil changes by 40 Wb during the same period. The mutual inductance of the coils is:
Mutual inductance is the flux change per unit change of current, M = ΔΦ ∕ ΔI = 40 ∕ 10 = 4.0 H. The time of 0.5 s is not needed at all — it is there so that you can also work out the induced emf if asked, and it tempts you into dividing by it unnecessarily.
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↓ Free download — Electromagnetic Induction PDF
All thirty questions with the formula sheet printed on the front page and ruled working space for your circuit reductions. Print it, solve it, keep it.
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