Class 12 : Physics (English) – Chapter 6: Electromagnetic Induction
EXPLANATION & SUMMARY
🌿 Introduction
Electromagnetic induction is one of the greatest contributions of 19th-century physics. It was discovered independently by Michael Faraday in England and Joseph Henry in America. Both showed that whenever the magnetic flux linked with a circuit changes, an emf is induced, which may cause a current in the circuit.
This chapter not only unifies electricity and magnetism but also serves as the foundation of electrical power generation, transformers, and modern technology.
💡 Concept: A changing magnetic environment around a conductor produces an emf.
🟢 Magnetic Flux (ΦB)
✏️ Definition: Magnetic flux through a surface = measure of the number of magnetic field lines passing through it.
Formula:
ΦB = B · A = BA cosθ
➡️ B = magnetic field strength
➡️ A = area of the loop
➡️ θ = angle between field and normal to surface
✔️ Magnetic flux is analogous to electric flux.
🔴 Faraday’s Laws of Electromagnetic Induction
Through careful experiments, Faraday concluded two laws:
First Law: An emf is induced in a circuit whenever the magnetic flux linked with it changes.
Second Law: The magnitude of the induced emf is proportional to the rate of change of flux linkage.
✏️ Formula:
e = – dΦB/dt
✔️ The negative sign, introduced by Lenz, indicates opposition to the cause.
🟡 Lenz’s Law
Statement: The direction of induced current is always such that it opposes the change in flux producing it.
This ensures energy conservation.
Example:
Magnet approaches coil → induced current repels magnet.
Magnet moves away → induced current attracts magnet back.
💡 Without Lenz’s law, energy could be created freely, violating conservation.
🔵 Ways of Changing Flux
Flux linkage through a circuit can change due to:
✔️ Changing B (magnetic field strength).
✔️ Changing A (area of the circuit).
✔️ Changing θ (orientation).
✔️ Motion of conductor in magnetic field.
🟢 Motional emf (Derivation in Detail)
Consider a rod of length ℓ moving with velocity v perpendicular to a magnetic field B.
Force on a charge q inside rod: F = q(v × B).
Electrons accumulate at one end, creating emf.
✏️ emf induced:
e = Bℓv
If the conductor moves at an angle, emf = Bℓv sinθ.
✔️ Motional emf is central in generators and rail–gun experiments.
🔴 AC Generator (Derivation Expanded)
An AC generator converts mechanical rotation into alternating current.
Construction: Coil of N turns, area A, rotating with angular velocity ω in uniform B.
Flux linked at time t: Φ = NBA cos(ωt).
emf induced:
e = – dΦ/dt = NBAω sin(ωt).
✔️ Thus, emf varies sinusoidally with time. Peak emf = NBAω.
💡 Real-life: Every power station uses Faraday’s principle.
🟡 Transformer (Principle)
A transformer works on mutual induction.
Primary coil with turns N₁ connected to AC supply.
Secondary coil with N₂ turns linked magnetically.
emf induced in secondary: e₂ = –M dI₁/dt.
✏️ Ratio:
V₂/V₁ = N₂/N₁
✔️ Step-up or step-down AC voltage depending on ratio of turns.
🔵 Eddy Currents (Expanded)
When a solid conductor is subjected to changing flux, induced circular currents (eddy currents) flow.
Discovered by Foucault → sometimes called Foucault currents.
Cause unwanted heating but also useful applications.
✔️ Applications:
Electromagnetic brakes (eddy currents oppose wheel motion).
Damping in galvanometers.
Induction heating furnaces.
Smart electric meters.
💡 Example: Aluminium plate swinging in magnetic field slows down because of eddy current damping.
🟢 Self-Induction (Detailed)
When current through a coil changes, it changes magnetic flux linked with the coil, inducing emf in same coil.
Formula: e = –L dI/dt
L = coefficient of self-induction, depends on geometry and medium.
Unit: Henry (H).
💡 Analogy: L behaves like inertia — resists change in current just as mass resists change in velocity.
🔴 Mutual Induction (Detailed)
When current in coil 1 changes, flux linked with coil 2 also changes, inducing emf in coil 2.
Formula: e₂ = –M dI₁/dt
M = mutual inductance.
Symmetric: M₁₂ = M₂₁.
✔️ Basis of transformers, wireless charging, induction coils.
🟡 Energy in Inductor (Expanded)
When current builds in an inductor, work must be done against induced emf. This energy is stored in magnetic field.
Formula: U = ½ L I²
Energy density in field: u = B²/(2μ₀)
💡 Analogy: Capacitor stores energy in electric field, inductor stores in magnetic field.
🔵 Conservation of Energy (with Lenz’s Law)
Consider motional emf: If a conductor moves in field, induced current produces magnetic force opposing motion. Work done by external agent appears as:
Electrical energy in circuit, and/or
Heat in resistance.
✔️ Thus, conservation of energy is never violated.
🟢 Real-Life Applications (Expanded)
Generators: Power stations generate AC using electromagnetic induction.
Transformers: Step-up or step-down voltage in transmission.
Induction Cooker: Eddy currents heat vessel directly.
Magnetic Brakes: Trains stop smoothly with eddy current brakes.
Wireless charging: Based on mutual induction.
Choke coils: Limit AC current in circuits.
🔴 Common Misconceptions Cleared
❌ Steady magnetic field can induce emf → Wrong. ✔️ emf induced only if flux changes.
❌ Lenz’s law creates energy → Wrong. ✔️ It resists change, requires work input.
❌ Induction only by motion → Wrong. ✔️ Any change in flux (field strength, orientation, area) can cause induction.
🟢 Summary (~300 words)
Electromagnetic induction is the phenomenon of emf generation when magnetic flux changes through a circuit.
Flux: Φ = BA cosθ
Faraday’s Laws: Induced emf ∝ rate of change of flux; e = – dΦ/dt
Lenz’s Law: Direction opposes flux change → energy conservation.
Motional emf: e = Bℓv when conductor moves.
AC Generator: emf = NBAω sin(ωt).
Transformer: V₂/V₁ = N₂/N₁, works on mutual induction.
Eddy currents: Circular induced currents in bulk conductors → heating/damping.
Self-induction: e = –L dI/dt, with L as inductance.
Mutual induction: e₂ = –M dI₁/dt.
Energy in inductor: U = ½ L I², energy stored in field.
Applications:
Generators, transformers, induction cookers, brakes, wireless charging.
Every electric grid is built on electromagnetic induction.
💡 Core Idea: emf is induced only when flux changes — not by static fields.
📝 Quick Recap
✔️ Φ = BA cosθ
✔️ e = – dΦ/dt
✔️ Lenz’s law = opposition (energy conserved)
✔️ Motional emf = Bℓv
✔️ Generator emf = NBAω sin(ωt)
✔️ Transformer ratio = N₂/N₁
✔️ Self-induction = –L dI/dt
✔️ Mutual induction = –M dI/dt
✔️ Energy in inductor = ½ L I²
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QUESTIONS FROM TEXTBOOK
Question 6.1
Predict the direction of induced current in the situations described by the following Figs. 6.15 (a) to (f).
Answer
➡️ Apply Lenz’s Law: induced current opposes the change in flux.
(a) Magnet moves towards solenoid: Induced current opposes approach, so current flows anticlockwise (viewed from magnet side).
(b) Magnet moves away from solenoid: Induced current attracts magnet, so current flows clockwise (viewed from magnet side).
(c) Key just closed: Current in primary increases, flux increases through secondary, induced current opposes increase. If primary current is anticlockwise, induced is clockwise.
(d) Rheostat setting changed → current in primary changes. If resistance decreases (I increases), induced current in secondary opposes increase (opposite sense to primary). If resistance increases (I decreases), induced current supports primary’s direction.
(e) Key just released: Primary current falls, flux decreases. Induced current in secondary tries to support it (same direction as primary’s earlier current).
(f) Current in circular coil decreases steadily: Induced current supports existing current direction (so as to maintain flux).
Question 6.2
Use Lenz’s law to determine the direction of induced current in the situations described by Fig. 6.16:
(a) A wire of irregular shape turning into a circular shape.
(b) A circular loop being deformed into a narrow straight wire.
Answer
(a) When irregular loop reshapes into circle, magnetic flux enclosed increases (area increases). To oppose increase, induced current must produce opposite magnetic field. Hence, direction is such that it produces a field opposite to external.
(b) When circular loop is stretched into straight wire, area decreases. Flux decreases. Induced current will flow so as to support the lost flux (i.e., in such a direction that it maintains same magnetic field as before).
Question 6.3
A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Answer
➡️ Data:
Turns per cm = 15 → n = 1500 turns/m.
Area = 2.0 cm² = 2.0 × 10⁻⁴ m².
Change in current ΔI = 2 A.
Time Δt = 0.1 s.
✏️ Field inside solenoid: B = μ₀ n I.
Change in flux = A ΔB = A μ₀ n ΔI.
Induced emf = (ΔΦ/Δt).
= (2.0 × 10⁻⁴ × 4π × 10⁻⁷ × 1500 × 2) / 0.1
= (2.0 × 10⁻⁴ × 3.77 × 10⁻³) / 0.1
≈ 7.5 × 10⁻⁶ V.
✔️ emf = 7.5 μV (microvolt).
Question 6.4
A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s⁻¹ in a direction normal to the (a) longer side; (b) shorter side of the loop? For how long does the induced voltage last in each case?
Answer
➡️ Data:
Sides: 8 cm = 0.08 m, 2 cm = 0.02 m.
B = 0.3 T, v = 0.01 m/s.
(a) If velocity normal to longer side → effective length = 0.08 m.
emf = Bℓv = 0.3 × 0.08 × 0.01 = 2.4 × 10⁻⁴ V.
Time for leaving = shorter side/v = 0.02 / 0.01 = 2 s.
(b) If velocity normal to shorter side → effective length = 0.02 m.
emf = 0.3 × 0.02 × 0.01 = 6 × 10⁻⁵ V.
Time = longer side/v = 0.08 / 0.01 = 8 s.
✔️ Answers:
(a) emf = 2.4 × 10⁻⁴ V, lasts 2 s.
(b) emf = 6 × 10⁻⁵ V, lasts 8 s.
Question 6.5
A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
Answer
➡️ Data: ℓ = 1 m, ω = 400 rad/s, B = 0.5 T.
✏️ Formula for rotational emf:
e = ½ B ω ℓ²
= 0.5 × 0.5 × 400 × 1²
= 100 V.
✔️ emf = 100 V.
Question 6.6
A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s⁻¹, at right angles to the horizontal component of the Earth’s magnetic field 0.3 × 10⁻⁴ Wb m⁻².
(a) What is the instantaneous value of the emf induced in the wire?
(b) Which end of the wire is at the higher electrical potential?
Answer
➡️ Data: ℓ = 10 m, v = 5 m/s, B = 0.3 × 10⁻⁴ T.
✏️ emf = B ℓ v
= (0.3 × 10⁻⁴) × 10 × 5
= 1.5 × 10⁻³ V.
(a) emf = 1.5 mV.
(b) Direction: Use Fleming’s right-hand rule. For east–west wire falling, induced emf makes east end at higher potential.
✔️ Answers: emf = 1.5 mV, east end higher potential.
Question 6.7
Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V is induced, give an estimate of the self-inductance of the circuit.
Answer
➡️ Formula: e = L (ΔI/Δt).
Given e = 200 V, ΔI = 5 A, Δt = 0.1 s.
L = e Δt / ΔI = 200 × 0.1 / 5 = 4 H.
✔️ Self-inductance = 4 Henry.
Question 6.8
A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.5 s, what is the change of flux linkage with the other coil?
Answer
➡️ Formula: Φ₂ = M I₁.
M = 1.5 H, I₁ = 10 A.
Change in flux linkage = M ΔI = 1.5 × 10 = 15 Wb-turns.
✔️ Flux linkage change = 15 Wb-turns.
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OTHER IMPORTANT QUESTIONS
(CBSE MODEL QUESTIONS PAPER)
ESPECIALLY MADE FROM THIS LESSON ONLY
Section A (MCQs: Q1–Q18)
Question 1
The unit of magnetic flux is:
🔵 (A) Weber
🟢 (B) Tesla
🟠 (C) Gauss
🔴 (D) Ampere-turn
Answer: (A) Weber ✔️ (1 Weber = 1 Tesla·m²).
Question 2
Faraday’s second law of electromagnetic induction states that:
🔵 (A) emf is equal to magnetic flux
🟢 (B) emf is proportional to the rate of change of flux
🟠 (C) emf is constant for a coil
🔴 (D) emf is independent of flux
Answer: (B) emf ∝ dΦ/dt.
Question 3
Lenz’s law ensures conservation of:
🔵 (A) Momentum
🟢 (B) Energy
🟠 (C) Mass
🔴 (D) Flux
Answer: (B) Energy ✔️ Induced current resists flux change.
Question 4
Motional emf in a conductor of length ℓ moving with velocity v in magnetic field B is:
🔵 (A) e = Bv/ℓ
🟢 (B) e = Bℓv
🟠 (C) e = B/v
🔴 (D) e = ℓ/v
Answer: (B) e = Bℓv.
Question 5
Which phenomenon is used in AC generator?
🔵 (A) Self-induction
🟢 (B) Mutual induction
🟠 (C) Electromagnetic induction
🔴 (D) Eddy currents
Answer: (C) Electromagnetic induction.
Question 6
The SI unit of inductance is:
🔵 (A) Tesla
🟢 (B) Henry
🟠 (C) Weber
🔴 (D) Joule
Answer: (B) Henry (H).
Question 7
Which law gives the direction of induced emf?
🔵 (A) Ampere’s law
🟢 (B) Fleming’s right-hand rule
🟠 (C) Lenz’s law
🔴 (D) Biot-Savart law
Answer: (C) Lenz’s law.
Question 8
Energy stored in an inductor carrying current I is:
🔵 (A) LI
🟢 (B) ½ LI²
🟠 (C) I²/L
🔴 (D) L/I²
Answer: (B) ½ LI².
Question 9
Which current is produced in bulk metallic plates in varying field?
🔵 (A) Displacement current
🟢 (B) Eddy current
🟠 (C) Induced current
🔴 (D) Leakage current
Answer: (B) Eddy current.
Question 10
The direction of induced emf can be found using:
🔵 (A) Fleming’s left-hand rule
🟢 (B) Fleming’s right-hand rule
🟠 (C) Ampere’s rule
🔴 (D) Coulomb’s law
Answer: (B) Fleming’s right-hand rule.
Question 11
For a transformer: V₂/V₁ = ?
🔵 (A) N₂/N₁
🟢 (B) N₁/N₂
🟠 (C) √N₂/N₁
🔴 (D) V₁/N₁
Answer: (A) V₂/V₁ = N₂/N₁.
Question 12
Self-inductance is defined as:
🔵 (A) Flux per unit current
🟢 (B) Current per unit flux
🟠 (C) emf per unit resistance
🔴 (D) Flux per unit charge
Answer: (A) Flux linkage per unit current.
Question 13
Induced emf in coil depends on:
🔵 (A) Area of coil
🟢 (B) Number of turns
🟠 (C) Rate of change of flux
🔴 (D) All of these
Answer: (D) All of these.
Question 14
In eddy current damping, induced current:
🔵 (A) Supports motion
🟢 (B) Opposes motion
🟠 (C) Accelerates motion
🔴 (D) None
Answer: (B) Opposes motion.
Question 15
If current in a coil changes at 1 A/s and emf induced is 2 V, self-inductance is:
🔵 (A) 0.5 H
🟢 (B) 1 H
🟠 (C) 2 H
🔴 (D) 4 H
Answer: (C) 2 H (since e = L dI/dt).
Question 16
Which of these uses electromagnetic induction?
🔵 (A) Generator
🟢 (B) Transformer
🟠 (C) Induction cooker
🔴 (D) All of these
Answer: (D) All of these.
Question 17
Magnetic energy density in an inductor is:
🔵 (A) B²/2μ₀
🟢 (B) μ₀B²
🟠 (C) B²/μ₀
🔴 (D) μ₀/2B²
Answer: (A) B²/2μ₀.
Question 18
If mutual inductance between coils is M, emf induced in secondary =
🔵 (A) MI
🟢 (B) M dI/dt
🟠 (C) –M dI/dt
🔴 (D) –MI
Answer: (C) –M dI/dt.
Section B (Short Answer: Q19–Q23)
Question 19
State Faraday’s laws of electromagnetic induction.
Answer
✔️ First Law: Whenever magnetic flux linked with a circuit changes, an emf is induced in the circuit.
✔️ Second Law: The magnitude of induced emf is proportional to the rate of change of flux. Mathematically, e = – dΦ/dt.
Question 20
State Lenz’s law and its significance.
Answer
✏️ Lenz’s Law: The direction of induced current is always such that it opposes the cause of its production.
💡 Significance: Prevents violation of conservation of energy. If induced current aided the flux change, energy would be created freely, which is impossible.
Question 21
What is self-induction?
Answer
✔️ Phenomenon where changing current in a coil induces emf in the same coil.
Formula: e = –L dI/dt.
💡 L (inductance) is a measure of coil’s ability to oppose current change, analogous to inertia.
Question 22
What are eddy currents? Mention two uses.
Answer
✔️ Eddy currents are circulating induced currents in bulk metallic bodies when exposed to changing magnetic flux.
Uses:
In galvanometers to provide electromagnetic damping (needle comes to rest quickly).
In electromagnetic brakes of trains, where induced currents oppose wheel motion.
Question 23
What is energy stored in an inductor? Derive expression.
Answer
emf across inductor: e = L dI/dt.
Work done in small time: dW = e I dt = L I dI.
Total work W = ∫₀ᴵ L I dI = ½ L I².
✔️ Thus, energy stored = ½ L I².
Section C (Mid-length: Q24–Q28)
Question 24
A solenoid of 1000 turns/m carries current of 2 A. Find B inside solenoid.
Answer
B = μ₀ n I = 4π × 10⁻⁷ × 1000 × 2 = 2.51 × 10⁻³ T.
Question 25
Explain working of AC generator with expression for emf.
Answer
Rectangular coil of N turns, area A, rotated in B with angular velocity ω.
Magnetic flux: Φ = NBA cos(ωt).
Induced emf: e = – dΦ/dt = NBAω sin(ωt).
✔️ Peak emf = NBAω.
💡 Basis of electricity generation worldwide.
Question 26
A rod of length 0.5 m moves at 2 m/s perpendicular to B = 0.2 T. Find emf.
Answer
e = Bℓv = 0.2 × 0.5 × 2 = 0.2 V.
Question 27
Derive expression for energy density in inductor.
Answer
Energy stored in coil: U = ½ L I².
Magnetic field inside solenoid: B = μ₀ n I.
Energy per unit volume: u = U/volume = B²/2μ₀.
Question 28
State principle of transformer.
Answer
Works on mutual induction. AC in primary → varying flux → linked with secondary → emf induced.
Relation: V₂/V₁ = N₂/N₁.
Section D (Long Answer: Q29–Q31)
Question 29
Derive expression for motional emf.
Answer
Conductor of length ℓ moves with velocity v in field B.
Force on charge q: F = q(v × B).
Charges accumulate at ends → potential difference.
emf = Bℓv (maximum when v ⊥ B).
✔️ General case: e = Bℓv sinθ.
💡 This derivation directly explains operation of sliding conductor, rail–guns, and many measuring instruments.
Question 30
Explain transformer working with construction and principle.
Answer
Consists of two coils (primary, secondary) wound on soft iron core.
Primary connected to AC source → produces alternating flux in core.
This varying flux links secondary, inducing emf: V₂/V₁ = N₂/N₁.
If N₂ > N₁ → step-up; if N₂ < N₁ → step-down.
✔️ Used for power transmission with minimal loss.
💡 Efficiency is very high (~95–98%) in practical transformers due to laminated cores reducing eddy current losses.
Question 31
Explain eddy currents, their disadvantages and applications.
Answer
Eddy currents are induced circulating currents in bulk metals when exposed to changing flux.
They cause heating → energy loss (disadvantage in transformers, motors).
To reduce: cores laminated to minimize current paths.
Applications:
✔️ Eddy current damping in galvanometers (needle comes to rest quickly).
✔️ Magnetic brakes in trains (eddy currents oppose wheel motion).
✔️ Induction heating in furnaces.
✔️ Speedometers in vehicles (eddy currents oppose rotating disc).
Section E (Case/Application: Q32–Q33)
Question 32
A metallic rod moves with velocity 5 m/s in field B = 0.1 T, length 0.2 m. Resistance = 2 Ω. Find emf and induced current.
Answer
emf = Bℓv = 0.1 × 0.2 × 5 = 0.1 V.
Current = e/R = 0.1 / 2 = 0.05 A.
Question 33
A coil of inductance 2 H carries current 5 A. Current reduced to zero in 0.1 s. Find emf and energy lost.
Answer
emf = L ΔI/Δt = 2 × 5 / 0.1 = 100 V.
Energy lost = ½ LI² = ½ × 2 × 25 = 25 J.
💡 The energy stored in coil’s magnetic field is released as heat in resistance during decay of current.
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NEET QUESTIONS FROM THIS LESSON
Question 1: An ideal transformer has 500 turns in primary and 5000 turns in secondary. If primary is connected to 220 V AC supply, secondary voltage is
🔵 (A) 22 V
🟢 (B) 220 V
🟠 (C) 2200 V
🔴 (D) 110 V
Answer: (C) 2200 V
Year: 2025
Question 2: Eddy currents are produced when
🔵 (A) a conductor is placed in changing magnetic field
🟢 (B) a current is passed through a conductor
🟠 (C) a conductor moves in uniform magnetic field
🔴 (D) a conductor has constant flux linked
Answer: (A) a conductor is placed in changing magnetic field
Year: 2025
Question 3: A coil of 100 turns and area 0.1 m² rotates in a magnetic field B = 0.5 T at frequency 50 Hz. Maximum emf induced is
🔵 (A) 1570 V
🟢 (B) 785 V
🟠 (C) 314 V
🔴 (D) 628 V
Answer: (A) 1570 V
Year: 2024
Question 4: The unit of self inductance is
🔵 (A) Tesla
🟢 (B) Henry
🟠 (C) Weber
🔴 (D) Joule
Answer: (B) Henry
Year: 2024
Question 5: Lenz’s law is in accordance with
🔵 (A) conservation of charge
🟢 (B) conservation of momentum
🟠 (C) conservation of energy
🔴 (D) conservation of mass
Answer: (C) conservation of energy
Year: 2024
Question 6: A transformer is used to light a lamp of 12 V supply from 220 V mains. The ratio of turns Np:Ns is
🔵 (A) 1:20
🟢 (B) 20:1
🟠 (C) 220:12
🔴 (D) 12:220
Answer: (B) 20:1
Year: 2024
Question 7: The self inductance of a solenoid increases if
🔵 (A) number of turns decreases
🟢 (B) area decreases
🟠 (C) length decreases
🔴 (D) core of steel is used
Answer: (C) length decreases
Year: 2023
Question 8: The current induced in a coil is maximum when
🔵 (A) flux changes slowly
🟢 (B) flux changes rapidly
🟠 (C) flux is constant
🔴 (D) flux decreases to zero
Answer: (B) flux changes rapidly
Year: 2023
Question 9: A straight conductor of length L is moved with velocity v perpendicular to magnetic field B. Induced emf is
🔵 (A) BLv
🟢 (B) B/vL
🟠 (C) B/Lv
🔴 (D) v/LB
Answer: (A) BLv
Year: 2023
Question 10: Two coils are wound on the same iron core. If one coil is connected to AC source, emf will be induced in the other coil due to
🔵 (A) self induction
🟢 (B) mutual induction
🟠 (C) resonance
🔴 (D) capacitance
Answer: (B) mutual induction
Year: 2023
Question 11: The direction of induced emf is given by
🔵 (A) Fleming’s left hand rule
🟢 (B) Fleming’s right hand rule
🟠 (C) Lenz’s law
🔴 (D) Right-hand thumb rule
Answer: (C) Lenz’s law
Year: 2022
Question 12: The energy stored in an inductor is
🔵 (A) ½ LI²
🟢 (B) ½ L²I
🟠 (C) ½ I²/L
🔴 (D) LI
Answer: (A) ½ LI²
Year: 2022
Question 13: The emf induced in a coil of N turns due to change of flux ΔΦ in time Δt is
🔵 (A) NΔΦ/Δt
🟢 (B) ΔΦ/NΔt
🟠 (C) Δt/NΔΦ
🔴 (D) NΔt/ΔΦ
Answer: (A) NΔΦ/Δt
Year: 2022
Question 14: A 220 V input is supplied to transformer primary having 50 turns. Secondary has 500 turns. Output voltage is
🔵 (A) 22 V
🟢 (B) 220 V
🟠 (C) 2200 V
🔴 (D) 110 V
Answer: (C) 2200 V
Year: 2022
Question 15: In a transformer, power is lost due to
🔵 (A) Eddy currents
🟢 (B) Hysteresis
🟠 (C) Copper loss
🔴 (D) All of these
Answer: (D) All of these
Year: 2021
Question 16: The unit of magnetic flux is
🔵 (A) Weber
🟢 (B) Tesla
🟠 (C) Gauss
🔴 (D) Henry
Answer: (A) Weber
Year: 2021
Question 17: An induced emf is produced when a conductor cuts
🔵 (A) electric field lines
🟢 (B) magnetic field lines
🟠 (C) equipotential lines
🔴 (D) current lines
Answer: (B) magnetic field lines
Year: 2021
Question 18: The self inductance of a long solenoid does not depend on
🔵 (A) area
🟢 (B) number of turns
🟠 (C) current flowing
🔴 (D) length
Answer: (C) current flowing
Year: 2021
Question 19: Faraday’s laws are consequence of conservation of
🔵 (A) charge
🟢 (B) energy
🟠 (C) linear momentum
🔴 (D) angular momentum
Answer: (B) energy
Year: 2020
Question 20: A current of 2 A is switched off through a coil of self-inductance 0.5 H in 0.1 s. The emf induced is
🔵 (A) 5 V
🟢 (B) 10 V
🟠 (C) 2 V
🔴 (D) 1 V
Answer: (B) 10 V
Year: 2020
Question 21: Which device is based on the principle of mutual induction?
🔵 (A) Generator
🟢 (B) Transformer
🟠 (C) Galvanometer
🔴 (D) Inductor
Answer: (B) Transformer
Year: 2020
Question 22: The core used in a transformer is laminated to reduce
🔵 (A) resistance
🟢 (B) hysteresis loss
🟠 (C) eddy current loss
🔴 (D) flux leakage
Answer: (C) eddy current loss
Year: 2019
Question 23: A coil of inductance 2 H is carrying a current of 1 A. Energy stored is
🔵 (A) 2 J
🟢 (B) 1 J
🟠 (C) 0.5 J
🔴 (D) 4 J
Answer: (B) 1 J
Year: 2019
Question 24: A DC current is passed through a coil. The emf induced is
🔵 (A) constant
🟢 (B) zero
🟠 (C) infinite
🔴 (D) alternating
Answer: (B) zero
Year: 2019
Question 25: The phenomenon of self induction is similar to
🔵 (A) inertia
🟢 (B) momentum
🟠 (C) charge
🔴 (D) work
Answer: (A) inertia
Year: 2019
Question 26: A metal rod of length l rotates with angular velocity ω in a magnetic field B perpendicular to the plane of rotation. Induced emf is
🔵 (A) Blω
🟢 (B) ½ Bl²ω
🟠 (C) Bω/l
🔴 (D) zero
Answer: (B) ½ Bl²ω
Year: 2018
Question 27: In a coil, the current changes from 2 A to zero in 0.05 s. If induced emf is 200 V, self-inductance of coil is
🔵 (A) 2.5 H
🟢 (B) 5 H
🟠 (C) 10 H
🔴 (D) 20 H
Answer: (C) 10 H
Year: 2018
Question 28: An inductor opposes change of
🔵 (A) charge
🟢 (B) current
🟠 (C) voltage
🔴 (D) resistance
Answer: (B) current
Year: 2018
Question 29: Lenz’s law gives
🔵 (A) direction of induced emf
🟢 (B) magnitude of induced emf
🟠 (C) both
🔴 (D) neither
Answer: (A) direction of induced emf
Year: 2017
Question 30: Which of the following is not an application of eddy currents?
🔵 (A) Induction furnace
🟢 (B) Electric brakes in trains
🟠 (C) Dead-beat galvanometer
🔴 (D) Dynamo
Answer: (D) Dynamo
Year: 2017
Question 31: If number of turns of coil is doubled, self inductance becomes
🔵 (A) four times
🟢 (B) half
🟠 (C) double
🔴 (D) one-fourth
Answer: (A) four times
Year: 2017
Question 32: A generator works on principle of
🔵 (A) electrostatics
🟢 (B) electromagnetic induction
🟠 (C) thermoelectric effect
🔴 (D) photoelectric effect
Answer: (B) electromagnetic induction
Year: 2016
Question 33: The induced emf in a coil of resistance R due to change of flux Φ is dissipated as
🔵 (A) heat (I²R)
🟢 (B) work function
🟠 (C) stored potential
🔴 (D) acceleration energy
Answer: (A) heat (I²R)
Year: 2016
Question 34: A 44/220 V transformer is used for a 200 W lamp. Current in secondary is
🔵 (A) 0.2 A
🟢 (B) 0.9 A
🟠 (C) 1 A
🔴 (D) 4.5 A
Answer: (C) 1 A
Year: 2016
Question 35: The mutual inductance between two coils depends on
🔵 (A) geometry of coils and separation
🟢 (B) resistance of coils
🟠 (C) current in coils
🔴 (D) potential across coils
Answer: (A) geometry of coils and separation
Year: 2015
Question 36: In an AC generator, induced emf is given by
🔵 (A) NABω sin ωt
🟢 (B) NABω cos ωt
🟠 (C) NAB sin ωt
🔴 (D) NAB cos ωt
Answer: (A) NABω sin ωt
Year: 2015
Question 37: When a coil rotates in a uniform magnetic field, induced emf is maximum when the plane of coil is
🔵 (A) parallel to field
🟢 (B) perpendicular to field
🟠 (C) at 45°
🔴 (D) at 60°
Answer: (A) parallel to field
Year: 2015
Question 38: The self-inductance of a coil having N turns, area A, and length l is proportional to
🔵 (A) N²A/l
🟢 (B) NA/l
🟠 (C) N/l
🔴 (D) N²/lA
Answer: (A) N²A/l
Year: 2014
Question 39: An ideal transformer has primary to secondary turns ratio 2:1. If power output is 100 W at 10 A, input current is
🔵 (A) 5 A
🟢 (B) 10 A
🟠 (C) 20 A
🔴 (D) 50 A
Answer: (A) 5 A
Year: 2014
Question 40: The emf induced in a coil of resistance R carrying current i is given by
🔵 (A) L di/dt
🟢 (B) Ri
🟠 (C) Li
🔴 (D) L/i
Answer: (A) L di/dt
Year: 2013
Question 41: The efficiency of an ideal transformer is
🔵 (A) 0%
🟢 (B) 50%
🟠 (C) 100%
🔴 (D) 75%
Answer: (C) 100%
Year: 2013
Question 42: Which device does not work on electromagnetic induction?
🔵 (A) AC generator
🟢 (B) Transformer
🟠 (C) Moving coil galvanometer
🔴 (D) Induction motor
Answer: (C) Moving coil galvanometer
Year: 2012
Question 43: An emf of 2 V is induced when current in a coil changes at rate of 0.01 A/s. Self inductance is
🔵 (A) 100 H
🟢 (B) 200 H
🟠 (C) 400 H
🔴 (D) 600 H
Answer: (A) 200 H
Year: 2012
Question 44: The induced emf is not affected by
🔵 (A) number of turns
🟢 (B) rate of change of flux
🟠 (C) area of coil
🔴 (D) resistance of coil
Answer: (D) resistance of coil
Year: 2011
Question 45: The working of induction furnace is based on
🔵 (A) Joule’s heating
🟢 (B) Faraday’s law
🟠 (C) Coulomb’s law
🔴 (D) Kirchhoff’s law
Answer: (B) Faraday’s law
Year: 2010
Question 46: The unit of inductance is equivalent to
🔵 (A) Weber/Ampere
🟢 (B) Joule/Weber
🟠 (C) Tesla/Ampere
🔴 (D) Weber/second
Answer: (A) Weber/Ampere
Year: 2009
Question 47: The induced current produced in a coil always flows in such direction that it opposes
🔵 (A) applied voltage
🟢 (B) change in flux
🟠 (C) current
🔴 (D) resistance
Answer: (B) change in flux
Year: 2008
Question 48: Which device uses eddy currents to work?
🔵 (A) Transformer
🟢 (B) Induction motor
🟠 (C) Ballistic galvanometer
🔴 (D) Electric stove
Answer: (B) Induction motor
Year: 2007
Question 49: The unit of mutual inductance is
🔵 (A) Weber
🟢 (B) Henry
🟠 (C) Tesla
🔴 (D) Joule
Answer: (B) Henry
Year: 2006
Question 50: The relation between flux linkage and current in a coil is
🔵 (A) Φ = LI
🟢 (B) Φ = L/I
🟠 (C) Φ = I/L
🔴 (D) Φ = IL²
Answer: (A) Φ = LI
Year: 2005
————————————————————————————————————————————————————————————————————————————
JEE MAINS QUESTIONS FROM THIS LESSON
Part 1 (Q1–Q25)
Question 1: A conducting ring of radius r is placed in a magnetic field B perpendicular to its plane. If B changes with time at rate dB/dt, the induced emf is
🔵 (A) πr² dB/dt
🟢 (B) 2πr dB/dt
🟠 (C) r dB/dt
🔴 (D) zero
Answer: (A) πr² dB/dt
Year: 2025 | Shift 1
Question 2: Lenz’s law is in accordance with the law of conservation of
🔵 (A) charge
🟢 (B) energy
🟠 (C) momentum
🔴 (D) angular momentum
Answer: (B) energy
Year: 2025 | Shift 2
Question 3: A solenoid of length L, cross-sectional area A, and N turns carries current I. Its self-inductance is
🔵 (A) μ₀N²A/L
🟢 (B) μ₀NA/L
🟠 (C) μ₀N²AL
🔴 (D) μ₀NL/A
Answer: (A) μ₀N²A/L
Year: 2024 | Shift 1
Question 4: A current is induced in a coil due to
🔵 (A) electric flux change
🟢 (B) magnetic flux change
🟠 (C) area of coil change
🔴 (D) constant flux
Answer: (B) magnetic flux change
Year: 2024 | Shift 2
Question 5: The induced emf in a coil is zero when
🔵 (A) coil moves parallel to B
🟢 (B) coil moves perpendicular to B
🟠 (C) coil rotates in B
🔴 (D) flux linked changes
Answer: (A) coil moves parallel to B
Year: 2023 | Jan Shift 1
Question 6: The SI unit of inductance is
🔵 (A) Henry
🟢 (B) Weber
🟠 (C) Tesla
🔴 (D) Joule
Answer: (A) Henry
Year: 2023 | Apr Shift 2
Question 7: An emf of 2 V is induced in a coil when current changes at rate of 0.1 A/s. Its self-inductance is
🔵 (A) 2 H
🟢 (B) 10 H
🟠 (C) 20 H
🔴 (D) 0.2 H
Answer: (B) 20 H
Year: 2023 | Apr Shift 1
Question 8: A coil of N turns, area A, is rotated with angular velocity ω in a uniform magnetic field B. Maximum emf induced is
🔵 (A) BANω
🟢 (B) BAω
🟠 (C) BNA
🔴 (D) 2BAN
Answer: (A) BANω
Year: 2022 | Jun Shift 1
Question 9: The average emf induced in a coil rotating in magnetic field is
🔵 (A) 2fNAB
🟢 (B) NABω
🟠 (C) 2BANω
🔴 (D) BAN
Answer: (A) 2fNAB
Year: 2022 | Jul Shift 2
Question 10: The induced emf is not affected by
🔵 (A) speed of coil
🟢 (B) magnetic field strength
🟠 (C) resistance of coil
🔴 (D) number of turns
Answer: (C) resistance of coil
Year: 2022 | Jun Shift 2
Question 11: In an AC generator, maximum emf is
🔵 (A) NABω
🟢 (B) NAB/ω
🟠 (C) BA/ω
🔴 (D) BAN
Answer: (A) NABω
Year: 2021 | Mar Shift 1
Question 12: The direction of induced current in a coil is given by
🔵 (A) Coulomb’s law
🟢 (B) Ampere’s law
🟠 (C) Lenz’s law
🔴 (D) Gauss law
Answer: (C) Lenz’s law
Year: 2021 | Feb Shift 2
Question 13: A solenoid is connected to a battery through a switch. When switch is closed, emf is induced in
🔵 (A) solenoid only
🟢 (B) nearby coil only
🟠 (C) both solenoid and nearby coil
🔴 (D) neither
Answer: (C) both solenoid and nearby coil
Year: 2021 | Mar Shift 2
Question 14: The coefficient of mutual induction depends on
🔵 (A) number of turns only
🟢 (B) geometry of coils and medium
🟠 (C) current in coils
🔴 (D) emf induced
Answer: (B) geometry of coils and medium
Year: 2020 | Jan Shift 1
Question 15: The induced emf is directly proportional to
🔵 (A) flux
🟢 (B) time
🟠 (C) rate of change of flux
🔴 (D) resistance
Answer: (C) rate of change of flux
Year: 2020 | Sept Shift 2
Question 16: The eddy currents are produced when
🔵 (A) conductor is kept in varying magnetic field
🟢 (B) conductor is stationary in constant magnetic field
🟠 (C) charge flows in closed path
🔴 (D) current flows in resistance
Answer: (A) conductor is kept in varying magnetic field
Year: 2020 | Jan Shift 2
Question 17: The self-inductance of a long solenoid is proportional to
🔵 (A) l
🟢 (B) 1/l
🟠 (C) l²
🔴 (D) √l
Answer: (A) l
Year: 2019 | Apr Shift 1
Question 18: A metallic rod moves perpendicular to magnetic field B with velocity v. The emf induced is
🔵 (A) Blv
🟢 (B) Bv/l
🟠 (C) v/Bl
🔴 (D) B²lv
Answer: (A) Blv
Year: 2019 | Jan Shift 2
Question 19: The induced emf in a coil rotating in uniform magnetic field is maximum when angle between normal to coil and field is
🔵 (A) 0°
🟢 (B) 45°
🟠 (C) 90°
🔴 (D) 180°
Answer: (C) 90°
Year: 2019 | Jan Shift 1
Question 20: Power loss due to eddy current can be reduced by using
🔵 (A) laminated core
🟢 (B) thick conductor
🟠 (C) high resistivity material
🔴 (D) both A and C
Answer: (D) both A and C
Year: 2018
Question 21: The time constant of an LR circuit is
🔵 (A) L/R
🟢 (B) R/L
🟠 (C) 1/√(LR)
🔴 (D) √(L/R)
Answer: (A) L/R
Year: 2018
Question 22: An inductor of inductance L and resistance R is connected to a battery. The current after time t is
🔵 (A) (E/R)(1 − e^(−Rt/L))
🟢 (B) (E/R)e^(−Rt/L)
🟠 (C) (E/L)(1 − e^(−t))
🔴 (D) Ee^(−t/L)
Answer: (A) (E/R)(1 − e^(−Rt/L))
Year: 2018
Question 23: The self-inductance of a coil is 1 H. Current through it increases uniformly from 0 to 2 A in 4 s. The emf induced is
🔵 (A) 0.25 V
🟢 (B) 0.5 V
🟠 (C) 1 V
🔴 (D) 2 V
Answer: (B) 0.5 V
Year: 2017
Question 24: A coil of inductance 0.5 H carries current 2 A. The energy stored is
🔵 (A) 1 J
🟢 (B) 2 J
🟠 (C) 0.5 J
🔴 (D) 4 J
Answer: (A) 1 J
Year: 2017
Question 25: When a magnet is pushed into a coil, induced current is such that it opposes motion. This is consequence of
🔵 (A) Gauss law
🟢 (B) Ampere’s law
🟠 (C) Lenz’s law
🔴 (D) Coulomb’s law
Answer: (C) Lenz’s law
Year: 2017
Question 26: The emf induced in the secondary coil of a transformer depends on
🔵 (A) current in primary
🟢 (B) turns ratio
🟠 (C) resistance of coil
🔴 (D) insulation
Answer: (B) turns ratio
Year: 2017
Question 27: The unit of magnetic flux is
🔵 (A) Weber
🟢 (B) Tesla
🟠 (C) Henry
🔴 (D) Joule
Answer: (A) Weber
Year: 2016
Question 28: An alternating emf E = E₀ sin ωt is induced in a coil. The maximum value of induced emf is
🔵 (A) E₀
🟢 (B) ωE₀
🟠 (C) E₀/ω
🔴 (D) zero
Answer: (A) E₀
Year: 2016
Question 29: A conductor of length l is moving with velocity v perpendicular to magnetic field B. Induced emf = ?
🔵 (A) Blv
🟢 (B) B/vl
🟠 (C) v/Bl
🔴 (D) B²lv
Answer: (A) Blv
Year: 2016
Question 30: The energy stored in an inductor of inductance L carrying current I is
🔵 (A) ½ LI²
🟢 (B) L²I
🟠 (C) LI²
🔴 (D) ½ L²I²
Answer: (A) ½ LI²
Year: 2015
Question 31: The phenomenon of production of emf in a conductor due to change of magnetic flux is
🔵 (A) Electromagnetic induction
🟢 (B) Electrostatics
🟠 (C) Magnetostatics
🔴 (D) Current electricity
Answer: (A) Electromagnetic induction
Year: 2015
Question 32: The direction of induced emf is given by
🔵 (A) Ampere’s law
🟢 (B) Faraday’s law
🟠 (C) Lenz’s law
🔴 (D) Gauss law
Answer: (C) Lenz’s law
Year: 2015
Question 33: The time constant of LR circuit is
🔵 (A) L/R
🟢 (B) R/L
🟠 (C) 1/LR
🔴 (D) √(L/R)
Answer: (A) L/R
Year: 2014
Question 34: An emf of 200 V is induced in a coil when current falls at rate of 10⁴ A/s. The self-inductance is
🔵 (A) 0.02 H
🟢 (B) 0.2 H
🟠 (C) 2 H
🔴 (D) 20 H
Answer: (A) 0.02 H
Year: 2014
Question 35: The induced emf in coil is proportional to
🔵 (A) flux
🟢 (B) rate of change of flux
🟠 (C) resistance
🔴 (D) area
Answer: (B) rate of change of flux
Year: 2014
Question 36: The current in an inductor changes from 2 A to 6 A in 0.5 s. The emf induced is 40 V. Inductance is
🔵 (A) 2 H
🟢 (B) 5 H
🟠 (C) 10 H
🔴 (D) 20 H
Answer: (B) 5 H
Year: 2013
Question 37: Mutual inductance between two coils depends on
🔵 (A) distance between coils
🟢 (B) relative orientation
🟠 (C) medium
🔴 (D) all of these
Answer: (D) all of these
Year: 2013
Question 38: The induced emf in a straight conductor of length l moving with velocity v in a magnetic field B depends on
🔵 (A) Blv sinθ
🟢 (B) Blv cosθ
🟠 (C) Blv tanθ
🔴 (D) Blv cotθ
Answer: (A) Blv sinθ
Year: 2013
Question 39: A current of 2 A is established in a coil of self-inductance 5 H in 1 s. The emf induced is
🔵 (A) 2.5 V
🟢 (B) 5 V
🟠 (C) 10 V
🔴 (D) 20 V
Answer: (B) 5 V
Year: 2012 (AIEEE)
Question 40: The emf induced in secondary coil of a transformer is
🔵 (A) inversely proportional to turns ratio
🟢 (B) directly proportional to turns ratio
🟠 (C) inversely proportional to current
🔴 (D) directly proportional to resistance
Answer: (B) directly proportional to turns ratio
Year: 2012 (AIEEE)
Question 41: Which of the following devices works on principle of electromagnetic induction?
🔵 (A) Transformer
🟢 (B) Electric motor
🟠 (C) Voltmeter
🔴 (D) Ammeter
Answer: (A) Transformer
Year: 2011 (AIEEE)
Question 42: The self-inductance of a coil of N turns and area A is proportional to
🔵 (A) N²
🟢 (B) A²
🟠 (C) 1/A
🔴 (D) 1/N
Answer: (A) N²
Year: 2011 (AIEEE)
Question 43: An inductor opposes
🔵 (A) change in current
🟢 (B) steady current
🟠 (C) resistance
🔴 (D) emf
Answer: (A) change in current
Year: 2010 (AIEEE)
Question 44: A metal rod of length l moves with velocity v in a magnetic field B perpendicular to both. The emf induced is
🔵 (A) Blv
🟢 (B) Bv/l
🟠 (C) v/Bl
🔴 (D) B²lv
Answer: (A) Blv
Year: 2010 (AIEEE)
Question 45: Which of the following reduces eddy current loss?
🔵 (A) solid iron core
🟢 (B) laminated iron core
🟠 (C) thick conductor
🔴 (D) superconductor
Answer: (B) laminated iron core
Year: 2009 (AIEEE)
Question 46: The induced emf is maximum when angle between plane of coil and magnetic field is
🔵 (A) 0°
🟢 (B) 45°
🟠 (C) 90°
🔴 (D) 180°
Answer: (C) 90°
Year: 2009 (AIEEE)
Question 47: The energy stored in magnetic field of an inductor is
🔵 (A) ½ LI²
🟢 (B) LI²
🟠 (C) L²I
🔴 (D) ½ L²I²
Answer: (A) ½ LI²
Year: 2008 (AIEEE)
Question 48: The phenomenon of electromagnetic induction was discovered by
🔵 (A) Faraday
🟢 (B) Oersted
🟠 (C) Ampere
🔴 (D) Henry
Answer: (A) Faraday
Year: 2008 (AIEEE)
Question 49: The induced emf in coil is given by
🔵 (A) E = −dϕ/dt
🟢 (B) E = −ϕ/dt
🟠 (C) E = dϕ/dt
🔴 (D) E = IdR
Answer: (A) E = −dϕ/dt
Year: 2007 (AIEEE)
Question 50: The direction of eddy currents is given by
🔵 (A) Ampere’s law
🟢 (B) Lenz’s law
🟠 (C) Gauss law
🔴 (D) Coulomb law
Answer: (B) Lenz’s law
Year: 2007 (AIEEE)
————————————————————————————————————————————————————————————————————————————
JEE ADVANCED QUESTIONS FROM THIS LESSON
Paper 1 (Q1–Q17)
Question 1: Faraday’s law of electromagnetic induction states that induced emf is proportional to
🔵 (A) flux
🟢 (B) rate of change of flux
🟠 (C) flux density
🔴 (D) current
Answer: (B) rate of change of flux
Year: 2023 | Paper 1
Question 2: A conducting loop is moved in a uniform magnetic field. The emf induced depends on
🔵 (A) shape of loop
🟢 (B) velocity of loop
🟠 (C) strength of field
🔴 (D) both B and v
Answer: (D) both B and v
Year: 2023 | Paper 1
Question 3: Lenz’s law is a consequence of
🔵 (A) conservation of energy
🟢 (B) conservation of momentum
🟠 (C) conservation of charge
🔴 (D) conservation of flux
Answer: (A) conservation of energy
Year: 2022 | Paper 1
Question 4: The self-inductance of a coil is defined as
🔵 (A) emf/current
🟢 (B) flux/current
🟠 (C) emf/flux
🔴 (D) flux/emf
Answer: (B) flux/current
Year: 2022 | Paper 1
Question 5: An ideal inductor is connected to an AC source. Average power consumed is
🔵 (A) zero
🟢 (B) maximum
🟠 (C) infinite
🔴 (D) finite
Answer: (A) zero
Year: 2021 | Paper 1
Question 6: A metal rod moves in a uniform magnetic field. The induced emf between its ends is proportional to
🔵 (A) velocity
🟢 (B) magnetic field
🟠 (C) length of rod
🔴 (D) all of these
Answer: (D) all of these
Year: 2021 | Paper 1
Question 7: A coil of inductance L and resistance R is connected to a battery. Current at time t is
🔵 (A) (E/R)(1 − e^(−Rt/L))
🟢 (B) (E/R)(e^(−Rt/L))
🟠 (C) (E/L)(1 − e^(−t/RC))
🔴 (D) Ee^(−Rt/L)
Answer: (A) (E/R)(1 − e^(−Rt/L))
Year: 2020 | Paper 1
Question 8: The energy stored in an inductor carrying current I is
🔵 (A) ½LI²
🟢 (B) LI²
🟠 (C) ½I²/L
🔴 (D) I²L²
Answer: (A) ½LI²
Year: 2020 | Paper 1
Question 9: In an AC circuit containing pure inductor, current lags behind voltage by
🔵 (A) 0°
🟢 (B) 90°
🟠 (C) 180°
🔴 (D) 45°
Answer: (B) 90°
Year: 2019 | Paper 1
Question 10: The time constant of an LR circuit is
🔵 (A) R/L
🟢 (B) L/R
🟠 (C) 1/RC
🔴 (D) RC
Answer: (B) L/R
Year: 2019 | Paper 1
Question 11: In any coil, the flux linkage and current are related by
🔵 (A) Φ = LI
🟢 (B) NΦ = LI
🟠 (C) Φ = L/NI
🔴 (D) NΦ = I/L
Answer: (B) NΦ = LI
Year: 2018 | Paper 1
Question 12: The unit of inductance is
🔵 (A) Tesla
🟢 (B) Henry
🟠 (C) Weber
🔴 (D) Joule
Answer: (B) Henry
Year: 2018 | Paper 1
Question 13: A transformer works on principle of
🔵 (A) self-induction
🟢 (B) mutual induction
🟠 (C) resonance
🔴 (D) conduction
Answer: (B) mutual induction
Year: 2017 | Paper 1
Question 14: An eddy current is produced when
🔵 (A) conductor is stationary
🟢 (B) flux linked is constant
🟠 (C) flux linked changes
🔴 (D) resistance is zero
Answer: (C) flux linked changes
Year: 2017 | Paper 1
Question 15: A choke coil is used in AC circuit to
🔵 (A) reduce current
🟢 (B) increase current
🟠 (C) block DC and allow AC
🔴 (D) store energy
Answer: (A) reduce current
Year: 2016 | Paper 1
Question 16: In an LR circuit, current rises to half of steady value in 2 s. The time constant is
🔵 (A) 1 s
🟢 (B) 2 s
🟠 (C) 3 s
🔴 (D) 4 s
Answer: (C) 3 s
Year: 2016 | Paper 1
Question 17: In a generator, maximum emf is induced when coil rotates
🔵 (A) parallel to field
🟢 (B) perpendicular to field
🟠 (C) at 45°
🔴 (D) random
Answer: (B) perpendicular to field
Year: 2015 | Paper 1
Paper 2 (Q18–Q34)
Question 18: Mutual inductance depends on
🔵 (A) geometry
🟢 (B) number of turns
🟠 (C) permeability
🔴 (D) all of these
Answer: (D) all of these
Year: 2023 | Paper 2
Question 19: A coil of inductance 2 H opposes current change from 3 A to 1 A in 0.2 s. Average emf induced is
🔵 (A) 10 V
🟢 (B) 20 V
🟠 (C) 5 V
🔴 (D) 2 V
Answer: (B) 20 V
Year: 2023 | Paper 2
Question 20: For a long solenoid of length ℓ, cross-section area A and N turns, the self-inductance is
🔵 (A) L = μ₀ N A / ℓ
🟢 (B) L = μ₀ N² A / ℓ
🟠 (C) L = μ₀ N² / A
🔴 (D) L = μ₀ A² / ℓ
Answer: (B) L = μ₀ N² A / ℓ
Year: 2022 | Paper 2
Question 21: An AC circuit has R and L in series. At resonance, the current is
🔵 (A) zero
🟢 (B) maximum
🟠 (C) minimum
🔴 (D) none
Answer: (B) maximum
Year: 2022 | Paper 2
Question 22: Induced emf in a coil is not affected by
🔵 (A) resistance of coil
🟢 (B) number of turns
🟠 (C) rate of change of flux
🔴 (D) area of coil
Answer: (A) resistance of coil
Year: 2021 | Paper 2
Question 23: Energy stored in a 10 H inductor carrying 2 A is
🔵 (A) 20 J
🟢 (B) 10 J
🟠 (C) 40 J
🔴 (D) 5 J
Answer: (A) 20 J
Year: 2021 | Paper 2
Question 24: A 100-turn coil of area 0.01 m² rotates in a uniform field 0.1 T with 50 Hz. The maximum emf induced is
🔵 (A) 31.4 V
🟢 (B) 314 V
🟠 (C) 3.14 V
🔴 (D) 3140 V
Answer: (A) 31.4 V
Year: 2020 | Paper 2
Question 25: The emf induced in the secondary of a transformer depends on
🔵 (A) turns ratio
🟢 (B) flux change
🟠 (C) frequency
🔴 (D) all of these
Answer: (D) all of these
Year: 2020 | Paper 2
Question 26: An LR series circuit connected to an AC supply has power factor
🔵 (A) 0
🟢 (B) 1
🟠 (C) R / √(R² + (ωL)²)
🔴 (D) ωL / R
Answer: (C) R / √(R² + (ωL)²)
Year: 2019 | Paper 2
Question 27: Which device primarily exploits eddy currents?
🔵 (A) Induction furnace
🟢 (B) Electric heater
🟠 (C) Transformer
🔴 (D) Motor
Answer: (A) Induction furnace
Year: 2019 | Paper 2
Question 28: The dimensional formula of inductance is
🔵 (A) [ML²T⁻²A⁻²]
🟢 (B) [ML²T⁻²A⁻¹]
🟠 (C) [ML²T⁻³A⁻²]
🔴 (D) [MLT⁻²A⁻²]
Answer: (A) [ML²T⁻²A⁻²]
Year: 2018 | Paper 2
Question 29: In an AC circuit, emf and current are in phase if the circuit has
🔵 (A) pure inductance
🟢 (B) pure resistance
🟠 (C) pure capacitance
🔴 (D) both B and C
Answer: (B) pure resistance
Year: 2018 | Paper 2
Question 30: A straight conductor of length l moving at velocity v in a magnetic field B. Induced emf is
🔵 (A) Blv
🟢 (B) Blv sinθ
🟠 (C) zero
🔴 (D) both A and B
Answer: (B) Blv sinθ
Year: 2017 | Paper 2
Question 31: The unit of power factor is
🔵 (A) watt
🟢 (B) joule
🟠 (C) dimensionless
🔴 (D) volt
Answer: (C) dimensionless
Year: 2017 | Paper 2
Question 32: In a step-up transformer
🔵 (A) Es < Ep 🟢 (B) Ns > Np
🟠 (C) Is > Ip
🔴 (D) Vs < Vp Answer: (B) Ns > Np
Year: 2016 | Paper 2
Question 33: The induced emf in a rotating coil in a uniform magnetic field is maximum when the plane of the coil is
🔵 (A) parallel to B
🟢 (B) perpendicular to B
🟠 (C) at 45°
🔴 (D) any angle
Answer: (A) parallel to B
Year: 2016 | Paper 2
Question 34: An inductor has reactance 100 Ω at 50 Hz. The inductance is
🔵 (A) 0.318 H
🟢 (B) 0.636 H
🟠 (C) 1.59 H
🔴 (D) 3.18 H
Answer: (A) 0.318 H
Year: 2015 | Paper 2
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PRACTICE SETS FROM THIS LESSON
🔵 NEET Level (Q1–Q20)
Q1. A loop of area 0.02 m² is placed in magnetic field 0.5 T. If it is rotated quickly from parallel to perpendicular orientation, the change in flux is:
🔵 (A) 0.01 Wb
🟢 (B) 0.02 Wb
🟠 (C) 0.005 Wb
🔴 (D) 0.0 Wb
Answer: (B) 0.02 Wb
Q2. A coil of 100 turns, area 0.1 m² is placed in uniform B = 0.2 T. If field drops to zero in 0.05 s, average emf is:
🔵 (A) 0.4 V
🟢 (B) 0.2 V
🟠 (C) 0.8 V
🔴 (D) 1 V
Answer: (C) 0.8 V
Q3. Lenz’s law explains which principle?
🔵 (A) Conservation of energy
🟢 (B) Conservation of mass
🟠 (C) Conservation of flux
🔴 (D) Conservation of momentum
Answer: (A) Conservation of energy
Q4. A bar magnet moves towards coil. The induced current in coil will:
🔵 (A) Oppose motion
🟢 (B) Assist motion
🟠 (C) Remain zero
🔴 (D) None
Answer: (A) Oppose motion
Q5. A 0.5 m rod moves at 3 m/s in 0.1 T field perpendicular. emf = ?
🔵 (A) 0.05 V
🟢 (B) 0.1 V
🟠 (C) 0.15 V
🔴 (D) 0.2 V
Answer: (C) 0.15 V
Q6. Which device does not use electromagnetic induction?
🔵 (A) Generator
🟢 (B) Transformer
🟠 (C) Capacitor
🔴 (D) Induction cooker
Answer: (C) Capacitor
Q7. Induced emf depends on:
🔵 (A) Rate of flux change
🟢 (B) Area of loop
🟠 (C) Number of turns
🔴 (D) All of these
Answer: (D) All of these
Q8. A coil has 200 turns, flux per turn = 5 × 10⁻⁴ Wb. Total flux linkage = ?
🔵 (A) 0.01 Wb-turns
🟢 (B) 0.1 Wb-turns
🟠 (C) 0.2 Wb-turns
🔴 (D) 1.0 Wb-turns
Answer: (C) 0.2 Wb-turns
Q9. Energy stored in inductor L = 1 H with I = 2 A = ?
🔵 (A) 1 J
🟢 (B) 2 J
🟠 (C) 4 J
🔴 (D) 0.5 J
Answer: (A) 1 J
Q10. Which one is NOT an application of eddy currents?
🔵 (A) Induction heating
🟢 (B) Magnetic brakes
🟠 (C) Transformer losses
🔴 (D) Capacitor charging
Answer: (D) Capacitor charging
Q11. Direction of induced emf is given by:
🔵 (A) Fleming’s right-hand rule
🟢 (B) Ampere’s law
🟠 (C) Coulomb’s law
🔴 (D) Gauss’s law
Answer: (A) Fleming’s right-hand rule
Q12. A coil of inductance 2 H carries 3 A. Energy stored = ?
🔵 (A) 3 J
🟢 (B) 6 J
🟠 (C) 9 J
🔴 (D) 12 J
Answer: (B) 6 J
Q13. Induced emf is zero when:
🔵 (A) Flux changes
🟢 (B) Flux constant
🟠 (C) Conductor moves perpendicular to field
🔴 (D) Area changes
Answer: (B) Flux constant
Q14. Transformer works on:
🔵 (A) Mutual induction
🟢 (B) Eddy currents
🟠 (C) Self-induction
🔴 (D) None
Answer: (A) Mutual induction
Q15. A 1 H inductor carries current 4 A. Stored energy = ?
🔵 (A) 4 J
🟢 (B) 8 J
🟠 (C) 10 J
🔴 (D) 12 J
Answer: (B) 8 J
Q16. If current increases in coil, induced emf will:
🔵 (A) Oppose increase
🟢 (B) Support increase
🟠 (C) Remain constant
🔴 (D) Be zero
Answer: (A) Oppose increase
Q17. Efficiency of ideal transformer = ?
🔵 (A) 100%
🟢 (B) 80%
🟠 (C) 0%
🔴 (D) <100%
Answer: (A) 100%
Q18. Which of these is an application of eddy currents?
🔵 (A) Speedometer
🟢 (B) Magnetic brakes
🟠 (C) Galvanometer damping
🔴 (D) All of these
Answer: (D) All of these
Q19. A solenoid has n = 1000 turns/m, area = 10⁻³ m², I = 2 A. Magnetic flux through one turn = ?
🔵 (A) 2.5 × 10⁻⁶ Wb
🟢 (B) 2.5 × 10⁻³ Wb
🟠 (C) 2.5 × 10⁻⁴ Wb
🔴 (D) 2.5 × 10⁻⁵ Wb
Answer: (C) 2.5 × 10⁻⁴ Wb
Q20. Energy density in magnetic field is:
🔵 (A) B²/2μ₀
🟢 (B) μ₀B²/2
🟠 (C) B²/μ₀
🔴 (D) None
Answer: (A) B²/2μ₀
🟢 JEE Main Level (Q21–Q40)
Q21. A solenoid with n turns/m carries current I. Its self-inductance for length L is:
🔵 (A) μ₀n²AL
🟢 (B) μ₀nI/L
🟠 (C) μ₀n²A/I
🔴 (D) μ₀n²L/A
Answer: (A) μ₀n²AL
Q22. Work done against induced emf to increase current from 0 to I in inductor L is:
🔵 (A) LI
🟢 (B) ½ LI²
🟠 (C) I²/L
🔴 (D) None
Answer: (B) ½ LI²
Q23. emf induced in rotating coil (N turns, area A, angular speed ω, field B) is:
🔵 (A) NBA cos(ωt)
🟢 (B) NBAω cos(ωt)
🟠 (C) NBAω sin(ωt)
🔴 (D) None
Answer: (C) NBAω sin(ωt)
Q24. In a step-up transformer, which increases?
🔵 (A) Current
🟢 (B) Voltage
🟠 (C) Power
🔴 (D) Resistance
Answer: (B) Voltage
Q25. If emf induced in coil is doubled, which is changed?
🔵 (A) Rate of flux change
🟢 (B) Area
🟠 (C) Number of turns
🔴 (D) All of these
Answer: (D) All of these
Q26. A coil has inductance 2 H. Current decreases from 5 A to 0 A in 0.5 s. emf induced is:
🔵 (A) 10 V
🟢 (B) 20 V
🟠 (C) 15 V
🔴 (D) 5 V
Answer: (B) 20 V
Q27. Which method reduces eddy current loss?
🔵 (A) Laminating core
🟢 (B) Using solid iron core
🟠 (C) Increasing resistance of coil
🔴 (D) None
Answer: (A) Laminating core
Q28. Mutual inductance between coils depends on:
🔵 (A) Geometry of coils
🟢 (B) Number of turns
🟠 (C) Distance between coils
🔴 (D) All of these
Answer: (D) All of these
Q29. A conducting rod of length 0.5 m moves at 10 m/s in field 0.2 T. emf = ?
🔵 (A) 0.5 V
🟢 (B) 1 V
🟠 (C) 0.25 V
🔴 (D) 2 V
Answer: (B) 1 V
Q30. In a transformer, power in primary = 100 W. Efficiency 80%. Power output = ?
🔵 (A) 180 W
🟢 (B) 80 W
🟠 (C) 20 W
🔴 (D) 100 W
Answer: (B) 80 W
Q31. Which device uses eddy current damping?
🔵 (A) Transformer
🟢 (B) Galvanometer
🟠 (C) Generator
🔴 (D) Motor
Answer: (B) Galvanometer
Q32. If inductance is doubled, energy stored for same current:
🔵 (A) Doubled
🟢 (B) Halved
🟠 (C) Same
🔴 (D) Quadrupled
Answer: (A) Doubled
Q33. For perfect transformer:
🔵 (A) Power input = Power output
🟢 (B) Power input > Power output
🟠 (C) Power input < Power output
🔴 (D) Power = 0
Answer: (A) Power input = Power output
Q34. If angular velocity of generator coil is doubled, emf:
🔵 (A) Halved
🟢 (B) Doubled
🟠 (C) Same
🔴 (D) Zero
Answer: (B) Doubled
Q35. Self-inductance of long solenoid depends on:
🔵 (A) Area
🟢 (B) Number of turns
🟠 (C) Length
🔴 (D) All of these
Answer: (D) All of these
Q36. Energy stored in magnetic field per unit volume:
🔵 (A) B²/2μ₀
🟢 (B) μ₀B²/2
🟠 (C) 2μ₀/B²
🔴 (D) None
Answer: (A) B²/2μ₀
Q37. A step-down transformer decreases:
🔵 (A) Voltage
🟢 (B) Current
🟠 (C) Power
🔴 (D) Energy
Answer: (A) Voltage
Q38. An emf of 2 V is induced when current in coil changes by 0.1 A in 0.5 s. Inductance = ?
🔵 (A) 10 H
🟢 (B) 5 H
🟠 (C) 20 H
🔴 (D) 0.1 H
Answer: (A) 10 H
Q39. The core of transformer is laminated to reduce:
🔵 (A) Magnetic field
🟢 (B) Eddy current loss
🟠 (C) Flux
🔴 (D) Voltage
Answer: (B) Eddy current loss
Q40. Which is NOT an application of electromagnetic induction?
🔵 (A) Generator
🟢 (B) Transformer
🟠 (C) Capacitor
🔴 (D) Induction heating
Answer: (C) Capacitor
🔴 JEE Advanced Level (Q41–Q50)
Q41. A coil of inductance L is connected to AC source E = E₀ sin(ωt). Instantaneous emf across inductor = ?
🔵 (A) 0
🟢 (B) E₀ cos(ωt)
🟠 (C) E₀ sin(ωt)
🔴 (D) L dI/dt
Answer: (D) L dI/dt
Q42. A rod rotates in field B with angular velocity ω. emf induced between ends length ℓ:
🔵 (A) Bℓ²ω
🟢 (B) ½ Bℓ²ω
🟠 (C) 2Bℓ²ω
🔴 (D) None
Answer: (B) ½ Bℓ²ω
Q43. In transformer, copper losses are proportional to:
🔵 (A) Voltage²
🟢 (B) Current²
🟠 (C) Resistance
🔴 (D) Frequency
Answer: (B) Current²
Q44. If magnetic flux in coil is Φ = 5t², emf induced at t = 2 s = ?
🔵 (A) 10 V
🟢 (B) 20 V
🟠 (C) 5 V
🔴 (D) 40 V
Answer: (B) 20 V
Q45. Which material reduces hysteresis loss?
🔵 (A) Steel
🟢 (B) Soft iron
🟠 (C) Copper
🔴 (D) Aluminium
Answer: (B) Soft iron
Q46. The emf induced in secondary of transformer is maximum when:
🔵 (A) Flux is constant
🟢 (B) Flux changes most rapidly
🟠 (C) Primary current is zero
🔴 (D) Primary current is steady
Answer: (B) Flux changes most rapidly
Q47. A conductor of length ℓ moves at angle θ with velocity v in field B. emf = ?
🔵 (A) Bℓv cosθ
🟢 (B) Bℓv sinθ
🟠 (C) Bℓ cosθ/v
🔴 (D) None
Answer: (B) Bℓv sinθ
Q48. Energy stored in inductor with current I is:
🔵 (A) LI
🟢 (B) ½ LI²
🟠 (C) I²/L
🔴 (D) None
Answer: (B) ½ LI²
Q49. If N turns of coil linked with flux Φ, total flux linkage = ?
🔵 (A) Φ/N
🟢 (B) NΦ
🟠 (C) Φ²
🔴 (D) N/Φ
Answer: (B) NΦ
Q50. emf induced in straight conductor length ℓ moving in uniform B in time t:
🔵 (A) Bℓ/t
🟢 (B) Bℓv
🟠 (C) Bℓ²/t
🔴 (D) None
Answer: (B) Bℓv
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MIND MAP
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