Chapter summary — Electromagnetic Induction
Electromagnetic induction studies how a changing magnetic flux through a circuit induces an emf. Faraday's law states induced emf ε = −dΦ/dt (magnitude |ε| = rate of change of flux); Lenz's law gives direction of induced current (opposes change). Important topics: motional emf, self-inductance (L) and mutual inductance (M), energy stored in inductor (½LI²), RL transients with time constant τ = L/R, eddy currents and their reduction, AC generators and transformers (ideal transformer relations Vp/Vs = Np/Ns, power conservation), electromagnetic damping, and applications. Key formulas and concepts should be practiced with sign conventions, Fleming's right-hand/left-hand rules, and circuit analysis.
Revision tips: Learn Faraday's law, Lenz's law sign, units of inductance (Henry), behavior of RL circuits at t=0 and t→∞, transformer ideal equations, and examples of motional emf and eddy currents.
1. Faraday's law of electromagnetic induction relates induced emf to:
A) Magnetic field only
B) Rate of change of magnetic flux through the circuit (−dΦ/dt) ✅
C) Electric field only
D) Charge density
2. Lenz's law states that the direction of induced current is such that it:
A) Reinforces the change in magnetic flux
B) Opposes the change in magnetic flux ✅
C) Is independent of change
D) Maximizes energy
3. SI unit of inductance is:
A) Tesla
B) Weber
C) Henry (H) ✅
D) Ohm
4. The emf induced in a rod of length l moving with velocity v perpendicular to magnetic field B is given by:
A) ε = B l v ✅
B) ε = B l / v
C) ε = Blv^2
D) ε = B / (l v)
5. Motional emf arises due to:
A) Changing electric field
B) Changing resistance
C) Motion of conductor through magnetic field (v × B) ✅
D) Temperature change
6. Self-inductance of a coil is defined as:
A) Ratio of change in current to flux
B) Magnetic flux linkage per unit current (Φ/N)/I = L ✅
C) Current per unit flux
D) Voltage per unit resistance
7. Mutual inductance M between two coils depends on:
A) Geometry and coupling between coils ✅
B) Resistance only
C) Type of battery
D) Temperature only
8. Energy stored in an inductor carrying current I is:
A) ½ L I² ✅
B) L I
C) I²/L
D) LI
9. The induced emf in a coil is zero when:
A) Magnetic flux is changing rapidly
B) Magnetic flux through coil is constant ✅
C) Coil is moving in non-uniform field
D) Coil area is changing
10. In an RL circuit, the time constant τ is given by:
A) τ = R/L
B) τ = L/R ✅
C) τ = L·R
D) τ = 1/(L R)
11. When a steady current is established in an inductor, the potential difference across it is:
A) Maximum
B) Zero (no change in current ⇒ no induced emf) ✅
C) Infinite
D) Depends on resistance only
12. Eddy currents are induced in conductors subjected to changing magnetic flux. They cause:
A) Heating and energy loss (damping) ✅
B) Increased conductivity
C) No effect
D) Magnetic monopoles
13. A transformer works on the principle of:
A) Motional emf
B) Mutual induction between primary and secondary coils ✅
C) Self-induction only
D) Electrostatic induction
14. For an ideal transformer, the relation between primary and secondary voltages is:
A) Vp/Vs = Np/Ns ✅
B) Vp·Vs = Np·Ns
C) Vp + Vs = Np + Ns
D) Vp = Vs always
15. In a step-up transformer:
A) Secondary voltage < primary voltage
B) Secondary voltage > primary voltage (Ns > Np) ✅
C) Current increases in secondary
D) Power is not conserved
16. Lenz's law ensures conservation of:
A) Charge
B) Energy (induced current opposes change ⇒ work done) ✅
C) Mass
D) Entropy
17. When a bar magnet is pushed rapidly into a coil, induced current direction is such that it:
A) Attracts the magnet further
B) Opposes the motion (repels if north pole enters) ✅
C) Has no interaction
D) Depends only on coil resistance
18. The unit of magnetic flux is:
A) Tesla
B) Henry
C) Ampere
D) Weber (Wb) ✅
19. Faraday's ring demonstration illustrates:
A) Self-induction only
B) Mutual induction between coils and effect of induced emf ✅
C) Electrostatic induction
D) Photoelectric effect
20. In a coil, if the number of turns is doubled, self-inductance L:
A) Halves
B) Remains same
C) Quadruples (L ∝ N²) ✅
D) Doubles
21. The polarity of induced emf in a moving conductor is determined by:
A) Fleming's right-hand rule ✅
B) Fleming's left-hand rule
C) Ohm's law
D) Coulomb's law
22. In a series RL circuit when switch is closed, current:
A) Immediately reaches steady value
B) Rises exponentially and approaches steady state with time constant L/R ✅
C) Decreases
D) Oscillates indefinitely
23. A conducting loop rotating in a magnetic field acts as:
A) Transformer
B) AC generator (emf alternates) ✅
C) Motor only
D) Capacitor
24. The instantaneous emf in a rotating coil of area A in field B with angular speed ω is:
A) ε = NBAω sin(ωt) ✅
B) ε = NBA cos(ωt)
C) ε = NBAω
D) ε = NBA/ω
25. A superconducting loop has zero resistance. If magnetic flux through it is changed, induced current will be:
A) Zero
B) Finite and persistent to oppose change (no decay) ✅
C) Damped quickly
D) Random
26. In an ideal transformer, if primary voltage is 230 V and turns ratio Np:Ns = 1:2, secondary voltage is:
A) 115 V
B) 230 V
C) 460 V ✅
D) 920 V
27. The back emf in a coil opposing change in current is given by:
A) ε = L (dI/dt) with plus sign
B) ε = −L (dI/dt) ✅
C) ε = IR
D) ε = L/I
28. Which phenomenon is utilized in metal detectors and induction cooktops?
A) Photoelectric effect
B) Eddy currents and induction heating ✅
C) Static electricity
D) Electrolysis
29. The mutual inductance between two coils is measured in units of:
A) Weber
B) Tesla
C) Henry ✅
D) Ohm
30. In Lenz's law, the negative sign in ε = −dΦ/dt indicates:
A) Magnitude relation only
B) Direction of induced emf opposes change in flux ✅
C) emf is always negative
D) Flux decreases always
31. A metallic plate moving into region of magnetic field experiences eddy currents that:
A) Accelerate the plate
B) Oppose motion and produce heating ✅
C) Cause superconductivity
D) Create light emission
32. The phenomenon where changing magnetic flux induces electric field in space is captured by:
A) Ampère's law only
B) Faraday's law / Maxwell-Faraday equation ✅
C) Gauss's law
D) Ohm's law
33. If frequency of alternating current in transformer increases, core losses due to hysteresis and eddy currents generally:
A) Decrease
B) Increase ✅
C) Remain same
D) Become zero
34. The RMS value of an AC emf with peak E0 is:
A) E0 ✅
B) E0/√2 ✅ (note: RMS = E0/√2)
C) 2E0
D) E0/2
35. An inductor opposes change in current most strongly when:
A) dI/dt is large ✅
B) dI/dt is zero
C) Current is steady
D) Resistance is zero
36. In a perfectly coupled transformer (ideal), efficiency is approximately:
A) 0%
B) 50%
C) 100% (neglecting losses) ✅
D) 10%
37. Which of the following reduces eddy current losses in transformer cores?
A) Using solid iron core
B) Using laminated core (insulated thin sheets) ✅
C) Increasing frequency
D) Increasing thickness of core
38. When magnetic flux through a closed loop increases, induced current flows so as to produce a magnetic field that _____ the increase.
A) Aids
B) Opposes ✅
C) Doubles
D) Has no relation
39. The expression for motional emf between ends of rod moving in B is given by ε = Blv. This assumes:
A) v not perpendicular to B
B) Rod moving perpendicular to both B and its length ✅
C) Rod stationary
D) No magnetic field
40. If a coil is rapidly disconnected from DC source, the induced emf can be large because:
A) dI/dt is large (rapid change) ⇒ ε = −L dI/dt ✅
B) Current increases
C) Flux remains constant
D) Resistance becomes zero
41. The direction of induced emf in a loop can be found using:
A) Fleming's left-hand rule
B) Right-hand slap method
C) Lenz's law and right-hand rule ✅
D) Ohm's law only
42. A coil of resistance R and inductance L is connected to a battery. Energy stored in the inductor when steady current I flows is:
A) Zero
B) ½ L I² ✅
C) I²R
D) L I
43. The phenomenon of electromagnetic braking relies on:
A) Static friction
B) Eddy currents producing opposing magnetic forces ✅
C) Chemical reaction
D) Optical reflection
44. If a straight conductor of length l moves with velocity v in magnetic field B, charge separation leads to an emf ε = B l v. The sign depends on:
A) Direction of motion and orientation of B (use right-hand rule) ✅
B) Magnitude of B only
C) Temperature only
D) Resistance only
45. In mutual induction, the induced emf in coil 2 is proportional to:
A) Rate of change of current in coil 1 and mutual inductance M ✅
B) Square of current in coil 1
C) Resistance of coil 2 only
D) Temperature
46. Transformers do not work with DC because:
A) DC produces constant flux (no changing flux ⇒ no induced emf in secondary) ✅
B) DC is too strong
C) DC has no electrons
D) Transformers burn with AC
47. The Maxwell-Faraday equation in differential form expresses:
A) Curl of electric field equals negative rate of change of magnetic field (∇×E = −∂B/∂t) ✅
B) Divergence of E
C) Curl of B
D) Gauss's law
48. A rectangular loop moving out of a uniform magnetic field experiences induced emf. When it fully leaves the field region, induced emf is:
A) Maximum
B) Zero (no change in flux once outside) ✅
C) Constant
D) Infinite
49. Thomson's experiment (or ringing a bell due to induced current) historically demonstrated:
A) Electrostatic forces
B) Existence of induced currents and mutual induction ✅
C) Photoelectric effect
D) Thermal expansion
50. Which of the following reduces hysteresis losses in transformer cores?
A) Using hard magnetic materials
B) Using soft magnetic materials with narrow hysteresis loop ✅
C) Increasing core thickness
D) Using superconductors only