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Electromagnetic Induction
Physics · Class 12 · Part 1NCERT pp. 154–1732 sets × 25 questions
Key facts and formulas for Electromagnetic Induction, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Magnetic flux | Φ = B A cos θ, θ is the angle between B and the normal to the coil |
| Faraday's law | ε = −N dΦ/dt; average emf = N ΔΦ / Δt; charge q = ΔΦ / R |
| Lenz's law | The induced current opposes the change of flux (energy conservation) |
| Motional emf | ε = B l v (B, l, v mutually perpendicular); with angle, B l v sin θ; use the chord for bent wires |
| Rotating rod | ε = ½ B ω R², ω = 2π ν; spokes are in parallel, so emf equals that of one spoke |
| Induced electric field | E × 2πr = π r² dB/dt, so E = (r/2) dB/dt inside the field region |
| Inductance | M = μ₀ n₁ n₂ π r₁² l; L = μ₀ n² A l; N Φ = L I; ε = −L dI/dt; M ≤ √(L₁ L₂) |
| Combinations | Series: L₁ + L₂ ± 2M; parallel (no coupling): 1/L = 1/L₁ + 1/L₂ |
| Energy | U = ½ L I²; energy density u = B² / 2μ₀ |
| AC generator and eddy currents | ε₀ = N B A ω, ε = ε₀ sin ωt; lamination reduces eddy currents |
Three sample questions
Q1. Faraday and Henry showed, around 1830, that
- a steady magnetic field induces a current in a coil
- a changing magnetic field induces a current in a closed coil
- a current in a wire deflects a compass needle
- a charge at rest produces a magnetic field
Hint and solution
Hint: Induction needs something to change with time. Which option talks about a changing field and a closed coil?
- Induction: changing B → current — Faraday and Henry found that current appears only when the magnetic field through a closed coil changes.
- Oersted: current → magnetic effect — Options C and D describe magnetic effects of currents and charges. They are Oersted and Ampere type results.
- Steady field → flux constant → no emf — Option A has a steady field, so the flux does not change and no current flows.
- So the answer is the changing field in a closed coil. Option B. — Only option B names a changing field and a closed coil, which is the condition for induction.
Answer: B. The second and third statements are Oersted and Ampere's results. Induction needs a changing field.
Q2. Which of these make a galvanometer connected to a coil deflect?
I. A magnet held at rest near the coil.
II. A magnet moved towards the coil.
III. The coil moved towards a fixed magnet.
- I and II only
- II only
- I, II and III
- II and III only
Hint and solution
Hint: Only relative motion changes the flux through the coil. Which cases have motion?
- Emf needs changing flux — Current is induced only when the flux through the coil changes with time.
- I: magnet at rest → flux steady — In case I nothing moves, so the flux is constant and the galvanometer stays at zero.
- II and III: relative motion — Moving the magnet or moving the coil changes the flux in the same way. Only relative motion matters.
- So II and III deflect the galvanometer. Option D. — Case I does not, cases II and III do, so the answer is II and III only. Option D.
Answer: D. Relative motion changes the flux, so II and III work. A magnet at rest gives a steady flux and no current.
Q3. Two coils are at rest. A key in the circuit of the first is pressed, held, and then released. The galvanometer in the second coil gives
- a kick, then zero, then a kick in the opposite direction
- a steady deflection while the key is pressed
- a kick on pressing only
- kicks in the same direction on pressing and releasing
Hint and solution
Hint: When does the current in the first coil change? Think of rising on press, steady while held, falling on release.
- emf ∝ rate of change of flux — The induced emf in the second coil exists only while the flux changes.
- Press: I rises from 0, flux rises — On pressing, the current grows from zero, so the flux grows and the galvanometer kicks.
- Held: I steady → zero; Release: I falls — While held, nothing changes, so zero. On release the flux falls, so the emf reverses.
- So kick, zero, then opposite kick. Option A. — This pattern matches only option A.
Answer: A. Flux changes only while the current rises (press) or falls (release), in opposite senses. A steady current gives nothing.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.