1📚 The 14 Topics
All 14 topics are live, plus a bonus Maths Toolkit — each a full deep-dive with worked Allen examples, Beginner's Box keys, a formula sheet and NEET practice with answers. The chapter is complete.
| # | Topic | What it covers | Status |
|---|---|---|---|
| 01 | Magnetic flux & flux linkage → | What flux means, the angle trap, dot product, flux linkage Nφ, units & dimensions, non-uniform fields, closed surfaces, changing flux by turning | Live |
| 02 | Faraday's experiments & laws → | Magnet and coil, effect of speed, two coils with a key, what the experiments share, both laws, emf from a flux-time graph, relative motion | Live |
| 03 | Lenz's law & direction of induced current → | Nature pushes back, the four-step method, magnets and poles, viewing side, wires/beams/shapes, two coils, energy conservation | Live |
| 04 | Induced emf, current, charge & heat → | The five induced quantities from one flux change, charge versus heat, the four types of change | Live |
| 05 | Self-inductance of a coil & solenoid → | Self-induction, what L depends on, emf from an I–t graph, circular coil and solenoid formulas | Live |
| 06 | Inductor in a circuit: potential, power & energy → | Potential across L, KVL with inductors, power, stored energy ½Li², energy density | Live |
| 07 | LR circuits: growth, decay & time constant → | Growth, time constant τ = L/R, decay, switching snapshots, combinations of inductors | Live |
| 08 | Mutual inductance & coupling → | Mutual induction, coaxial solenoids, concentric loops, coupling factor k, alternating primary | Live |
| 09 | Motional emf: rods, rails & moving loops → | Where the emf comes from, effective length, rod on rails, a loop crossing a field | Live |
| 10 | Rotating rods, wheels & discs → | Rotating rod ½Bωℓ², pivot along the rod, spokes of a wheel, the Faraday disc | Live |
| 11 | The induced electric field → | Force on charges at rest, how it differs from an electrostatic field, strength around a cylinder | Live |
| 12 | Periodic EMI & the AC generator → | Rotating coil, frequency and speed, e = NBAω sin ωt and the AC generator | Live |
| 13 | Eddy currents → | What they are and do, keeping them small (laminations), uses — braking, induction furnace, metal detectors | Live |
| 14 | The transformer → | What it does, ideal relations, what it cannot do, efficiency & losses, power transmission | Live |
| + | Maths toolkit for EMI → | Units & powers of ten, angles, vectors, differentiation, integration, exponentials & logs, ratios, reading graphs | Bonus |
2🧠 Core Ideas
1 · Flux is the quantity that matters foundation
Φ = B·A = BA cos θ, where θ is the angle between B and the area vector (the normal) — not between B and the plane of the coil. Flux is maximum when B is along the normal (θ = 0) and zero when B lies in the plane of the coil (θ = 90°). For N turns, flux linkage = NΦ. SI unit: weber (1 Wb = 1 T m²).
2 · Faraday: only change induces emf
A steady flux, however large, induces nothing. The magnitude is set by the rate of change: e = −N dΦ/dt. Move faster, use more turns, or change the field more sharply, and the emf grows.
3 · Lenz: the minus sign is energy conservation
The induced current always opposes the change that produced it — approach a coil with a north pole and the coil's near face becomes a north pole to push back. If it were the other way round you would get free energy. Work done against that opposition is what appears as electrical energy.
4 · The four-step direction method
(i) Which way does B point through the coil? (ii) Is the flux increasing or decreasing? (iii) The induced current opposes that change — so its own field must point with a falling flux, against a rising one. (iv) Apply the right-hand rule from the viewing side to convert that field direction into clockwise or anticlockwise.
3🧮 Formula Bank
| Quantity | Formula | Note |
|---|---|---|
| Magnetic flux | Φ = BA cos θ | θ with the normal; unit weber |
| Flux linkage | NΦ | N = number of turns |
| Faraday's law | e = −N dΦ/dt | minus sign = Lenz |
| Average emf | e = −N ΔΦ/Δt | for a finite change |
| Motional emf | e = Bℓv | rod ⊥ B, moving ⊥ to itself |
| Rotating rod | e = ½Bωℓ² | about one end |
| Induced current | i = e/R | R = total circuit resistance |
| Induced charge | q = NΔΦ/R | independent of time taken |
| Self-inductance | e = −L di/dt, Φ = Li | unit henry |
| Solenoid inductance | L = μ₀n²Aℓ | n = turns per unit length |
| Energy in an inductor | U = ½Li² | stored in the magnetic field |
| Mutual inductance | e₂ = −M di₁/dt, M = k√(L₁L₂) | k ≤ 1 |
| LR growth / decay | i = i₀(1 − e^(−t/τ)) / i₀e^(−t/τ) | τ = L/R |
| AC generator | e = NBAω sin ωt, e₀ = NBAω | peak at coil in the plane of B |
4⚠️ Traps
A coil lying in the field plane has θ = 90° and Φ = 0. Swapping the two angles inverts every flux answer.
Only dΦ/dt matters. A coil sitting in a huge but steady field has zero emf.
q = NΔΦ/R — pull the magnet fast or slow and the same charge flows; only the current and the time differ.
Flux falling ⟹ the induced current tries to maintain it (same direction as B), not oppose B itself.
"Clockwise" seen from the left is anticlockwise from the right. Always state which face you are looking at.
While current grows, back emf opposes growth; while it decays, the inductor drives current to keep it going.