Why electromagnetic induction matters
Ever wonder how a generator lights up a stadium or why your phone charger works? It’s all about changing magnetic fields.
In simple words, moving a magnet near a coil makes the coil push electrons around – that push is called induced emf. It’s like shaking a bottle to make the water splash out.
What is electromagnetic induction?
Electromagnetic induction is the process where a changing magnetic field creates an electric “push” (emf) in a nearby conductor. Think of water flowing through a pipe; if you squeeze the pipe, the water speed changes. Similarly, changing the magnetic “pipe” makes electrons move.
Induced emf (electromotive force)
Emf is not a force you can see; it’s a voltage that appears because of the changing field. The symbol is ε. It tells the electrons how hard to move.
Lenz's law – the “brake” rule
Lenz's law says the induced emf always tries to stop the change that created it. It’s like a car’s brakes: if you push the car forward, the brakes push back.
Self‑inductance and mutual inductance
Self‑inductance happens when a coil’s own changing current creates a magnetic field that then induces emf in the same coil. Mutual inductance is when one coil’s changing field induces emf in a nearby coil. These are measured in henries (H).
AC circuits – the playground of induction
Alternating current (AC) means the current flips direction many times a second. Because the direction keeps changing, the magnetic field around a coil also keeps changing, so the coil constantly creates and opposes emf.
Key formulas you’ll need
- ε = -N ΔΦ/Δt (ε: induced emf, N: number of turns, Φ: magnetic flux)
- Φ = B A cosθ (B: magnetic field strength, A: area, θ: angle between field and area)
- L = N² μ₀ A / l (L: self‑inductance, μ₀: permeability of free space, l: length of coil)
- V(t) = V₀ sin ωt (Voltage in a pure AC source, ω = 2πf, f = frequency)
Worked example: coil in a changing magnetic field
Imagine a square coil of 100 turns, each side 0.1 m, placed in a magnetic field that grows from 0 to 0.2 T in 0.05 s. Find the peak induced emf.
- Area A = side² = 0.01 m².
- Initial flux Φ₁ = B₁ A = 0 × 0.01 = 0 Wb.
- Final flux Φ₂ = 0.2 × 0.01 = 0.002 Wb.
- Change in flux ΔΦ = 0.002 Wb.
- Δt = 0.05 s, so ΔΦ/Δt = 0.04 Wb s⁻¹.
- ε = -N ΔΦ/Δt = -100 × 0.04 = -4 V. The magnitude is 4 V.
The negative sign just tells us the direction (Lenz’s law).
Comparison: DC vs AC circuits with inductors
| Feature | DC circuit with inductor | AC circuit with inductor |
|---|---|---|
| Current behavior | Rises gradually, then steady | Current constantly lags voltage |
| Induced emf | Only while current changes | Always present because current changes direction |
| Impedance (opposition) | Just resistance | Resistance + reactive part (X_L = ωL) |
| Energy storage | Magnetic field builds then holds | Magnetic field builds and collapses each cycle |
Quick recap
- Changing magnetic field → induced emf (Faraday’s law).
- Induced emf tries to stop the change (Lenz’s law).
- Self‑inductance: coil fights its own change.
- Mutual inductance: one coil fights another’s change.
- In AC, the fight is continuous, giving rise to reactance.
📝 Likely Exam Questions
- State Faraday’s law and explain the meaning of each symbol.
Answer: ε = -N ΔΦ/Δt, where ε is induced emf, N is number of turns, ΔΦ is change in magnetic flux, Δt is time interval. - A coil of 200 turns has an area of 5 cm². If the magnetic field through it changes from 0.1 T to 0.3 T in 0.02 s, calculate the induced emf.
Answer: A = 5 × 10⁻⁴ m², ΔΦ = (0.3‑0.1)×A = 0.2×5×10⁻⁴ = 1×10⁻⁴ Wb, ε = -200×(1×10⁻⁴/0.02) = -1 V (magnitude 1 V). - What is the difference between self‑inductance and mutual inductance?
Answer: Self‑inductance is the emf induced in a coil by the change of its own current; mutual inductance is the emf induced in one coil by the change of current in a nearby coil. - Explain why the current in an AC circuit containing only an inductor lags the applied voltage by 90°.
Answer: The induced emf always opposes the change in current (Lenz’s law). When voltage is at its maximum, the rate of change of current is highest, so current is still building up and reaches its maximum a quarter cycle later. - Draw and label a simple AC series R‑L circuit and write the expression for its impedance.
Answer: Diagram shows a resistor R and an inductor L in series connected to an AC source. Impedance Z = √(R² + (ωL)²), where ω = 2πf.