Electromagnetic Induction
Whenever the magnetic flux linked with a circuit changes, an EMF is induced in it. This single principle — discovered by Michael Faraday in 1831 — powers every generator, transformer, and induction motor. The AAMC MCAT content outline expects clarity on Faraday's law, Lenz's law, and the transformer.
Faraday's Law
Faraday found two ways to induce an EMF in a coil: (i) by moving a magnet relative to the coil, and (ii) by changing the current in a nearby coil. Both involve the same underlying cause — a changing magnetic flux.
Magnetic flux linkage
The flux through a single loop of area A in a uniform field B is Φ = BA cosθ, where θ is the angle between B and the area vector. For a coil of N turns the flux linkage is NΦ.
Faraday's law of induction
ε = −N (dΦ/dt)
The induced EMF is equal to the negative rate of change of the flux linkage. Three ways to change Φ in practice:
- Change B (e.g. switch a current on or off in a primary coil).
- Change the area A (e.g. a rod sliding along rails).
- Change the orientation θ (e.g. a rotating coil — AC generator).
A rod of length L moving with velocity v perpendicular to a field B sweeps area at the rate Lv. The induced EMF is ε = BLv. This is the operating principle of the simple AC and DC generators.
Lenz's Law
Lenz's law gives the direction of the induced current:
The induced current always opposes the change in magnetic flux that produced it.
The minus sign in Faraday's law is just Lenz's law expressed mathematically. Lenz's law is a direct consequence of energy conservation — if the induced current aided the change, the flux (and energy) would grow without bound for free.
Push the N-pole of a magnet towards a coil. The flux through the coil increases. The induced current must oppose this increase — so it flows in a direction that makes the near face of the coil itself a north pole, repelling the incoming magnet. You feel this repulsion in your hand: that's the work that becomes electrical energy.
Transformer
A transformer is a static device that transfers AC power between two coils linked by a common iron core, stepping voltage up or down without changing frequency. It uses the principle of mutual induction: alternating current in the primary creates a changing flux that induces an EMF in the secondary.
Transformer equations
For an ideal transformer (no losses) the same flux links every turn of both coils, so
Vs/Vp = Ns/Np
Power conservation gives VpIp = VsIs (ideal, η = 100%) — a step-up transformer raises voltage but reduces current by the same factor.
| Property | Step-up | Step-down |
|---|---|---|
| Turns ratio | Ns > Np | Ns < Np |
| Voltage | Vs > Vp (raised) | Vs < Vp (lowered) |
| Current | Is < Ip | Is > Ip |
| Wire thickness | Secondary thinner (lower I) | Secondary thicker (higher I) |
| Typical use | Power plant → transmission grid (e.g. 345 / 500 / 765 kV) | Grid → consumer (120 V), phone chargers, doorbells |
Real-world losses
- Copper losses: I2R heating in the windings — reduced by using thick low-resistance wire.
- Iron / hysteresis losses: heat from re-magnetising the core each cycle — reduced by using soft iron (low coercivity).
- Eddy-current losses: circulating currents in the core — reduced by laminating the core.
- Flux leakage: some flux from primary doesn't link the secondary — reduced by tight coupling (concentric or shell-type designs).
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. The induced EMF in a coil is given by ε = −N(dΦ/dt). The minus sign represents:
Faraday's law gives the magnitude of the induced EMF; the minus sign encodes Lenz's law — the induced current opposes the flux change that caused it. This in turn is a statement of energy conservation.
Q2. A transformer has 200 primary turns and 1000 secondary turns. If 220 V is applied to the primary, the secondary voltage is:
Vs/Vp = Ns/Np; Vs = 220 × (1000/200) = 1100 V. This is a step-up transformer (turns ratio 5:1). Current in the secondary is 1/5 of the primary current.
Q3. A magnet is dropped through a vertical copper pipe. The magnet falls more slowly than free-fall because:
Falling magnet changes flux through every horizontal slice of the pipe, inducing eddy currents. By Lenz's law these currents create magnetic fields that oppose the motion, slowing the magnet. A non-conducting pipe shows no effect.
Q4. The core of a transformer is laminated mainly to reduce:
Lamination breaks the core into thin insulated sheets, each with high resistance, so eddy currents cannot circulate in large loops. Hysteresis is reduced by using soft iron; copper losses by using thick wire.
Q5. A 0.5 m rod moves at 4 m s−1 perpendicular to a magnetic field of 0.2 T. The motional EMF induced is:
ε = BLv = 0.2 × 0.5 × 4 = 0.4 V. The rod must move perpendicular to both itself and the field for full effect; if it moves parallel to the field, the EMF is zero.
Quick Recap
- Magnetic flux: Φ = BA cosθ; flux linkage = NΦ.
- Faraday: ε = −N(dΦ/dt).
- Motional EMF: ε = BLv (rod cutting field lines).
- Lenz: induced current opposes the flux change — statement of energy conservation.
- Transformer: Vs/Vp = Ns/Np; VpIp = VsIs (ideal).
- Losses: copper (I2R), hysteresis, eddy currents (reduced by lamination), flux leakage.
- High-voltage transmission cuts I2R losses by factor n2.