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 PMDC MDCAT 2026 syllabus expects clarity on Faraday's law, Lenz's law, and the transformer. Expect 1-2 MCQs from this chapter.
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-station → transmission grid (132 / 220 / 500 kV) | Grid → consumer (220 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.