Applications of electromagnetic induction (Physics HL)

The big idea: Squeeze a wind-up torch and the bulb glows with no battery inside — you are spinning a coil to make electricity. A generator is a motor run backwards: instead of using current to spin a coil, you spin a coil in a magnetic field and it makes a current.

As the coil turns, the magnetic flux through it changes smoothly, so by Faraday's law it induces an emf (a driving voltage). Because the flux rises and falls as the coil rotates, the emf comes out as a sine wave — this is alternating current (AC).

Why a sine wave?: When the coil is flat to the field the flux is largest but momentarily unchanging, so the emf is zero. When the coil is edge-on to the field the flux is changing fastest, so the emf is at its peak. One full turn gives one full cycle of the sine.

The output is described by the rotational frequency of the coil: ω is the angular frequency (how fast it spins, in rad s⁻¹). The faster you spin it, the bigger and the more frequent the peaks.

For a coil of N turns and area A rotating with angular frequency ω in a magnetic field B, the induced emf follows a sine curve. Its highest value — the peak emf ε₀ — is reached each time the coil is edge-on to the field.

Four ways to get a bigger emf: ε₀ = BANω, so the peak voltage grows if you increase any of:

- B — a stronger magnet - A — a larger coil - N — more turns of wire - ω — spin it faster

Why we need rms: An AC voltage is constantly changing — its average over a cycle is zero, which is useless for describing how much power it delivers. So we quote the root-mean-square (rms) value instead.

The rms value is the steady DC value that would deliver the same average power (the same heating effect in a resistor). When the mains is called "230 V", that 230 V is the rms voltage.

What a transformer does: A transformer changes an AC voltage up or down. Two coils share an iron core: AC in the primary (N_p turns) makes a changing flux that induces an emf in the secondary (N_s turns).

The voltages are in the same ratio as the turns. More turns on the secondary ⇒ step-up (higher voltage); fewer turns ⇒ step-down (lower voltage).

An ideal transformer conserves power: An ideal (100% efficient) transformer wastes no energy, so the power in equals the power out: ε_p I_p = ε_s I_s.

That is why the current ratio is upside down: if a step-down transformer halves the voltage, it doubles the current — and vice versa.

Where it shows up: AC generators, rms and transformers are HL only (D.4):

- Paper 1A — a one-step 'find the rms value', 'is this step-up or step-down?', or 'what does an ideal transformer conserve?'. - Paper 2 — determine a peak emf with ε₀ = BANω, or use the transformer ratio (and power conservation) to find a secondary voltage or current.

Three easy marks: (1) rms = peak ÷ √2 (and peak = rms × √2 going the other way). (2) Voltage ratio = turns ratio; current ratio is inverted. (3) "Ideal transformer" ⇒ power in = power out (ε_p I_p = ε_s I_s).