Apply Faraday's law to relate induced EMF to the rate of change of magnetic flux through a coil.

What this dot point is asking

You need to define magnetic flux and apply Faraday's law to calculate the EMF induced when the flux through a coil changes.

Magnetic flux

Magnetic flux measures how much magnetic field passes through an area.

Flux changes if the field strength changes, the area changes, or the orientation of the coil relative to the field changes.

Faraday's law

The central law of induction states that the induced EMF equals the rate of change of flux linkage (flux times number of turns).

So you get a bigger induced voltage by:

• changing the flux faster (smaller $\Delta t$),
• using more turns (larger $N$),
• producing a larger flux change (stronger field, larger area, or bigger orientation change).

If the flux is not changing, there is no induced EMF: induction needs change.

Ways to induce an EMF

• Moving a magnet into or out of a coil changes the flux.
• Rotating a coil in a field changes $\theta$, hence the flux (the basis of generators).
• Changing the current in a nearby coil changes the field and so the flux (the basis of transformers).
• A conductor moving through a field cuts field lines, inducing a motional EMF $\varepsilon = BLv$.

These four routes cover essentially every SACE induction scenario, from a dropped magnet through a tube to a generator coil and the secondary of a transformer.

Motional EMF

A straight conductor of length $L$ moving at speed $v$ perpendicular to a field $B$ has an EMF induced across its ends, $\varepsilon = BLv$. This is a special case of Faraday's law: as the rod moves, the area of the circuit it forms with its rails changes, so the flux $\Phi = BA$ changes at the rate $B L v$. This is the principle behind a simple generator and the eddy-current effects seen in electromagnetic braking, and it shows that "cutting field lines" and "changing flux" are two descriptions of the same physics.

How SACE assesses this

SACE Stage 2 induction questions give a flux change (a field dropping to zero, a loop leaving a field, or a magnet passing a coil) over a stated time, and ask for the average EMF using $\varepsilon = N\dfrac{\Delta\Phi}{\Delta t}$. The reliable method is to compute the initial and final flux as $\Phi = BA$ (or $BA\cos\theta$ when an angle is given), find the change, divide by the time, and multiply by the number of turns. The two most common slips are forgetting the factor of $N$ for a multi-turn coil and using the field $B$ in place of the flux $BA$. Show the flux change as an explicit intermediate step before applying the rate, and quote the answer with units.