Apply Faraday's and Lenz's laws to magnetic flux, generators and transformers

What this dot point is asking

WACE wants you to define magnetic flux, use Faraday's law to calculate an induced emf, apply Lenz's law to find its direction, and explain generators and transformers in terms of changing flux. This topic closes Unit 3 by linking magnetism back to electricity: motion plus a magnetic field produces electricity.

Magnetic flux

Magnetic flux measures how much field passes through a surface,

where $A$ is the area of the loop and $\theta$ is the angle between the field and the normal to the loop. Flux is greatest when the field is perpendicular to the area ($\theta=0$) and zero when the field lies in the plane of the loop. Crucially, an emf is induced only when flux changes, which can happen by changing $B$, changing $A$, or rotating the loop to change $\theta$.

Faraday's law

The induced emf equals the rate of change of flux linkage, where $N$ is the number of turns,

A larger field change, a faster change, or more turns all increase the emf. On a flux-time graph the induced emf is proportional to the gradient, so a steep change gives a large emf and a constant flux gives none.

Lenz's law and the minus sign

The negative sign is Lenz's law: the induced current flows in the direction that opposes the change in flux producing it. If the flux through a coil is increasing, the induced current creates a field opposing that increase; if it is decreasing, the induced current tries to maintain it. This is energy conservation in disguise: the opposition is why you must do work to push a magnet into a coil, and that work becomes electrical energy.

Generators

An AC generator rotates a coil in a magnetic field. As the coil turns, the angle $\theta$ between the field and the coil normal changes continuously, so the flux varies sinusoidally and the induced emf varies sinusoidally too. The emf is maximum when the coil plane is parallel to the field (flux changing fastest) and zero when the plane is perpendicular (flux momentarily steady at its peak). Slip rings connect the rotating coil to the external circuit, delivering alternating current.

Transformers

A transformer uses a changing flux to transfer energy between two coils on a shared iron core. AC in the primary creates a changing flux that the core carries to the secondary, inducing an emf there. For an ideal transformer the voltages share the turns ratio,

Assuming no power loss, $V_pI_p=V_sI_s$, so stepping voltage up steps current down. Transformers work only on AC because they need a continually changing flux; this is the reason mains power is distributed as high-voltage AC to cut transmission losses.

Stating direction clearly

When asked for direction, name the change in flux first, then say the induced current opposes it, and give the current sense (for example clockwise viewed from a stated side). Marks are lost when students quote Faraday's law but never resolve the sign with Lenz's law.