TASPhysicsSyllabus dot point

What determines the size and direction of an induced voltage?

Apply Faraday's law and Lenz's law to determine the magnitude and direction of induced EMF.

Magnetic flux, Faraday's law relating induced EMF to the rate of change of flux, and Lenz's law giving the direction of the induced current from energy conservation.

Generated by Claude Opus 4.78 min answerUpdated 2026-05-30

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

This dot point is the quantitative heart of electromagnetic induction: how to find both the magnitude and the direction of an induced voltage.

Magnetic flux

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

\Phi = BA\cos\theta

where $B$ is the field strength, $A$ is the area of the loop, and $\theta$ is the angle between the field and the normal to the loop. Flux is measured in webers. Flux is largest when the field is perpendicular to the loop face and zero when the field lies in the plane of the loop. Induction depends on flux changing, which can happen by changing the field strength, the area, or the angle.

Faraday's law

Faraday found that the induced EMF equals the rate of change of flux linkage, where flux linkage is the flux multiplied by the number of turns $N$ :

\varepsilon = -N\frac{\Delta\Phi}{\Delta t}

So a faster change, a stronger field change, a larger area, or more turns all increase the induced EMF. If the flux is steady, no EMF is induced, which is why a stationary magnet in a coil produces nothing. On a flux-time graph the EMF is proportional to the gradient.

Lenz's law and the negative sign

The minus sign in Faraday's law is Lenz's law: the induced current flows in the direction that opposes the change in flux that produced it. If the flux through a coil is increasing, the induced current creates its own field to oppose the increase; if decreasing, it tries to maintain the flux.

This is conservation of energy in action. The opposing current means you must do work to push a magnet into a coil, and that work is what becomes electrical energy. If the induced current aided the change instead, it would create energy from nothing.

Worked example: EMF from a changing field

Problem

A coil of 200 turns and area $0.015\ \text{m}^2$ sits in a field that drops from $0.40\ \text{T}$ to $0.10\ \text{T}$ in $0.20\ \text{s}$ , with the field perpendicular to the coil. Find the average induced EMF.

Solution

Find the change in flux per turn:

\Delta\Phi = (\Delta B)A = (0.10 - 0.40)(0.015) = -4.5\times10^{-3}\ \text{Wb}

Apply Faraday's law (taking the magnitude):

|\varepsilon| = N\frac{|\Delta\Phi|}{\Delta t} = 200\times\frac{4.5\times10^{-3}}{0.20} = 4.5\ \text{V}

The average induced EMF is $4.5\ \text{V}$ .

In the exam, first work out the flux and what is changing about it, then apply Faraday's law for the size. Use Lenz's law separately for the direction: state which way the flux is changing, then choose the induced current direction that opposes that change. A clear sentence linking Lenz's law to energy conservation often earns the explanation marks.

Exam-style practice questions

Practice questions written in the style of TASC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2024 TASC3 marksIn a science museum an aluminium plate is levitated over a large coil carrying 800 A of alternating current changing at 800 Hz. Explain why the aluminium plate levitates, with reference to relevant principles and laws.

Show worked answer →

The alternating current produces a magnetic field that is constantly changing in both magnitude and direction at 800 Hz.

Faraday's law: this changing magnetic flux through the aluminium plate induces an EMF, which drives circulating eddy currents in the conducting plate.

Lenz's law: the induced eddy currents flow in the direction that opposes the change in flux that created them. The plate therefore behaves like a magnet whose poles oppose the coil's field, so the plate and coil repel each other.

Because the current alternates, this repulsion is sustained on average over each cycle and pushes the plate upward. When the repulsive force balances the plate's weight, it levitates.

Markers want: changing flux (Faraday), induced eddy currents, Lenz's law opposition producing a repulsive force that supports the weight.

2023 TASC2 marksA magneto is a simple generator. A magnet spins anticlockwise between the poles of a laminated iron horseshoe with a coil connected to a load XY. The north pole is entering the horseshoe at A and the south at B. Justify the direction of the induced current through the load resistor.

Show worked answer →

As the magnet rotates, the magnetic flux threading the coil around the horseshoe changes. With the north pole entering at A, the flux through the coil in that direction is increasing.

Faraday's law says the changing flux induces an EMF; Lenz's law says the induced current flows so as to oppose the change. To oppose the increasing flux from the approaching north pole, the coil must create a magnetic field that pushes back against it, that is, the coil's near face must become a north pole.

Applying the right-hand grip rule to the coil windings to make that face a north pole fixes the direction the current must flow through the windings, and hence through the load from one terminal to the other (the direction that opposes the rising flux).

Markers want the link: increasing flux, Lenz's law opposition, induced field set up to oppose it, then the grip rule giving the current direction through the load.

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