Physics · Units 3 & 4

Magnetic Flux and Electromagnetic Induction

Understand magnetic flux and electromagnetic induction the easy way, with plain English intuition, an interactive simulation, Faraday's law, Lenz's law, worked examples and an auto marked practice test. VCE Physics Units 3 and 4.

Learn

Move a magnet near a coil of wire and, out of nowhere, a current appears in the wire. Nothing is plugged in. The trick is change: as long as the amount of magnetic field threading through the coil keeps changing, the coil pushes a current around itself. Hold everything still and the current dies instantly. This single idea, a changing magnetic flux makes electricity, is how every power station on the grid generates its energy.

Flux is just how much field goes through the loop

Picture a wire loop held up in a magnetic field. Magnetic flux is simply how much of that field passes straight through the loop. A stronger field, or a bigger loop, means more flux.

When the field points straight through the loop (perpendicular to its area), the flux is the field strength times the area:

  • Φ=BA\Phi = BA, where Φ\Phi is the flux in webers (Wb), BB is the field strength in tesla, and AA is the loop area in square metres.
  • More field lines through the loop means more flux. Tilt the loop edge on to the field and the flux drops, because fewer lines get through.

Flux is the thing that has to change for anything interesting to happen.

SNpush inmagnetic flux Φcoil of wireGmeterMoving the magnet changes the flux, inducing a current that opposes the change

Pushing the magnet towards the coil makes the flux through the coil grow, and that growth is what drives a current through the meter. The red note shows Lenz law: the induced current always flows the way that fights the change pushing it.

A changing flux induces an EMF

Here is the heart of it. Whenever the flux through a coil changes, the coil develops a voltage, called an EMF, that tries to drive a current. The faster the flux changes, the bigger the EMF.

Faraday’s law puts a number on it. For a coil of NN turns:

ε=−NΔΦΔt\varepsilon = -N\frac{\Delta\Phi}{\Delta t}

The ΔΦ\Delta\Phi is the change in flux, and Δt\Delta t is the time it took. The NN is there because every turn of wire feels the same change, so more turns stack up more EMF. There are three ways to make the flux change and trigger an EMF:

  • The field BB gets stronger or weaker (move a magnet closer, or switch an electromagnet on or off).
  • The area of the loop changes (squash or stretch the loop).
  • The coil rotates so the field passes through it at a different angle. This is exactly how a generator works.

Lenz’s law: the meaning of the minus sign

That minus sign in Faraday’s law is not just bookkeeping. It is Lenz’s law, and it tells you which way the induced current flows.

The rule is short: the induced current always flows in the direction that opposes the change that caused it. Push a magnet in and the coil pushes back. Pull it out and the coil tries to hold it in. The coil is never on your side; it always resists whatever you are doing to the flux. This has to be true, otherwise you would get free energy out of nothing. The work you do fighting that opposition is exactly the electrical energy the coil produces.

Try one: a magnet is pulled away from a coil, north pole facing the coil, so the flux through the coil is shrinking. Which way does the induced current flow, and what does the coil try to do to the magnet?

See it for yourself

Drag the bar magnet through the coil and watch the bulb light up. Move it faster and the EMF grows; hold it still inside the coil and the bulb goes dark, because the flux has stopped changing. Flip the magnet around and the current reverses.

Interactive simulation, Faraday's Law Source: PhET Interactive Simulations, University of Colorado Boulder (CC BY 4.0)

How to actually solve one

The method is a short, repeatable recipe.

  1. Work out the flux at the start and at the end using Φ=BA\Phi = BA.
  2. Find the change in flux ΔΦ\Delta\Phi by subtracting one from the other.
  3. Divide by the time Δt\Delta t to get the rate of change.
  4. Multiply by the number of turns NN for the size of the EMF: ε=NΔΦΔt\varepsilon = N\dfrac{\Delta\Phi}{\Delta t}.

For the direction of the induced current, fall back on Lenz’s law: it flows so as to oppose whatever change you just calculated.

Lock it in with active recall

Cover the answer and say each one out loud before you flip. Rate yourself honestly — the cards you find hard come back sooner, the ones you know are spaced further out.

Active recall

Answer from memory first, then flip. Rate yourself and each card returns on a spaced schedule (1 → 3 → 7 → 16 days).

What is magnetic flux, and what is its formula when the field is perpendicular to the loop?
Write Faraday’s law for a coil of NN turns.
Why is the induced EMF zero when a coil sits in a steady, unchanging field?
What does Lenz’s law (the minus sign) tell you?
Name the three ways to change the flux through a coil and induce an EMF.
Why does Lenz’s law have to be true (link it to energy)?
Recall · Generators and AC
In a generator, when is the induced EMF greatest as the coil spins?
Recall · Transformers
Why does a transformer work on AC but not steady DC?

See the recipe in action in the Worked Examples tab, then test yourself in Try It.

Worked examples

Worked Example 1Flux growing through a coil

A coil of 5050 turns has the magnetic flux through it change from 0.0200.020 Wb to 0.0600.060 Wb in 0.100.10 s. Find the magnitude of the average induced EMF.

  1. 1

    Find how much the flux changed. Start by subtracting the old flux from the new flux.

    ΔΦ=0.060−0.020=0.040 Wb\Delta\Phi = 0.060 - 0.020 = 0.040 \text{ Wb}
  2. 2

    Faraday law says the EMF is the number of turns times how fast the flux changes. We want the magnitude, so we drop the minus sign.

    ε=NΔΦΔt=50×0.0400.10\varepsilon = N\dfrac{\Delta\Phi}{\Delta t} = 50 \times \dfrac{0.040}{0.10}
  3. 3

    Work out the division first, then multiply by the turns.

    ε=50×0.40=20 V\varepsilon = 50 \times 0.40 = 20 \text{ V}
Answer
ε=NΔΦΔt=50×0.060−0.0200.10=50×0.40=20 V\varepsilon = N\dfrac{\Delta\Phi}{\Delta t} = 50 \times \dfrac{0.060 - 0.020}{0.10} = 50 \times 0.40 = 20 \text{ V}
Worked Example 2Field switched off through a single loop

A single loop of area 0.0200.020 m2^2 sits perpendicular to a magnetic field that falls from 0.500.50 T to 00 in 0.200.20 s. Find the induced EMF.

  1. 1

    The area stays the same, so the flux changes only because the field changes. The change in flux is the area times the change in field.

    ΔΦ=A ΔB=0.020×0.50=0.010 Wb\Delta\Phi = A\,\Delta B = 0.020 \times 0.50 = 0.010 \text{ Wb}
  2. 2

    There is just one turn, so N=1N = 1. The magnitude of the EMF is the change in flux divided by the time.

    ε=ΔΦΔt=0.0100.20\varepsilon = \dfrac{\Delta\Phi}{\Delta t} = \dfrac{0.010}{0.20}
  3. 3

    Finish the division.

    ε=0.050 V\varepsilon = 0.050 \text{ V}
Answer
ΔΦ=A ΔB=0.020×0.50=0.010 Wb,ε=ΔΦΔt=0.0100.20=0.050 V\Delta\Phi = A\,\Delta B = 0.020 \times 0.50 = 0.010 \text{ Wb}, \quad \varepsilon = \dfrac{\Delta\Phi}{\Delta t} = \dfrac{0.010}{0.20} = 0.050 \text{ V}

Practice questions

Practice test

Try it yourself

6 questions, 9 marks

Choose your answers, then submit to see your score and the full worked solutions. Multiple choice is marked for you, just like Exam 2 Section A.

Q1.Magnetic flux through a flat loop is given by Φ=BA\Phi = BA when the field is perpendicular to the loop. The correct unit of magnetic flux is the:

1mark
Need a hint?
Flux is field strength times area. The tesla is the unit of field strength, not of flux.

Q2.A coil sits in a steady magnetic field that never changes. Nothing in the coil moves. The induced EMF in the coil is:

1mark
Need a hint?
An EMF is induced only when the flux through the coil changes. A steady flux induces nothing.

Q3.A coil of 100100 turns has the flux through it change by 0.0200.020 Wb in 0.500.50 s. The magnitude of the average induced EMF is closest to:

1mark
Need a hint?
Use ε=NΔΦΔt\varepsilon = N\dfrac{\Delta\Phi}{\Delta t} and watch the division.

Q4.A magnet is pushed north pole first towards a coil, increasing the flux through it. According to Lenz law, the induced current flows so that the coil:

1mark
Need a hint?
Lenz law is the minus sign in Faraday law. The induced current always opposes the change that caused it.

Q5.A coil of 200200 turns sits perpendicular to a magnetic field. The field through each turn changes from 0.300.30 T to 0.100.10 T in 0.400.40 s, and each turn has area 0.0100.010 m2^2. Find the magnitude of the average induced EMF. Show your working.

3marks

Work this on paper. The worked solution appears once you submit.

Q6.A bar magnet is dropped vertically so that it falls right through a solenoid connected to a sensitive ammeter. A current is observed while the magnet falls through the coil. Explain this observation.

2marks

Work this on paper. The worked solution appears once you submit.

VCAA 2025 Physics Exam, Section B Q10

Frequently asked questions

What is the difference between magnetic field and magnetic flux?
The magnetic field B tells you how strong the field is at a point, measured in tesla. The flux is the total amount of that field passing through a loop, measured in webers, and it depends on both the field strength and the area of the loop.
Why does the EMF only appear when the flux is changing?
A steady flux holds the charges in the coil in place, so nothing drives a current. It is the change in flux that pushes the charges around the loop. Faster change means a bigger push, which is why the EMF depends on how quickly the flux changes, not on its actual value.
What does the minus sign in Faraday's law mean?
The minus sign is Lenz's law. It tells you the induced current flows in whatever direction opposes the change that created it. If the flux is growing, the coil fights to keep it small, and if the flux is shrinking, the coil fights to keep it large.