Magnetic flux, Faraday's law and Lenz's law

Key ideas

Magnetic flux measures how much magnetic field passes through a loop:

$\phi = BA$

$\phi$ — the magnetic flux (weber, Wb)
$B$ — the magnetic flux density — the field strength (tesla, T)
$A$ — the area of the loop the field passes through, face-on (m²)
Faraday's law — a changing flux induces a voltage (EMF) in the loop:

$\varepsilon = -\frac{\Delta\phi}{\Delta t}$

For a coil of $N$ turns, each turn contributes, so the induced EMF is $N$ times larger.
Change the flux faster → bigger EMF. Steady flux → no EMF, no matter how strong.
Flux can change three ways: the field changes, the area changes, or the loop rotates relative to the field.
Lenz's law — the minus sign: the induced current flows in the direction whose own magnetic field opposes the change that made it.
- Push a magnet's north pole toward a coil → the coil's face becomes a north pole to repel it.
- Pull it away → the face becomes south to attract it back.
Lenz's law is conservation of energy in disguise: the induced effects resist you, so you must do work to generate electrical energy.

Worked ExampleEMF from a collapsing field

A $50$ -turn coil of area $3.0\times10^{-3}$ m² sits in a field of $0.40$ T, face-on. The field drops steadily to zero in $0.20$ s. Find the induced EMF.

Step 1 — Flux change through one turn

$\Delta\phi = \Delta B \times A = (0.40)(3.0\times10^{-3}) = 1.2\times10^{-3} \text{ Wb}$

Step 2 — Faraday's law, multiplied by the $N = 50$ turns

$\varepsilon = N\frac{\Delta\phi}{\Delta t} = 50 \times \frac{1.2\times10^{-3}}{0.20} = 0.30 \text{ V}$

Tips

For Lenz's-law directions, ask two questions in order: which way is the flux changing? then which current direction would oppose that change? Skipping straight to the second is where signs go wrong.
Quote Lenz's law as opposing the change in flux, not "opposing the field" — if the flux is decreasing, the induced current acts to maintain it.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A field of $0.25$ T passes face-on through a loop of area $0.020$ m².

Show that the flux through the loop is $5.0\times10^{-3}$ Wb.

Merit

The flux through a $200$ -turn coil falls from $8.0\times10^{-4}$ Wb to zero in $0.040$ s.

Calculate the induced EMF.

Excellence

A bar magnet is dropped, north pole first, through a horizontal coil.

Use Lenz's law to explain the direction of the induced current as the magnet approaches and as it leaves, and explain why the magnet falls slower than it would in free fall.

Magnetic flux, Faraday's law and Lenz's law

Covers AS91526

Key ideas

Magnetic flux measures how much magnetic field passes through a loop:

$\phi = BA$

$\phi$ — the magnetic flux (weber, Wb)
$B$ — the magnetic flux density — the field strength (tesla, T)
$A$ — the area of the loop the field passes through, face-on (m²)
Faraday's law — a changing flux induces a voltage (EMF) in the loop:

$\varepsilon = -\frac{\Delta\phi}{\Delta t}$

For a coil of $N$ turns, each turn contributes, so the induced EMF is $N$ times larger.
Change the flux faster → bigger EMF. Steady flux → no EMF, no matter how strong.
Flux can change three ways: the field changes, the area changes, or the loop rotates relative to the field.
Lenz's law — the minus sign: the induced current flows in the direction whose own magnetic field opposes the change that made it.
- Push a magnet's north pole toward a coil → the coil's face becomes a north pole to repel it.
- Pull it away → the face becomes south to attract it back.
Lenz's law is conservation of energy in disguise: the induced effects resist you, so you must do work to generate electrical energy.

Worked ExampleEMF from a collapsing field

A $50$ -turn coil of area $3.0\times10^{-3}$ m² sits in a field of $0.40$ T, face-on. The field drops steadily to zero in $0.20$ s. Find the induced EMF.

Step 1 — Flux change through one turn

$\Delta\phi = \Delta B \times A = (0.40)(3.0\times10^{-3}) = 1.2\times10^{-3} \text{ Wb}$

Step 2 — Faraday's law, multiplied by the $N = 50$ turns

$\varepsilon = N\frac{\Delta\phi}{\Delta t} = 50 \times \frac{1.2\times10^{-3}}{0.20} = 0.30 \text{ V}$

Tips

For Lenz's-law directions, ask two questions in order: which way is the flux changing? then which current direction would oppose that change? Skipping straight to the second is where signs go wrong.
Quote Lenz's law as opposing the change in flux, not "opposing the field" — if the flux is decreasing, the induced current acts to maintain it.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A field of $0.25$ T passes face-on through a loop of area $0.020$ m².

Show that the flux through the loop is $5.0\times10^{-3}$ Wb.

Merit

The flux through a $200$ -turn coil falls from $8.0\times10^{-4}$ Wb to zero in $0.040$ s.

Calculate the induced EMF.

Excellence

A bar magnet is dropped, north pole first, through a horizontal coil.

Use Lenz's law to explain the direction of the induced current as the magnet approaches and as it leaves, and explain why the magnet falls slower than it would in free fall.

Magnetic flux, Faraday's law and Lenz's law

Key ideas

Step 1 — Flux change through one turn

Step 2 — Faraday's law, multiplied by the N=50N = 50N=50 turns

Tips

Test yourself

Practice by grade

Magnetic flux, Faraday's law and Lenz's law

Key ideas

Step 1 — Flux change through one turn

Step 2 — Faraday's law, multiplied by the N=50N = 50N=50 turns

Tips

Test yourself

Practice by grade

Step 2 — Faraday's law, multiplied by the $N = 50$ turns

Step 2 — Faraday's law, multiplied by the $N = 50$ turns