A single-turn coil of area 0.01 m² rotates at ω = 10 rad/s in B = 0.5 T. What is the peak EMF?

You can work it out this way: use ε_peak = NBAω with N = 1.

What physical law does Lenz's Law ultimately conserve?

You can work it out this way: think about what would happen if induced current aided the flux change.

If the number of turns N is doubled, how does the peak EMF change?

You can work it out this way: look at the formula ε_peak = NBAω.

Pro 🔒~30 min

Electromagnetic Induction

See how changing magnetic flux generates EMF — Faraday's and Lenz's Laws in action

How it works

Electromagnetic Induction demonstrates a key principle: Faraday's Law states that the induced EMF in a coil equals the negative rate of change of magnetic flux through it: ε = −N dΦ/dt. Faraday's Law states that the induced EMF in a coil equals the negative rate of change of magnetic flux through it: ε = −N dΦ/dt. For a coil of N turns and area A rotating at angular velocity ω in field B, the flux varies as Φ = BA cos(ωt), giving a peak EMF of NBAω. Lenz's Law determines the polarity of the induced EMF: it always opposes the change that caused it, which is a direct statement of energy conservation.

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Step-by-step

Use the B field and angular velocity sliders to change the EMF waveform and watch the real-time graph.
Unlock Pro mode to vary coil turns and area, then verify that peak EMF scales linearly with each parameter.

Key formulas

$\Phi = B \cdot A \cdot \cos(\theta)$ Magnetic Flux
$\varepsilon = -N\frac{d\Phi}{dt}$ Faraday's Law of Induction
$\varepsilon = NBA\omega\sin(\omega t)$ Peak EMF for rotating coil
$\text{Lenz's Law: induced current opposes change in flux}$ Direction of induced current

Frequently asked questions

A single-turn coil of area 0.01 m² rotates at ω = 10 rad/s in B = 0.5 T. What is the peak EMF?: You can work it out this way: use ε_peak = NBAω with N = 1.
What physical law does Lenz's Law ultimately conserve?: You can work it out this way: think about what would happen if induced current aided the flux change.
If the number of turns N is doubled, how does the peak EMF change?: You can work it out this way: look at the formula ε_peak = NBAω.