Physic Labs

Electricity and magnetism

Electromagnetic induction, Faraday–Lenz law

Watch the magnetic flux through a coil change with field strength and rotation angle. Verify ΦB=BAcos⁡θ\Phi_B = BA\cos\theta and the Faraday–Lenz law E=−N dΦB/dt\mathcal{E} = -N\,d\Phi_B/dt via the sign and magnitude of the induced emf.

High school

Equipment

  • Virtual loop/coil in a uniform magnetic field, projected 3D on canvas
  • Slider for magnetic field level
  • Slider for the loop's angle / rotation rate
  • Induced-emf graph and Pause button

Procedure

  1. Change flux via the rotation angle

    Hold the field fixed and drag the angle slider to rotate the loop: flux is maximal when the loop plane is perpendicular to the field, zero when parallel. Read values on the graph and compare with ΦB=BAcos⁡θ\Phi_B = BA\cos\theta.

  2. Check the sign of the emf

    Raise then lower the field slider and watch the sign of E\mathcal{E} reverse: the induced current opposes the change in flux — Lenz's rule, i.e. the minus sign in E=−N dΦB/dt\mathcal{E} = -N\,d\Phi_B/dt. Press Pause to read the exact moment of sign reversal.

  3. Vary the rate of flux change

    Raise the angle/rate slider so the flux swings faster at the same amplitude: the emf amplitude must grow in proportion to ∣dΦB/dt∣|d\Phi_B/dt|. Before dragging, predict whether the E(t)\mathcal{E}(t) trace becomes wider or taller, then compare.

Simulation

Experiment history

On 29 August 1831, Michael Faraday discovered electromagnetic induction: current appeared in a second coil wound on an iron ring only while the first coil's current was switched on or off — that is, while flux changed. Joseph Henry in Albany found the same effect at nearly the same time but published later. In 1834 Heinrich Lenz stated the rule for the induced current's direction; in 1845–1846 Franz Neumann gave the quantitative form E=−dΦB/dt\mathcal{E} = -d\Phi_B/dt. James Clerk Maxwell incorporated induction into the field equations in 1861–1865. The principle underlies every generator and transformer today.

Related physicists

Michael FaradayHeinrich LenzJames Clerk MaxwellJoseph Henry

Related library topics

Electromagnetic induction, Faraday–Lenz law