Three ways to change the flux.

A loop in a field with Φ = NBA cos θ plotted against time and the emf −N dΦ/dt below it, changed by B, by area or by angle.

Show a ten-times stronger steady field still gives zero emf, then ramp 0.10 T at 45° to zero through a 10 cm loop so the emf reads 1.0 mV (≈0.71 s)

Expecting an emf from a strong steady field; using sin θ with θ from the normal.

• Faraday's law: an emf is induced in a circuit whenever the magnetic flux through it changes, and the size of the emf equals the rate of change of flux: ε = −dΦB/dt.
• The minus sign fixes the direction of the emf (Lenz's law, next section).
• For a closely wound coil of N turns, each turn links the same flux, so ε = −N dΦB/dt. More turns give more emf.
• Experiment 6.3 explained: pressing the key makes the current, and so the flux through the other coil, rise quickly; a steady current means steady flux and no emf; releasing the key makes the flux fall, giving an emf the other way.
• Example 6.2: a 10 cm square loop of resistance 0.5 Ω has a 0.10 T field at 45° to its normal. The field falls steadily to zero in 0.70 s. Initial flux = 0.1 × 10⁻² × cos 45° = 10⁻³/√2 Wb, so ε = 1.0 mV and I = 2 mA.
• The earth's field also threads such a loop, but it is steady over the experiment, so it induces nothing.
• Example 6.3: a 500-turn coil of radius 10 cm and resistance 2 Ω faces the earth's horizontal field of 3.0 × 10⁻⁵ T and is turned through 180° in 0.25 s. The flux per turn goes from +3π × 10⁻⁷ to −3π × 10⁻⁷ Wb, so the average emf is about 3.8 × 10⁻³ V and the current 1.9 × 10⁻³ A.
• Switching a large electromagnet on or off can induce emfs large enough to damage sensitive instruments close by.

Teaching this idea? Put the simulation on your own page or LMS with this code.