5.4 Electromagnetic Induction

Faraday's Law of Induction

A changing magnetic flux through a loop induces an EMF: ε = -N(dΦ_B/dt), where Φ_B = ∫B·dA. Flux can change due to a changing B-field, changing area, or changing angle between B and the loop's normal. More loops (N) or faster flux change means larger induced EMF.

Lenz's Law and the Minus Sign

The negative sign in Faraday's Law encodes Lenz's Law: the induced current flows in the direction that opposes the change in flux (creates a magnetic field fighting the change). This reflects conservation of energy — nature resists the change rather than amplifying it.

Motional EMF

A conducting rod of length L moving with velocity v perpendicular to B experiences motional EMF: ε = BLv. This arises from the magnetic force qv×B pushing charges along the rod, creating separation of charge until electric force balances magnetic force — equivalent to Faraday's law applied to a changing area.

Key terms

Faraday's Law

ε = -N(dΦ_B/dt); induced EMF equals negative the number of turns times the rate of change of magnetic flux.

Magnetic flux Φ_B

Φ_B = ∫B·dA; measures how much magnetic field passes through a surface, depends on B, area, and angle.

Lenz's Law

The induced current flows in the direction that opposes the change in flux that created it, conserving energy.

Motional EMF

ε = BLv; EMF induced in a conducting rod of length L moving with speed v perpendicular to field B.

Ways flux can change

Changing magnetic field strength B, changing area A of the loop, or changing angle between B and the loop's normal.

Try an AP-style question

The flux through a coil is Φ(t) = 3t² (Wb). What is the induced emf magnitude at t = 2 s (one turn)?

1. 12 V
2. 3 V
3. 6 V
4. 24 V