6.1 Electromagnetic Induction

Magnetic Flux

Magnetic flux through a surface is Φ_B = ∫B·dA, measuring how much magnetic field passes through an area. It depends on field strength, area, and the angle between B and the area's normal vector. Flux is maximized when B is parallel to the normal and zero when B is perpendicular to it (parallel to the surface).

Faraday's Law

Faraday's Law states that a changing magnetic flux through a loop induces an EMF: ε = -dΦ_B/dt. This EMF can drive a current if the loop is part of a closed circuit. Flux can change by varying B, the area of the loop, or the angle between them — any of these induces EMF.

Lenz's Law and Direction

Lenz's Law gives the negative sign in Faraday's Law: the induced current opposes the change in flux that created it. This reflects conservation of energy — the induced current creates its own magnetic field fighting the original change, requiring external work to maintain the change in flux.

Key terms

Magnetic flux (Φ_B)

Φ_B = ∫B·dA; measures the amount of magnetic field passing through a surface, depending on field strength, area, and angle.

Faraday's Law

ε = -dΦ_B/dt; a changing magnetic flux through a loop induces an EMF.

Lenz's Law

The induced current flows in a direction that opposes the change in magnetic flux that created it (conservation of energy).

Ways to change flux

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

Why induced current opposes flux change

If it aided the change instead, energy would be created from nothing, violating conservation of energy.

Try an AP-style question

A 50-turn coil of area 0.02 m² sits in a field that changes from 0.1 T to 0.5 T in 0.2 s. What is the average emf?

1. 0.04 V
2. 2 V
3. 20 V
4. 0.1 V