Questions: Faraday's Law of Electromagnetic Induction

Question 1

A bar magnet is held perfectly stationary inside a coil of wire. What is the induced EMF in the coil?

• A. Maximum — the magnetic flux through the coil is at its highest
• B. Zero — there is no change in flux, so Faraday's law gives ε = −dΦ/dt = 0
• C. Proportional to the magnetic field strength of the magnet
• D. Proportional to the number of turns in the coil

Answer: (B)

Faraday's law states ε = −dΦ_B/dt. A stationary magnet produces constant magnetic flux — dΦ/dt = 0, so EMF = 0 and no current flows. This directly attacks the most common misconception: that the presence of a magnetic field induces current. It is the *change* in flux, not the flux itself, that drives induction. The moment the magnet moves, dΦ/dt becomes nonzero and EMF appears.

Question 2

A generator coil rotating at constant speed in a uniform magnetic field produces maximum EMF at the instant when:

• A. The coil face is perpendicular to the field — maximizing flux through the coil
• B. The coil face is parallel to the field — flux is zero but changing at its fastest rate
• C. The coil is halfway between the two extreme positions — flux and rate of change are both moderate
• D. Rotation stops momentarily at the peak position — flux is maximum and stable

Answer: (B)

EMF = −dΦ/dt, not EMF = −Φ. When the coil face is perpendicular to the field (Φ = BA, maximum), the rate of change of flux is actually zero — the coil momentarily isn't changing how much field passes through it. When the coil face is parallel to the field (Φ = 0), the coil crosses the 'equator' of its rotation and flux changes at its fastest rate — dΦ/dt is maximum, giving maximum EMF. This counterintuitive result is fundamental to understanding AC generators.

Question 3

Lenz's law, encoded in the negative sign of Faraday's law, is a consequence of energy conservation: you must do work against the induced field to change the magnetic flux.

• T. True
• F. False

Answer: True

Yes. If the induced EMF reinforced rather than opposed the flux change, you could move a magnet into a coil and the resulting current would pull the magnet in even faster, generating electrical energy without any input work — a perpetual motion machine. The opposition expressed by Lenz's law ensures that you must do work to change the flux, satisfying energy conservation. The negative sign is not a mere convention; it encodes a physical constraint.

Question 4

The direction of the induced current in a loop is generally the same, regardless of whether the magnetic flux through the loop is increasing or decreasing.

• T. True
• F. False

Answer: False

Lenz's law states that the induced current opposes the *change* in flux, so direction depends entirely on whether flux is increasing or decreasing. If flux is increasing, the induced current creates a magnetic field opposing the increase — one current direction. If flux is decreasing, the induced current tries to maintain it — the opposite direction. A magnet approaching a coil and the same magnet receding produce opposite current directions in the coil.

Question 5

Why does a stationary magnet inside a coil produce no current, while a moving magnet produces current? What does this reveal about the true content of Faraday's law?

Model answer: Faraday's law states ε = −dΦ_B/dt: only a *change* in magnetic flux induces EMF. A stationary magnet creates constant flux through the coil — the field is present but not changing, so dΦ/dt = 0 and EMF = 0. When the magnet moves, the amount of magnetic flux passing through the coil changes with time, producing a nonzero dΦ/dt and therefore a nonzero EMF. This reveals that induction is fundamentally about flux changing over time, not about the presence or strength of a field at any moment.

The distinction matters enormously in applications. A transformer works because alternating current continuously changes the magnetic flux in its iron core, inducing EMF in the secondary coil — DC would produce constant flux and no induction. A microphone works because sound waves vibrate a coil in a magnetic field, changing flux and generating a signal proportional to the sound.