Questions: Faraday's Law and Induced EMF

Question 1

A strong permanent magnet is held perfectly still inside a closed copper loop. A student predicts this will generate a continuous current. What is wrong with this prediction?

• A. Copper is not ferromagnetic, so it cannot respond to a static magnetic field
• B. A static magnetic field produces zero induced EMF — only a changing flux can drive current
• C. The loop would need multiple turns of wire for any induction to occur
• D. The magnet must be oriented so its poles are perpendicular to the loop's plane

Answer: (B)

Faraday's law states ε = −dΦ_B/dt. A stationary magnet produces a constant flux through the loop, so dΦ_B/dt = 0 and therefore ε = 0 — regardless of field strength. It is the rate of change of flux that matters, not the flux itself. This is the central insight of Faraday's law and the most common point of confusion: a powerful static field does nothing.

Question 2

What does the negative sign in ε = −dΦ_B/dt encode?

• A. That EMF has a negative value when measured in standard SI units
• B. That the induced current flows in a direction that opposes the flux change producing it
• C. That the formula applies only when magnetic flux is decreasing
• D. That the induced electric field points opposite to the magnetic field direction

Answer: (B)

The negative sign encodes Lenz's law: the induced current creates its own magnetic field that opposes whatever change in flux caused the induction. If flux through a loop is increasing, the induced current creates a field opposing the increase; if flux is decreasing, the induced current tries to sustain it. This 'electromagnetic inertia' is not a curiosity — it is the mechanism behind regenerative braking and transformer operation.

Question 3

A very strong but perfectly stationary magnetic field through a loop will induce a larger EMF than a weak but rapidly changing field through the same loop.

• T. True
• F. False

Answer: False

EMF is determined by dΦ_B/dt — the rate of change of flux — not by the magnitude of the flux or field. A strong static field has dΦ_B/dt = 0, so it induces zero EMF. A weak but rapidly oscillating field can produce a large dΦ_B/dt and therefore a large EMF. Field strength matters only insofar as it contributes to how quickly flux changes.

Question 4

The electric field induced by Faraday's law is non-conservative — it can do net work on a charge carried around a closed loop.

• T. True
• F. False

Answer: True

Electrostatic fields are conservative: they do zero net work around any closed path (∮E⃗·dℓ⃗ = 0). The induced electric field arising from a changing magnetic flux is fundamentally different: ∮E⃗·dℓ⃗ = −dΦ_B/dt ≠ 0. This circulating field can continuously accelerate charges around a loop — exactly what a battery does with chemical energy, but here achieved through electromagnetic induction.

Question 5

Why does a rotating coil in a steady magnetic field produce alternating current rather than direct current?

Model answer: As the coil rotates, the angle between the magnetic field and the coil's normal changes continuously. The flux through the coil is Φ_B = BA cos(θ), where θ = ωt. Differentiating, dΦ_B/dt = −BAω sin(ωt), so the induced EMF ε = BAω sin(ωt) oscillates sinusoidally — positive for half a rotation, negative for the other half. This sign reversal every half-cycle is what makes the output alternating current.

The sinusoidal variation arises because the projection of the coil area onto the field direction varies as cos(ωt). To produce DC, a commutator can be used to flip the external connection every half-cycle, always presenting the positive half of the EMF waveform to the external circuit — this is how DC generators work.