Questions: Faraday's Law of Electromagnetic Induction

Question 1

A circular wire loop sits in a uniform magnetic field. An EMF is induced in the loop when...

• A. The field is very strong
• B. The magnetic flux through the loop is changing
• C. The loop is oriented parallel to the field
• D. Current is already flowing in the loop

Answer: (B)

Faraday's law states EMF = −dΦ_B/dt — only a changing flux induces an EMF. A strong but constant field produces no EMF at all. Flux can change because B changes in magnitude, because the loop's area changes, or because the angle between B and the loop's normal changes.

Question 2

A strong, steady magnetic field passing through a conducting loop induces a large EMF in that loop.

• T. True
• F. False

Answer: False

EMF = −dΦ_B/dt — it is the rate of change of flux that matters, not the magnitude. A constant field, however strong, produces dΦ_B/dt = 0 and therefore zero EMF. This is why transformers require alternating current: a DC source produces a static field that induces nothing in the secondary coil.

Question 3

The negative sign in Faraday's law (EMF = −dΦ_B/dt) is associated with Lenz's law. What does this sign physically mean?

Model answer: The induced EMF drives a current whose own magnetic field opposes the change in flux that caused the induction — the induced effect resists the change.

Lenz's law is energy conservation in disguise. If the induced EMF reinforced the change in flux instead of opposing it, the growing EMF would increase the flux, which would increase the EMF further — a runaway process requiring no energy input. The negative sign prevents this by ensuring external work must be done to maintain the changing flux, consistent with conservation of energy.