Which quantity determines the magnitude of the induced emf according to Faraday's law?

Which quantity determines the magnitude of the induced emf according to Faraday's law?

• A. The rate of change of electric flux
• B. The rate of change of magnetic flux
• C. The product of turns and the rate of change of magnetic flux
• D. The product of turns and the rate of change of electric flux

Answer: (C)

Faraday’s law ties the induced electromotive force to how quickly magnetic flux through a circuit is changing. For a coil with N turns, the total emf is proportional to both the number of turns and the rate at which the magnetic flux through the coil changes. The magnitude is given by |ε| = N |dΦ_B/dt|. This is why the correct choice combines the turns with the rate of change of magnetic flux. The rate of change of electric flux isn’t what governs induction in this context, so that part doesn’t fit. And using the rate of change of magnetic flux alone would omit the amplification from multiple turns. So multiplying the rate of change of magnetic flux by the number of turns captures the proper quantity that determines the induced emf.

Faraday’s law ties the induced electromotive force to how quickly magnetic flux through a circuit is changing. For a coil with N turns, the total emf is proportional to both the number of turns and the rate at which the magnetic flux through the coil changes. The magnitude is given by |ε| = N |dΦ_B/dt|. This is why the correct choice combines the turns with the rate of change of magnetic flux.

The rate of change of electric flux isn’t what governs induction in this context, so that part doesn’t fit. And using the rate of change of magnetic flux alone would omit the amplification from multiple turns. So multiplying the rate of change of magnetic flux by the number of turns captures the proper quantity that determines the induced emf.