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Difficulty: MediumFundamentals of Electromagnetism and Induction

In an electromagnetic generator, a coil of wire rotates through a uniform magnetic field. If the rotational speed of the coil is doubled while all other physical parameters remain constant, what happens to the peak induced electromotive force (voltage)?

  1. A
    It remains unchanged, because peak voltage is determined solely by the electrical resistance of the wire.
  2. It doubles, because the rate of cutting magnetic lines of force is doubled.Answer
  3. C
    It is halved, because higher rotational speeds reduce the amount of direct current flowing into the coil.
  4. D
    It drops to zero, because alternating voltage can only be induced at low, steady frequencies.

Answer

The peak induced electromotive force doubles because the rate of cutting magnetic lines of force is doubled.
The peak electromotive force (EMF) induced in a rotating coil is directly proportional to the strength of the magnetic field, the number of turns in the coil, and the velocity at which the coil cuts through the magnetic flux lines. Doubling the rotational speed doubles the rate of flux cutting per unit time, which doubles the peak induced voltage.

Step-by-Step Solution

1
Identify the fundamental physical relationship governing induced voltage.
According to Faraday's law of electromagnetic induction, induced voltage is directly proportional to the rate of change of magnetic flux: E=−NΔΦΔt\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}.
Establishes the governing formula relating coil movement to generated electromotive force.
2
Determine the effect of doubling the coil's rotational speed on the rate of flux change.
Doubling the rotational speed doubles the velocity at which the conductors pass through the magnetic field lines, doubling ΔΦΔt\frac{\Delta \Phi}{\Delta t}.
Connects rotational mechanical speed directly to the rate of cutting magnetic flux lines.
3
Calculate the resulting change in peak induced voltage.
Since the magnetic field strength and the number of turns (NN) remain unchanged, doubling the rate of flux cutting doubles the peak induced voltage ( extEMFnew=2×EMForiginal\ ext{EMF}_{\text{new}} = 2 \times \text{EMF}_{\text{original}}).
Applies the proportional factor to determine the final output voltage.

Key Concept

Faraday's Law of Induction and rate of flux cutting
Estimated Time:1m 0s
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Topics

Fundamentals of Electromagnetism and Induction

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