Whenever magnetic flux linked with a coil changes, induced EMF in circuit will change

Question

BlackTom AI · Accepted Answer

Faraday's law states that the induced emf in a coil is proportional to the negative rate of change of magnetic flux linkage: emf = −N dΦ/dt (N = number of turns). Lenz's law gives the sign (direction) of that emf so it opposes the change in flux.

1) Relevant knowledge points and concepts
- Magnetic flux Φ through a coil and flux linkage NΦ.
- Faraday’s law: emf = −N (dΦ/dt). Emf is nonzero only when dΦ/dt ≠ 0.
- Lenz’s law: induced emf acts to oppose the change that produced it.

2) Step-by-step reasoning
- If the flux Φ(t) varies with time, compute dΦ/dt. Whenever dΦ/dt ≠ 0, emf ≠ 0.
- If flux becomes time-independent (dΦ/dt = 0), induced emf becomes zero immediately.

3) Calculations / intermediate steps (example)
- Example: N = 100 turns, suppose Φ(t) increases linearly at 0.001 Wb/s so dΦ/dt = 0.001 Wb/s.
- emf = −N dΦ/dt = −100 × 0.001 = −0.1 V. As long as that rate continues, the coil has −0.1 V induced.
- If the flux rate drops to zero (flux stops changing), dΦ/dt = 0 ⇒ emf = 0 V.

4) Why the correct answer is correct
- The formula shows the induced emf exists for exactly the duration that the flux is changing. There is no intrinsic “short” or “long” duration in the law—only whether dΦ/dt is nonzero. Thus the correct description is “as long as change in flux.”

5) Why other options are incorrect
- a. “for a short time” — too restrictive; the change might persist indefinitely or for any duration.
- b. “forever” — incorrect because if the flux stops changing, emf ceases.
- d. “for a long time” — vague and incorrect; duration depends on how long the flux changes, not an inherent “long” timescale.

6) Conclusion
Therefore the induced emf will be present as long as the magnetic flux through the coil is changing. This matches option c.

Whenever magnetic flux linked with a coil changes, induced EMF in circuit will change单项选择题

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