Faraday's Law of Electromagnetic Induction states that the induced electromotive force (EMF) in any closed circuit is equal to:

Question

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Faraday’s law states EMF = −dΦB/dt, where the magnetic flux ΦB through a loop is ΦB = ∫ B · dA (for a uniform field, ΦB = B A cosθ).

1) Relevant knowledge points and concepts
- Magnetic flux ΦB measures how much magnetic field passes through a surface: ΦB = ∫ B · dA = B A cosθ for uniform B.
- Faraday’s law (integral form): EMF = ∮ E · dl = − dΦB/dt. The minus sign is Lenz’s law (induced EMF opposes the change).
- A change in flux can come from changes in B, area A, or orientation θ.

2) Step-by-step reasoning
- Start from the integral form: EMF = ∮ E · dl.
- Maxwell–Faraday relation gives ∮ E · dl = − d/dt ∫ B · dA.
- Therefore the induced EMF equals the negative time derivative of the magnetic flux through the closed circuit.

3) Intermediate/calculation steps (example)
- For a circular loop of fixed area A in a uniform B perpendicular to the plane (θ = 0): ΦB = B A.
- If B varies with time: EMF = − d/dt (B A) = − A (dB/dt).
- If area changes but B constant: EMF = − B (dA/dt).
- If orientation changes: EMF = − B A (d/dt cosθ) = + B A sinθ (dθ/dt) (sign per Lenz’s law).

4) Why the correct answer is correct
- The law explicitly ties EMF to the rate of change of magnetic flux (ΦB), not directly to just the magnetic field magnitude. Flux incorporates field strength, area, and angle; any of these changing produce EMF. The precise statement is the time derivative of magnetic flux.

5) Why other options are incorrect
- “Rate of change of magnetic field in the circuit”: incomplete — EMF depends on flux change (field × area × orientation), so changing B alone describes only one possible cause.
- “Rate of change of electric field in the circuit”: incorrect — changing electric fields relate to displacement current, not the induced EMF described by Faraday.
- “Rate of change of electric flux through the circuit”: incorrect — Faraday’s law involves magnetic flux, not electric flux.

6) Conclusion
This confirms the correct choice: “The rate of change of magnetic flux through the circuit.”

Faraday's Law of Electromagnetic Induction states that the induced electromotive force (EMF) in any closed circuit is equal to:单项选择题

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