Electromagnetic induction: a straight conductor cuts magnetic flux lines at some rate. Evaluate the claim that the induced electromotive force (emf) is directly proportional to the rate at which flux is cut (i.e., the time rate of change of magnetic flux linkage).

Introduction / Context:
Induction is one of the bedrock principles of electrical engineering. When a conductor experiences a changing magnetic environment, an electromotive force (emf) is produced. This question asks whether the induced emf is directly proportional to the rate at which magnetic flux is cut by the conductor, which is a practical phrasing of Faraday’s law.

Given Data / Assumptions:

• The conductor and magnetic field are arranged so that the conductor cuts magnetic flux lines (either by motion or by a time-varying field).
• Lenz’s law establishes the polarity opposing the causative change.
• We neglect parasitic capacitances and nonlinear magnetic effects for first-order reasoning.

Concept / Approach:
Faraday’s law states that induced emf, e_ind, is proportional to the negative time derivative of the magnetic flux linkage. For a single conductor moving with velocity v across a uniform field B and conductor length l, the motional form is e_ind = B * l * v. More generally, e_ind = d(lambda)/dt, where lambda is flux linkage. Both expressions show a direct proportionality to the rate of cutting or the rate of change of flux linkage.

Step-by-Step Solution:

Verification / Alternative check:
Doubling conductor speed v or doubling field B doubles the induced emf, confirming the direct proportionality and matching experiment.

Why Other Options Are Wrong:
Incorrect: contradicts Faraday’s law.

True only when resistance is zero: resistance affects current, not the proportionality of induced emf to the rate of change of flux.

True only for AC fields: a moving conductor in a steady DC field also induces emf; AC is not required.

Common Pitfalls:
Confusing induced emf with induced current (the latter also depends on circuit resistance/impedance). Assuming flux must be sinusoidal; any time rate of change qualifies.

Final Answer:
Correct