Induction conditions: for a stationary conductor placed in a stationary (unchanging) magnetic field, what is the induced voltage across the conductor?

Introduction / Context:Induced voltages require change—either motion relative to a magnetic field or a time-varying magnetic field. This question probes the special case where both the conductor and the magnetic field are stationary.

Given Data / Assumptions:

• The conductor does not move (velocity v = 0).
• The magnetic field is constant in time and space (dB/dt = 0).
• No change in flux linkage with the conductor occurs.

Concept / Approach:Faraday’s law indicates induced emf is related to the time rate of change of magnetic flux linkage. Motional emf requires nonzero velocity v across B (e = B * l * v). Transformer emf requires time-varying flux (e ∝ dΦ/dt). With both v = 0 and dΦ/dt = 0, there is no mechanism to produce an induced voltage, so the induced voltage is zero.

Step-by-Step Solution:

Verification / Alternative check:An experiment with a stationary wire and a permanent magnet at rest shows no measurable emf; moving either the wire or the magnet produces a measurable voltage, confirming the need for change.

Why Other Options Are Wrong:“Usually very large”: contradicts the requirement for motion or time variation.

“Varies with time”: no time variation exists in this setup.

“Depends on field strength”: field strength alone without motion or change does not induce a voltage across a stationary conductor.

Common Pitfalls:Assuming a strong static magnet automatically induces emf; confusing static magnetic force effects with induction requirements.

Final Answer:equals 0 V