Induced EMF from changing flux: A 250-turn coil is in a magnetic field where flux changes at 8 Wb/s. Find the induced voltage across the coil.

Introduction / Context:
Faraday's law of electromagnetic induction states that a changing magnetic flux linking a coil induces an electromotive force (EMF) proportional to both the rate of change of flux and the number of turns. This principle underpins transformers, generators, and many sensors.

Given Data / Assumptions:

• Number of turns, N = 250.
• Rate of change of flux, d(phi)/dt = 8 Wb/s (assumed uniform linkage of all turns).
• Ideal conditions: negligible resistance and leakage for EMF magnitude calculation.

Concept / Approach:

Induced EMF magnitude is given by E = N * (d(phi)/dt). Polarity is determined by Lenz's law, but only magnitude is asked here. Units are consistent: Wb/s times turns gives volts.

Step-by-Step Solution:

Verification / Alternative check:

Sanity check: 10 Wb/s with 200 turns would give 2,000 V; here 8 * 250 produces exactly the same magnitude, confirming the arithmetic.

Why Other Options Are Wrong:

3,125 V and 1,000 V are incorrect products. 31.25 V is much too small (confuses division). 250 V would correspond to 1 Wb/s, not 8 Wb/s.

Common Pitfalls:

Mixing up flux and flux density, or forgetting that all turns must be linked by the changing flux for the simple formula to apply.

Final Answer:

2,000 V