Faraday's Law: EMF from a Changing Area

1 · Predict

A loop of wire sits in a fixed magnetic field, but the loop's own area oscillates (imagine it stretching and shrinking). Does this also induce an EMF, the same way a changing field strength does?

• Yes — Faraday's law only cares about the total flux Φ = BA changing, regardless of whether B or A is what's varying.
• No — only a changing field strength induces EMF, not a changing area.
• A changing area induces EMF, but through a completely different mechanism than a changing field.

2 · Set Up

1. Open the changing-flux-area preset and press Reset. The field is fixed at 0.5 T; the loop's area oscillates as A(t) = 0.025 m² × (1 + 0.35 cos(2π × 0.35Hz × t)).
2. Enable the induced-EMF readout.
3. Read the induced EMF at each listed time.

3 · Collect Data

Plot induced EMF (y-axis) against time t (x-axis) for your three readings, and sketch how it oscillates over one full period (≈2.86 s).

4 · Analyze

1. For one trial, compute EMF = −B·dA/dt = B₀·A₀·0.35·ω·sin(ωt) using B₀ = 0.5 T, A₀ = 0.025 m², ω = 2π×0.35 rad/s. Compare to the table.
2. Compare this formula's structure to the changing-flux-b experiment's. Explain why both give an EMF proportional to the product of the FIXED quantity (B here, A there) and the rate of change of the VARYING quantity.

5 · Extend

1. A classic 'sliding rod' generator changes a circuit's enclosed area by physically moving one side, inducing EMF = BLv (field × rod length × sliding speed) — a mechanical version of exactly this changing-area effect. Explain why sliding the rod faster increases the induced EMF.
2. Some microphones work by having a magnet vibrate near (or a coil's effective area change relative to) a fixed field, converting sound vibrations into a changing flux and therefore a voltage signal. Why does a louder sound (bigger vibration amplitude) produce a bigger EMF signal?

The Physics Behind This Experiment

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