Electromagnetism
Changing loop area (ΔA)
Press Play — loop area breathes; EMF follows −dΦ/dt.
Changing loop area (ΔA) — interactive Electromagnetism simulation. Press Play — loop area breathes; EMF follows −dΦ/dt. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Flux from area change
Press Play — loop area breathes; EMF follows −dΦ/dt.
With uniform B held constant, changing loop area A modulates flux Φ = BA. Press Play — the loop breathes and EMF = −dΦ/dt appears whenever area changes. Compare this case (dA/dt) with the changing-B preset (dB/dt) to see the same law from two causes.
- EMF = −dΦ/dt
- Φ = BA
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Time t (s)
What you measure:
- Induced EMF (mV)
How the investigation runs
- 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)).
- Enable the induced-EMF readout.
- Read the induced EMF at each listed time.
Governing equation
Faraday's Law (Changing Area) — Φ = B·A
Magnetic flux through a loop is Φ = BA. When A changes in time (B fixed), Faraday's law still applies: EMF = −dΦ/dt = −B·dA/dt — the same law, just with the roles of B and A swapped.
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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.
- 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?
- AP Physics 2 — Unit 12: Magnetism and Electromagnetism
- AP Physics C: Electricity and Magnetism — Unit 13: Electromagnetic Induction
- IB Physics — D.4 Induction
- General High School Physics — Magnetism & electromagnetism
- NGSS High School Physics — Electric current and magnetic fields
- Welcome to Changing Flux Area
- Select the loop
- Press Play
- EMF from changing area
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.