Electromagnetism
Changing magnetic flux (ΔB)
Press Play — B oscillates, Φ(t) and EMF(t) trace on the graph.
Changing magnetic flux (ΔB) — interactive Electromagnetism simulation. Press Play — B oscillates, Φ(t) and EMF(t) trace on the graph. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Faraday's law
Press Play — B oscillates, Φ(t) and EMF(t) trace on the graph.
Faraday's law: EMF = −dΦ/dt when magnetic flux Φ = BA through a loop changes. Here B oscillates while area A stays fixed, so Φ(t) follows B(t). Press Play — the graph traces Φ and induced EMF; EMF peaks when |dB/dt| is largest, not when B itself is maximum.
- 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 magnetic field whose strength oscillates in time (the loop's area stays fixed). Does an EMF appear in the loop even though the loop itself isn't moving?
Predictions to weigh
- No — EMF requires physical motion of the loop or field source.
- Yes — Faraday's law says a changing flux induces an EMF, even in a stationary loop, as long as the field itself is changing.
- EMF only appears if the loop is moving through the field.
Variable roles
What you set:
- Time t (s)
What you measure:
- Induced EMF (mV)
How the investigation runs
- Open the changing-flux-b preset and press Reset. The loop's area is fixed at 0.02 m²; the field oscillates as B(t) = 0.6 T × (1 + 0.5 sin(2π × 0.4Hz × t)).
- Enable the induced-EMF readout.
- Read the induced EMF at each listed time.
Governing equation
Faraday's Law (Changing Field) — Φ = B·A
Magnetic flux through a loop is Φ = BA. When B changes in time (A fixed), Faraday's law gives an induced EMF = −dΦ/dt = −A·dB/dt — proportional to the loop's area and the field's rate of change.
What the printable worksheet asks students to work out
- For one trial, compute EMF = −A·dB/dt = −A·B₀·0.5·ω·cos(ωt) using A = 0.02 m², B₀ = 0.6 T, ω = 2π×0.4 rad/s. Compare to the table.
- Explain why the induced EMF is proportional to how FAST the field is changing (dB/dt), not to the field's instantaneous value — the EMF can be large even when B itself is near its average value, if B is changing quickly there.
Where this shows up beyond the lab
- This is the basic principle behind an AC generator: rather than changing B directly, a generator rotates a loop through a fixed field, which changes the flux just as effectively. Explain why generator design usually rotates the coil instead of oscillating the magnet.
- The negative sign in EMF = −dΦ/dt (Lenz's law) means the induced current opposes the change that caused it. Explain what 'opposing the change' means physically for a loop in an increasing field versus a decreasing field.
- 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 B
- Select the loop
- Press Play
- EMF from changing B
- 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.