Electromagnetism
Faraday–Lenz (ΔB + ΔA)
Both B and area change — compare Φ and EMF curves.
Faraday–Lenz (ΔB + ΔA) — interactive Electromagnetism simulation. Both B and area change — compare Φ and EMF curves. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Faraday–Lenz law
Both B and area change — compare Φ and EMF curves.
When both B and loop area vary, Φ = BA changes from two contributions. Lenz's law: the induced EMF (and current) oppose the flux change that caused them. Press Play and compare Φ(t) with EMF(t) — note the EMF sign flips to fight increasing vs decreasing flux.
- EMF opposes ΔΦ
- 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's area AND the magnetic field through it are both oscillating simultaneously. Can you still find the induced EMF by simply adding the two separate effects (changing B alone, changing A alone) together?
Predictions to weigh
- No — you need the full product rule d(BA)/dt = A·dB/dt + B·dA/dt, which is more than just adding the two separate EMFs.
- Yes — you can just add the changing-flux-b and changing-flux-area EMF formulas together.
- You multiply the two separate EMF formulas together.
Variable roles
What you set:
- Time t (s)
What you measure:
- Induced EMF (mV)
How the investigation runs
- Open the faraday-lenz preset and press Reset. Both B(t) and A(t) oscillate: B₀ = 0.45 T, A₀ = 0.018 m², at 0.5 Hz.
- Enable the induced-EMF readout.
- Read the induced EMF at each listed time.
Governing equation
Faraday's Law (Product Rule) — Φ = B·A
When both B and A change with time, Faraday's law requires the full product rule: EMF = −d(BA)/dt = −(A·dB/dt + B·dA/dt). Each term captures one factor's contribution while the other is held at its instantaneous value.
What the printable worksheet asks students to work out
- For one trial, compute B(t) = B₀(1 + 0.5sin(ωt)), A(t) = A₀(1 + 0.35cos(ωt)), B'(t) = B₀·0.5ω·cos(ωt), A'(t) = −A₀·0.35ω·sin(ωt), then EMF = −(A·B' + B·A') using B₀ = 0.45 T, A₀ = 0.018 m², ω = 2π×0.5 rad/s. Compare to the table.
- Explain why the product rule d(BA)/dt = A·dB/dt + B·dA/dt is exactly the right tool here — flux is a PRODUCT of B and A, and calculus's product rule (not simple addition) tells you how a product's rate of change depends on both factors changing together.
Where this shows up beyond the lab
- Compare this experiment's EMF values to changing-flux-b's and changing-flux-area's at similar times. Explain why you can't simply predict this combined result by adding the other two experiments' EMF values at the same time, even though all three use the product rule underneath.
- A transformer's changing flux comes from a changing current in one coil (which changes B), not from any moving parts (A is fixed there). Explain why the faraday-lenz experiment's combined-change scenario is more general than what a stationary transformer actually needs.
- 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
- Can you just add them?
- Isolate the field
- Capture the flux
- Open the data
- Explain your evidence
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.