Electromagnetism · Free game
Induction Racer
Drag the magnet through the coil. Your drag speed is dΦ/dt — keep the induced voltage inside the green band, and feel Lenz’s law drag back.
Sweep the magnet through the coil and hold 5–15 V for 2.5 s.
First Pass ready. Sweep the magnet through the coil and hold 5–15 V for 2.5 s.
Prefer not to drag? Hold a button, or focus the play area and hold ← →. Enter starts a run.
How the physics works
- Simple definition
- Electromagnetic induction turns a changing magnetic flux into a voltage: the faster the flux linkage changes, the bigger the induced e.m.f.
- Example
- Thrust a magnet into a coil quickly and the meter kicks hard; ease the same magnet in slowly and it barely twitches — same flux change, different rate.
The e.m.f. is the rate of change of flux linkage. Stop the magnet anywhere — even dead inside the coil, where the flux is greatest — and the meter reads exactly zero.
The magnet gives Φ(x) = B₀A·a³/(x² + a²)^3/2, drawn under the track with B₀ = 0.42 T, A = 6 × 10⁻³ m² and a = 0.06 m. Your voltage is the tangent to that curve times your speed, so it vanishes at the centre where the curve is flat.
Lenz’s law: the induced current I = ε/R opposes the change, so it pushes back on you. The mechanical power you spend against it, F·v, is exactly ε²/R — the power the load receives.
Every time you turn around, ε changes sign. Spin that same coil instead of sliding it and you get ε = NBAω sin ωt — a generator. That, and the transformer that follows it, are in the Generators & Transformers lesson.
The magnet is an on-axis dipole and the coil is a point along the track; bearing friction is a small constant plus a viscous term. Your pointer holds the magnet through a stiff, damped spring, so the gap between the gold grip dot and the magnet is Lenz braking you can see. The dashed “peak” line on the voltmeter previews the |ε| your current speed would reach at the steepest part of the flux curve — if it sits above the red breaker line, this pass will trip it. Everything — flux, e.m.f., current, force — comes straight from the definitions, integrated at 240 steps per second.