EngineerHub.orgWhat this simulator teaches
Faraday's law is about change: a large magnetic flux produces no EMF if it is steady, while a modest flux can produce a large EMF if it changes rapidly. Lenz's law supplies the sign — the induced response opposes the change that created it.
magnetic fluxfaraday's lawlenz's lawmotional emfgeneratortransformerenergy conversioninduction braking
Select induction model6 animated learning modes
Moving magnet controls
Moving magnet
Relative motion changes linked magnetic fluxMoving magnet and coil — flux changes because geometry changes
The magnet oscillates along the coil axis. Watch the induced voltage reverse when the magnet changes from approaching to receding, and pass through zero where flux is momentarily stationary.
ℰ = −N dΦ/dt
Magnetic field / fluxInduced EMF / currentFlux linkageMechanical / source action
Four ideas behind induction
01 / Magnetic fluxFor a uniform field, Φ = BA cosθ. Flux changes if field strength, loop area or orientation changes.
02 / Faraday's lawThe induced EMF equals the negative time rate of change of total flux linkage: ℰ = −d(NΦ)/dt.
03 / Lenz's lawThe minus sign is physical: induced current creates a magnetic effect that opposes the change in flux, preserving energy conservation.
04 / Motional EMFA conductor moving through B can separate charge through q(v×B). In the rail model this gives ℰ = Bℓv.
Model assumptions & limits
The page intentionally separates textbook induction mechanisms while keeping the same sign convention and energy logic across modes. High-frequency cases are automatically shown in slow motion so the animation does not alias against the display refresh rate; the equations and reported physical frequencies are unchanged.
The magnet is represented as an axial magnetic dipole and the loop flux is calculated from the dipole vector potential. This is useful for qualitative and intermediate-distance behavior, but a real finite magnet differs close to the coil.
Where current is displayed, the electrical loop is treated as purely resistive: I = ℰ/R. Coil self-inductance is neglected, so fast transients in a real coil would be smoother and phase-shifted. In the rail mode a fixed load closes the circuit and the bar reverses ideally at the selected travel limits.
The transformer view assumes sinusoidal steady state and treats the coupling control as an educational leakage factor. Magnetizing current, winding resistance, leakage inductance and core loss are not solved explicitly.
The braking view uses a conducting rectangular loop entering and leaving a uniform-field region. It demonstrates the same energy mechanism as eddy-current braking, but it is not a full distributed eddy-current solution for a solid plate.
Background & FAQ
Not in a stationary loop merely because the field is strong. Faraday's law depends on the time derivative of flux. A constant flux gives zero transformer EMF.
Because the sign of dΦ/dt changes. Increasing flux and decreasing flux must drive opposite induced polarities if the induced magnetic response is to oppose the change.
For a coil rotating uniformly in a uniform field, linked flux varies as cosωt. Differentiating flux gives a sinωt induced EMF.
It is another manifestation of electromagnetic induction. In a moving conductor, magnetic Lorentz force q(v×B) separates charge. For moving circuits, the general EMF expression includes both electric-field and motion terms.
The induced current interacts with the magnetic field so that mechanical work is converted into electrical resistance heating. A force that aided the motion would create energy instead of conserving it.
A steady DC current produces steady flux after the transient, so the secondary Faraday EMF falls to zero. Transformers require changing flux, normally produced by AC.