FARADAY LOOP
Exact finite-field overlap drives Φ, ε, the full RL transient, signed magnetic force, and Wext = QR + UL on one clock.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Ideal field and loop
A rigid N-turn loop translates through a finite strip of uniform magnetic field. The field is sharp-edged, exactly zero outside, and tall enough to cover the loop; the drawn top and bottom are only diagram cropping. This is an inspectable ideal field region, not a claim that a bar magnet is uniform.
Exact overlap and flux
The linked external flux is N B times the exact rectangular overlap area. Entry grows the overlap linearly, fully enclosed is the middle branch, and exit removes it linearly. Flux stays continuous even though the ideal field gradient changes abruptly.
EMF, current, and force
The exact RL state responds to each constant EMF pulse. Its signed current drives the magnetic force I times the flux gradient, so the force arrow comes from the calculation. Inductive lag can briefly return stored energy instead of pretending the force always brakes.
One synchronized crossing
The loop now crosses the entire field on one physical clock. At 1× speed, six seconds of scene playback represents 1.5 physical seconds, or 0.25 times real-time. The loop, current arrows, force vector, live values, and all four graph cursors are the same numerical state.
Energy audit
At the just-exited endpoint, external mechanical work equals resistor heat plus the magnetic energy still stored in L. The instantaneous identity also closes from the actual force. Any residual current then decays outside the field with zero external power, converting its remaining stored energy into heat.