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Physics
Electromagnetic induction
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Move a magnet or rotate a coil. Compare magnetic flux, emf and current over time.
Drag the magnet along x; click switch K to open or close the circuit; drag the background to orbit. The needle of meter G swings right for I > 0 and left for I < 0. Equivalent controls are in the left panel.
Preparing the 3D scene…
Φ0.270µWbε0.000mVI0.000µA
Time traces
Separate flux, emf and current plots share a time axis. Blue is the current trial and its dot the latest sample; dashed lines are saved trials of the same experiment.
━ Current
Φ (µWb)±0.011
ε (mV)±0.001
I (µA)±0.001
0.0 sTime →1.0 s
Start a trial to record a trace.
Latest samples
| t (s) | Φ (µWb) | ε (mV) | I (µA) |
|---|
Drag the magnet through the coil or start a trial, then watch the needle of meter G.
Total resistance
Changing the configuration or setting position/angle stops motion and starts a fresh trace. ε reflects the ongoing motion only.
- Mean normal field B̄⊥
- 13.42 µT
- Flux Φ per turn
- 0.270 µWb
- Induced emf ε
- 0.000 mV
- Current I
- 0.000 µA
- Time
- 0.00 s
Flux is constant in time: ε = 0 and I = 0. A magnetic field alone does not imply induction.
I = 0: the needle rests at 0, no current
Keep up to two trials. Change one condition and repeat the same journey to compare.
No saved trials yet.
Peaks cover the recorded part of a journey; compare equal motion intervals.
n points along +x in the magnet experiment. Positive I runs from +y toward +z: counterclockwise when viewed from +n toward the coil centre. Negative ε and I have the opposite sense.
B̄⊥ is the mean normal field (T); Φ = B̄⊥S (Wb) is flux per turn; ε = −d(NΦ)/dt (V). B̄⊥ is not the field at the centre.
Flux linkage NΦ: 26.99 µWb·turns
ε = −N (dΦ/dx) v
Model notes
- The magnet is a softened axial dipole distribution: length 12 cm, smoothing radius 2.5 cm, moment 1 A·m². The thin coaxial coil has equal flux in every turn. The drawn helix represents the turns; it does not show all N turns.
- Φ is flux per turn and ε = −N·dΦ/dt. B̄⊥ = Φ/S is the mean normal field over the coil area, not the field at its centre. The rotating-coil experiment uses a uniform external field; θ is measured from +x to n.
- Total resistance is set independently of turns and radius to isolate each factor. A closed, purely resistive circuit obeys I = ε/R; an open circuit has I = 0 even when emf is nonzero. Self-inductance, capacitance, eddy currents, heating, mechanical reaction and feedback on the source field are omitted.
- Changing configuration, polarity or the initial position/angle prepares a new experiment; that transition is not simulated. Direct dragging uses pointer speed and stops on release. At most 480 samples and two comparison trials are retained, for this visit only.
- Field lines are computed from the same softened field model as the flux, follow B, and continue inside the opaque magnet. Each drawn line carries the same amount of flux, so lines crowd where B is strong; a line turns cyan while it threads the coil. Only four levels near the magnet are drawn, so the count through the coil changes in steps while the measured Φ changes smoothly. The flux surface brightens with |Φ|, including in an open circuit.
- Meter G is an ideal ammeter in series, its resistance included in R; the needle shows I at once, without inertia. Its scale is ±40 µA for the magnet and ±5 mA for the rotating coil; beyond that the needle rests on its end stop. Yellow dots move in the conventional current direction at a speed proportional to I, as an illustration, not electron motion. The stand, coil rims, slip rings and brushes are illustrative and contain no iron core. Values describe an ideal model, not predictions for real laboratory apparatus.