1. Predict
Predict the peak voltage when turns are doubled with all other settings fixed.
Electromagnetic induction
A magnet, a coil, a changing flux.
Follow the flux, induced voltage and current as a magnet moves through a coil.
Why is the voltage zero when the magnet is at the centre of the coil?
2. Run a controlled experiment
Set T = 6 s, N = 200 and moment = 3 A·m². Fit the scope; observe the centre crossing and turning point. Record time, flux and voltage.
3. Compare and measure
Double only N, then restore the baseline and double only the moment. Calculate peak-voltage ratios and record mV/div if the scale changes.
4. Examine the relationship
Halve the period; then restore it and reduce only playback speed. Which changes the physical voltage? Explain using Faraday’s law.
5. Conclusions and limits
Reverse the poles and compare voltage signs. Include the ideal-dipole assumption, neglected self-inductance and unmodelled parameter-change transients in your conclusion.
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Electromagnetic induction
Ready02 / LIVE MEASUREMENTS
Flux through one turn Φ—µWb
Induced voltage ε—mV
Induced current I—mA
Magnet position z—m
Axial velocity v—m/s
Peak voltage |ε|—mV
One circuit, two measurements
Oscilloscope CH1
Instantaneous voltage V(t)
Out of range; increase the display scale.
The voltage can be zero when the flux is largest.
Analog voltmeter
Instantaneous voltage V(t)
Instantaneous magnitude |V(t)|
Out of range; increase the display scale.
Ask. Test. Explain.
Ask a question
Does a large flux necessarily mean a large voltage?
Test it
Watch the flux curve and voltmeter as the magnet crosses the coil centre.
Interpret the result
Should voltage be related to flux itself or to its rate of change?
Setup and measurement notes
Schematic view; the drawn magnet size is not to scale.
Each line represents 25 turns in this diagram. Coil dimensions remain fixed.
Oscilloscope CH1 and the voltmeter are connected in parallel across load R. Both measure with the same sign convention.
Positive z points right. Positive current is counterclockwise when viewing the coil from the +z side.
Pausing freezes physical time. Changing the moment pauses at the current instant; other physical settings start a new run.
DC coupling; the zero line is fixed. The screen sweeps again each cycle. Fit signal changes only the vertical scale; the new mV/division is shown.
Solid blue line: flux through one turn (left axis, µWb). Dashed orange line: emf (right axis, mV). The curves build up as the bold time cursor advances. The horizontal axis shows total physical time; each sweep covers one period. The vertical axes are scaled according to the parameters.
Ideal center-zero indicator. Mechanical needle lag is not modeled; the reading is not RMS.
Changing the moment pauses time at the same instant: compare voltages at the same position. Parameter-change transients are not modeled. Peak voltage is the largest calculated over one cycle.
It is the change in flux that matters.
Faraday’s law relates the induced voltage to the rate of change of flux. The minus sign expresses Lenz’s law: the induced current’s magnetic effect opposes the flux change that produces it.
Model and assumptions
Ideal model: a compact magnet on the coil axis, approximated as a dipole whose dimensions are much smaller than the coil radius. Thin circular coil: a = 0.12 m; motion amplitude A = 0.35 m. Motion is externally prescribed. Self-inductance, a magnetic core, radiation and magnetic backreaction are omitted. Current uses the resistance-only approximation . We use μ₀ ≈ 4π × 10⁻⁷ H/m.
Instrument input resistance is infinite, coil internal resistance is zero, and self-inductance is neglected. Terminal voltage therefore equals ε and . Overrange limits only the drawing, not the calculated values.
Symbols and derivatives: how to read them
| Notation | Meaning and unit |
|---|---|
| Time; s denotes seconds. The light clock uses ns = 10⁻⁹ s. | |
| Φ is flux per turn (Wb), N turns, ε induced emf/voltage (V), I current (A), R external resistance (Ω). mV = 10⁻³ V; µWb = 10⁻⁶ Wb. | |
| Time derivative of flux: how fast flux changes (Wb/s). The minus sign in Faraday’s law encodes Lenz’s law. | |
| μ₀ is vacuum permeability (H/m); m magnetic dipole moment (A·m², not mass here); a coil radius (m); z axial position (m); A motion amplitude (m); T period (s). |
References and further reading
The books below offer further study of the relevant concepts. The simulation’s assumptions are stated separately above.
- David J. Griffiths. Introduction to Electrodynamics. Edition 5 · Section 7.2. Cambridge University Press. View source ↗
- Hugh D. Young, Roger A. Freedman. University Physics with Modern Physics. Edition 15 · Chapter(s) 29. Pearson. View source ↗
- David Halliday, Robert Resnick, Jearl Walker. Fundamentals of Physics. Edition 12 · Chapter(s) 30. Wiley. View source ↗