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# Showing Faraday's Law with an Oscilloscope

According to Faraday's law of electromagnetic induction, an electromotive force (emf) is induced in a conducting coil by a time-varying magnetic flux through the coil. This can be written , where the magnetic flux through the coil is given by . For a circular search coil of radius wound with turns of wire, , where is the angle of the coil to the magnetic induction , which is assumed uniform over its cross section, although variable over time. The function generator varies the voltage through the Helmholtz coils, which produces a time-dependent magnetic induction mirroring the signal profile. The induced signal is then proportional to the time derivative of the input signal, thus depending linearly on both its amplitude and frequency. Both the function generator and oscilloscope show stroboscopic plots of voltage versus time. The dual-trace oscilloscope can show both signals simultaneously, and we have taken the liberty of coloring the search-coil signal red.

### DETAILS

Snapshot 1: when the magnetic induction varies linearly with time, as in each segment of the sawtooth wave, the induced voltage is constant in alternating directions, thus varying as a square wave in sync with the input signal
Snapshot 2: a sinusoidally varying magnetic induction produces a sinusoidal voltage lagging by 90°
Snapshot 3: rotating the search coil reduces the magnetic flux by a factor of

### PERMANENT CITATION

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