This is a vivid demonstration of the concept of mutual inductance. A function generator and audio amplifier drive current through a homemade solenoid. The frequency range of interest is up to 20 KHz. Another piece of wire is wound around the solenoid, which picks up an induced emf. This emf is filtered and amplified. Both the primary and induced voltages are compared on an oscilloscope.
The real fun is when you see the induced emf grow as you keep on winding multiple turns of wire around the solenoid. You start unwinding or winding a few turns in the opposite sense, the induced emf starts to drop. When the same loop’s position is changed so that it does not enclose the primary solenoid, the induced emf drops again to zero. If the bunch of wires are placed vertically inside the primary, no emf is developed. Furthermore, change the frequency and notice the dependence of the induced emf. Last, the phase difference between the source and induced voltages is a clear demonstration of the time derivative of a sinusoid.