Final answer:
True, induction coils in an electromagnet only have significant current when there's a change in magnetic flux, which results in work being done by the electromagnetic force. Without this change, such as when the magnet is stationary relative to the coil, no current is induced.
Step-by-step explanation:
The statement that a properly designed induction coil in an electromagnet will have very little current flowing through it when the electromagnetic force is not doing any work is true. According to Faraday's Law of electromagnetic induction, a current is induced in a coil only when there is a change in magnetic flux through the coil. Therefore, if there is no movement of the magnet with respect to the coil, or if there is no change in the magnetic flux, there is no work done on the electrons in the conductor, and thus no current flows.
For example, when a bar magnet is dropped through a copper tube, it induces an electric current in the tube because the relative motion between the magnet and the tube causes a change in magnetic flux. This induced current creates an electromagnetic field that opposes the magnet's motion (Lenz's Law), which manifests as a resistance to the falling magnet, demonstrating work being done by the electromagnetic force. In contrast, if the magnet is held stationary within the tube, there would be no change in magnetic flux, no induced current, and therefore no work done by the electromagnetic force.