Final answer:
An induction cannon works based on Faraday's and Lenz's laws by inducing a current that creates a magnetic field opposing the original change in flux, expelling the metal cylinder within. The cylinder heats due to resistive heating caused by the flow of induced current through its resistance.
Step-by-step explanation:
Understanding Induction Cannons
Induction cannons work based on Faraday's law of electromagnetic induction and Lenz's law. When a rapidly changing current is introduced into a solenoid coil, it induces a rapidly changing magnetic field. Faraday's law states that this changing magnetic field produces an electric field, which in turn induces a current in the metal cylinder located inside the solenoid. The direction of this induced current is such that, according to Lenz's law, it creates its own magnetic field that opposes the change in the original magnetic flux. This opposing magnetic field exerts a force on the metal cylinder, and because the fields are so designed, this force expels the cylinder from the solenoid coil.
The cylinder gets hot due to resistive heating, also known as the Joule heating effect. As the induced current flows through the metal's resistance, energy is dissipated in the form of heat. This heating can be significant, especially if high currents are involved, and can make the cylinder live/hot when the cannon is fired.