If the current in a conductor changes, its magnetic field also changes. The change in the magnetic field induces a voltage in the conductor, which in turn generates a current. When the magnetic field builds up, the induced voltage must be directed in such a way that it opposes the current flow through a counter-voltage. If the voltage had the opposite polarity, the current flow would increase without bound.
This principle, known as Lenz's Law, follows directly from the law of conservation of energy. It is expressed by the minus sign in Faraday’s law of induction.
Experiment: Falling Magnets
First, two copper tubes are placed vertically. A piece of metal is dropped through one tube, while a magnet is dropped through the other. The magnet reaches the ground much later than the piece of metal. As the magnet falls, the magnetic flux density changes with time at every point. The resulting induced voltage generates eddy currents in the tube, which themselves produce a magnetic field opposing that of the falling magnet.
This effect is used in eddy current brakes to slow down motors without friction. The drawback compared to braking with sliding friction is that the braking effect of eddy currents is not constant, but depends on the velocity.