30.3: Lenz’s Law

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to determine this direction with Lenz's law, named in honor of its discoverer, Heinrich Lenz (1804–1865). Lenz's law states that the direction of the induced emf drives the current around a wire loop always to oppose the change in magnetic flux that causes the emf.

If a bar magnet is moved toward a coil such that the magnetic flux through the coil increases, then an induced current is generated in the coil. This current produces a magnetic field that opposes the increasing magnetic field of the moving bar magnet. On the other hand, if the bar magnet is moved in such a way that it results in a decreasing magnetic flux through the coil, then the induced current creates a magnetic field that opposes the decrease in the magnetic field of the bar magnet. An induced current can also be created if the bar magnet is kept stationary and the coil is moved toward or away from it. In this case, the induced current exerts a magnetic force on the coil such that it opposes the motion of the coil.

Lenz's law can also be considered in terms of the conservation of energy. If pushing a magnet into a coil causes a current, the energy in that current must have come from somewhere. If the induced current opposes any increase in the magnetic field of the bar magnet that was pushed in, then the situation is clear. In this case, the magnet is pushed against an induced magnetic field and does work on the system, which results in a current. On the other hand, if the induced current and corresponding induced magnetic field did not oppose the magnetic field of the bar magnet, then the bar magnet would be pulled in without having to do any work, and an electric potential energy would be created, violating the conservation of energy.

Lenz's law states that the direction of induced current opposes the cause producing it. The cause can be either a time-varying magnetic field, a non-stationary conductor, or both the causes together.

If a bar magnet is moved toward a coil, then the magnetic flux passing through the coil changes. This induces a current that creates a magnetic field having a direction opposite to the original magnetic field.

If the stretched thumb of the right hand is in the opposite direction to the original magnetic field, then the curled fingers give the direction of the induced current.

On the other hand, if the polarity of the bar magnet is reversed, while it moves towards the coil, the induced current creates a magnetic field in the opposite direction to the original magnetic field.

Similarly, if the motion of the conductor changes the magnetic flux through the coil, the current is induced. This current is in a direction such that the magnetic force on the conductor opposes the motion of the conductor.