Lenz's law

Lenz's law gives the direction of the induced current:

The induced current flows so as to oppose the change in flux that produces it.

Nature resists change. In practice:

• If the flux through a loop is increasing, the induced current makes a field against the outside field.
• If the flux is decreasing, the induced current makes a field along the outside field, to try to keep it up.

Example: the N pole of a magnet is pulled away from a coil. The flux is falling, so the coil tries to hold on to the magnet: its near face becomes a S pole, which attracts the departing N pole.

Then use the right-hand rule to turn the needed field direction into a current direction (clockwise or anticlockwise).

The minus sign in ε = –N dΦ/dt is Lenz's law written in maths.

Why it must be so: conservation of energy. If the induced current helped the change, a magnet pushed slightly into a coil would be pulled in faster, making more current, and so on: energy from nothing. Instead, you must do work against the opposition, and that work becomes the electrical energy.

This opposition is easy to see: a magnet dropped through a copper pipe falls slowly, because the currents induced in the pipe oppose its motion.

No change, no current: a loop resting wholly inside a uniform field, even if it moves, has constant flux and no induced current.