Lenz's law and conservation of energy

Lenz's law (1834): the induced emf has the polarity that would drive a current opposing the change in flux that produced it. This is the minus sign in Faraday's law.

An N pole pushed towards a coil raises the flux, so the induced current makes the near face of the coil an N pole, which repels the magnet. Seen from the magnet's side the current runs anticlockwise.

Pulling the N pole away lowers the flux, so the current reverses (clockwise from the magnet's side) and the near face becomes an S pole, which pulls back on the retreating magnet.

With an open circuit no current flows, but an emf still appears across the open ends, and Lenz's law still gives its polarity.

If the induced current aided the change, a small push would make the magnet speed up by itself, giving energy for nothing. Lenz's law is what energy conservation demands.

In the real case you must push against the repulsion; the work you do appears as Joule heat from the induced current.

Example 6.4: a loop entering a field region gains flux and one leaving it loses flux, so the currents circulate in opposite senses. A loop wholly inside or wholly outside a uniform field region has no induced current.

Example 6.5: a still loop between fixed magnets, however strong, has no current, since the flux is not changing. A loop moving through a steady electric field gets no current either. A rectangular loop leaving a field region at steady speed has a constant emf; a circular one does not, as its area inside the field changes at a varying rate.