Show that Lenzâ??s law is a consequence of conservation of energy.

Lenz's Law states that, when you induce a current in a wire via a changing magnetic field, the current flows through the wire in such a direction so that its magnetic field opposes the change that produced the current.

So, what happens when you induce a current by, say, moving a wire through a magnetic field, is that you're converting mechanical energy (the energy of the wire's motion) into electrical energy (the energy carried by the induced current).

Lenz's Law ensures that the mechanical energy of the wire is reduced by the same amount of energy gained by the current. It does this by exerting a force on the wire opposing the wire's motion. This causes the wire to lose mechanical energy (its motion is impeded); it must do work against the induced magnetic field to generate current.

To make this a little more concrete, let's imagine a fictitious universe where Lenz's Law doesn't apply; i.e. a universe in which there's no force generated on the wire at all, despite the induced current.

In this fictitious universe, imagine that you give the wire one unit of mechanical energy. As the wire passes through a magnetic field, a current appears in the wire that also carries one unit of energy. But since no opposing force is generated, no mechanical energy is lost; the wire still has its original one unit of mechanical energy. Which means that the wire now has two units of total energy (one electrical; one mechanical). You've created energy from nothing!

In the real universe, Lenz's Law ensures that, if the electrical energy gained is one unit then the mechanical energy lost is also one unit, so that the net energy gain of the wire is zero. Energy is conserved.