conservation of energy in Lenz's law

Question

When we bring opposite poles of two magnets together, they attract each other (or vice versa). Now, we can say that the kinetic energy gained by the magnets is due to the attractive force.

Similarly, we say in Lenz's law that if the north pole of magnet is moved towards a solenoid (for example) then the north of the magnetic field produced by the induced current will be towards the north of the magnet to oppose the change in magnetic flux.

The explanation we give for the above (2nd paragraph) phenomena is the law of conservation of energy. Now, suppose that the opposition is not offered in the above phenomena and the south of the magnetic field produced by the induced current is towards the north pole of magnet. The motion of the magnet will be enhanced in this case and the magnitude of change of magnetic flux will increase. This is said to be the violation of law of conservation of energy. My question is that why is this violation of energy? if two opposite poles of magnet can attract each other why not the south of magnetic field of induced current and north of the magnet?

I know its a complicated question but that's is the best i could do with it. I will appreciate if anyone could edit it to make it better but don't change the question.

Answer 1

The difference between the solenoid and the magnet is that the magnetic field in the soleniod is a transitory thing, created by our motion of the second magnet. In the first case, the fixed magnet has it's own magnetic field and the system already has energy in it - put there when we first moved the magnets apart (or created the second magnet). We can get that energy back as work done on the magnets as we bring them together.

In the second case, there is no magnetic field in the solenoid until the approaching magnet starts to move - and hence no energy in the system. It is the work we do to move the magnet that creates the field, and if that field then acted to accelerate the magnet then obviously we would get out more energy than we have put in, and there is your violation of conservation of energy.

Answer 2

You can actually arrange a simpler experiment for this. Suppose that Lenz's law were reversed and induced currents reinforced the change of the magnetic flux. Now take a single loop of wire, and suppose that we produce a small current in it (with a battery or a magnet - it doesn't matter). An increasing magnetic flux is then created through the loop.

This changing flux will now induce a current in the wire loop. You'll see by the right hand rule and the modified Lenz's law that the induced current goes in the same direction as the existing current. So the induced current reinforces the existing current - the total current increases and so does the magnetic flux, which induces a further increase in the current etc... With a simple loop of wire you could power a city.

In the actual case the induced current resists the increase in mangetic flux and opposes the current already present in the wire, slowing and eventually stopping the growth in the current. This is the operating principle of an inductor.