I think that the energy runs out from the kinetic energy of the magnet. By the third newton´s law, if the magnet produce a force in the electrons of the coil, the electrons will make a force to the magnet. So it can´t move with constant velocity unless someone move the magnet too. If the magnet goes with constant velocity, the energy runs out from the subject who keep trhat velocity.

The word move is inadequate. Replace move by interaction with

In your question, you mentioned that you get electrical energy from voltage. to answer this question, you must take into account the following details.

1. voltage doesn't appear suddenly across the coil.

2. you can connect a capacitor or any measuring instrument which records the voltage rise

3. even such an equipment will present itself as a capacitor or a charge-integrator

4. this means some work is done to bring the voltage up (charge stored = work done)

taking into account the above details, there is some work done to bring the voltage from zero to induced voltage. during this period, the coil will oppose the motion of the magnet, and naturally the magnet will slow down , in accordance with the conservation of energy.

Further, if you were to draw current from the coil, the coil will further slow down the magnet.

So during the voltage rising period, the coil will produce a field to oppose the magnet's motion, and as long as the voltage is not rising or there is no current flow through the coil after that, the magnet will not experience any further resistance to its motion (from the coil)

Therefore, this phenomena does not violate the energy-conservation law.

But if there is no current flow as the coil is open and therefore there will be no opposition to the magnet.

The most simple answer I can offer to your question is to observe the voltage across the terminals to verify your claim. No sooner you observe, there will be a current and an opposing force against the magnet.

Avinash,

You are confusing a potential difference with energy.

An open loop of wire, if moved in a static magnetic field will indeed generate a potential difference across the two ends of the wire.

But no energy is expended in order to do this, as (in the limit) no current flows.

If one were to close the loop, then current would flow, and an opposing magnetic field would be created that leads to an opposing force that would, when taking into account the speed of the coil, exactly balance the energy dissipated by the current in the coil.

Lest we forget;

Integral (force.distance) = work performed

It cannot be otherwise.