Which provides the energy for induced current at the starting moment of the lenz's law

Question

I am learning about magnetic fields, but I get confused with the way energy is transmitted in Lenz's law.

As I read on the question Explaining Lenz's Law without conservation of energy:

Let's say you have a circular loop conductor. If you bring the north pole of a magnet towards the loop, current induced in the loop will be anti-clockwise when viewed from the side of the magnet. Remember, if the current is in the anti-clockwise direction it acts the same as a north pole. So, the north pole of the magnet and north pole of the coil repel each other. Thus, the induced EMF opposes the change in magnetic flux. Therefore, work has to be done in order change the magnetic flux linked with the coil. This work done will be converted into electrical energy. - @Immortal Player's answer

According to the phenomena, the induced current generated a repulsive force on the magnet, which we are moving and exerting effort opposite to the force from the coil. That energy causes us to generate electric energy. So, there is a moving magnet (changing flux), and an induced current, which produces repulsion of the magnet and generates an EMF.

Considering the starting moment how is a current induced to generate repulsion? For there to be repulsion, there must be an induced current, which means electrical energy. (When there is an induced current, that means there is electrical energy.) At the starting moment, where does that energy come from?

As per the Lenz's law energy conservation description:

The induced current electrical energy → causes repulsion → resulting in needing to spend mechanical energy to oppose the magnetic repulsion from the coil to move the magnet → which creates an induced current as electrical energy.

So, from where did the initial induced current get its energy?

It is very complicated for me to describe my concern, but if you can arrange this question to ask my question more clearly I would be thankful to you for editing the content without distorting the question.

Answer 1

"Considering the starting moment how do there is a induced current to generate a repulsion. For that there should be an induced current, that means an electrical energy(While there is an induced current there should be an electric energy) At the starting moment how does that energy gain from?"

As far as i understand, the energy gain is from the kinetic energy of the magnet.

Once the magnet is moved, the disturbance in the magnetic field reaches the coil practically immediately and there is thus, a change in the flux through it. Thus, an EMF is generated in the coil which results in a current through it.

The reason why i say 'practically immediately' is that there will be a short time interval between the moving of the magnet and the setting up of induced current, which is the time required for the change in the magnetic field to reach the coil. So you could say that just after the starting moment, there is no induced current. But once this short time interval is over, the induced EMF is set up and magnet will be repelled due to the opposing magnetic field generated by the induced current in the coil. So, the energy associated with the electric current is accounted for(comes from the kinetic energy of the magnet)...

In other words, there is no such starting moment at which there is an induced current without any change in the kinetic energy of the magnet. Hope that helps...

Answer 2

Maxwell’s equations are differential equations. In order to solve differential equations it is necessary to provide the initial conditions separately. The initial conditions are external and do not come from the differential equations.

So, in this case, the initial current would need to be provided as an input to the scenario. The initial current could be zero, or it could be some non zero value whose energy is supplied from some external source. In either case, there is no way to derive the amount of the initial current nor its energy from the given information