I If a magnet does not feel the Lenz force, will there be a violation of energy?

Hold on. If the magnet and the charge are both attached to the platform, then how can the magnet move towards the charge?

How? Aren’t they both attached to the platform?

A diagram might be helpful
Magnet can move towards charge. But it is constrained not to leave surface of platform. You can think of a track on which magnet moves towards charge.
 
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Magnet can move towards charge. But it is constrained not to leave surface of platform. You can think of a track on which magnet moves towards charge.
So the platform moves up and down and the magnet slides left and right on the platform? With the pole of the magnet oriented towards the charge.

Yes, this is precisely the sort of scenario that the general proof is valuable for.
 
So the platform moves up and down and the magnet slides left and right on the platform? With the pole of the magnet oriented towards the charge.

Yes, this is precisely the sort of scenario that the general proof is valuable for.
I know general proof. But I am wondering if there is no reaction force ( Lenz force ) on the magnet, what will conserve energy in this case.
 
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I know general proof. But I am wondering if there is no reaction force ( Lenz force ) on the magnet, what will conserve energy in this case.
I am not at all convinced that there is no reaction force. Clearly since your specific analysis contradicts the general proof your specific analysis is wrong. I suspect that it is the suggestion that there is no force on the magnet which is incorrect.
 

Ibix

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As magnet moves, charge experiences change in magnetic field. So, there is an electric field produced in peripheral direction of tube. If charge is happened to be slightly a side to the center of tube, then it will experience a force.
OK. Note that this is not the original scenario you specified, nor the second one, since the magnet is not moving towards the charge - rather, it's moving past the charge.

I'd suggest investigating the Poynting vector associated with the joint EM field of the charge and magnet. I rather suspect you'll find that it's not symmetric about the plane containing the magnet's velocity vector and the charge. Thus the EM field carries momentum away in one direction, which will conserve momentum.

I also note that the energy density of the field is unlikely to be constant with time. What's the total energy in the field? Does it change? If so, you have a likely source for any work.

Finally, if there is a net lateral force on the charge, then in the charge rest frame the magnet will not be moving along its symmetry axis and I would expect it to acquire an electric dipole character, which will feel a force from the field of the charge.
 

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