Not entirely sure here but from my understanding (Could be wrong lelele):
I see what you are trying to say ahah and you are sort of correct but the logical reasoning you have is a bit disjointed
When the magnet drops through the copper pipe, the pipe will experience a changing magnetic flux and hence according to Faraday's Law an emf proportional to the rate of change of magnetic flux will be induced into the copper pipe, generating eddy currents in the pipe. According to Lenz's law these eddy currents will produce a magnetic field which will directly counteract the original change in magnetic flux that produced them. So in this scenario, the magnet will fall slower due to the repulsive force of the induced magnetic field. Law of Conservation of energy says the net energy change of a system must be 0, and hence the kinetic energy loss must be a gain elsewhere. The loss of kinetic energy is equivalent to the gain in electrical energy in the conductor (which is proportional to the heat generated in the conductor). So while the kinetic energy is basically converted into heat in the end, it is not anywhere near a 1:1 conversion as your answer would imply. If I was going down the same path of reasoning as you (pipe and cooktop both generate heat and both use eddy currents) I would probably link it together using the electrical energy induced in the copper pipe.
Also if this was a compare question you really really don't need to go into this much detail, nor would I actually use this comparison
Similarities
- Both utilize eddy currents in order to do work, as there is a change in kinetic energy in the slowing down of the magnet, and there is a change in heat in the cooktop (Work equals change in energy)
- Both utilise the principle of Faraday's Law, where a change in magnetic flux is induces an emf - in the magnet this is a result of it falling, causing the pipe to experience a changing magnetic flux, whereas in the cooktop this is a result of the AC current in the solenoid causing the cooktop to experience a changing magnetic flux
Differences
- The application is different, as one slows the magnet down while the other is used to heat things
- One utilities a permanent magnet and a change in the relative motion between the conductor and the magnet to produce a changing magnetic flux, whereas the utilizes an electromagnet and AC to produce a changing magnetic flux.