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## Main Question or Discussion Point

I have a confusion about the energy effects of current induction. Suppose I place a coil of wire near a long, high-voltage AC power-line. The changing current and hence, the changing magnetic field it produces will induce current in my coil. Then, I can connect the coil to a resistor and get heat energy out of the system, apparently for nothing. I highly suspect that the induced current in my coil will slow down the current in the power-line, but how exactly? I know about mutual inductance, but if I understand correctly the energy lost in this process of "back emf" is retrievable whereas the energy lost via Joule heating is not. (assuming that the wire is infinite for instance).

Moreover, if I put my (say, circular) coil in a bigger loop of increasing current, a current will be induced in my coil such that its flux will oppose the change in the original one. Let's say that the original flux was "positive". Then, there will be an increasing flux in the opposite, negative direction through the bigger loop, causing a current producing a positive flux to increase even further! Clearly, this is absurd, yet I can't figure out exactly where is the caveat. My suspicion here is that I forget about the flux of the loop through itself and that if I look at the total flux, it stays such that its change is equal to the source emf or constant.

Can anyone settle my confusion?

Any comments will be greatly appreciated!

Moreover, if I put my (say, circular) coil in a bigger loop of increasing current, a current will be induced in my coil such that its flux will oppose the change in the original one. Let's say that the original flux was "positive". Then, there will be an increasing flux in the opposite, negative direction through the bigger loop, causing a current producing a positive flux to increase even further! Clearly, this is absurd, yet I can't figure out exactly where is the caveat. My suspicion here is that I forget about the flux of the loop through itself and that if I look at the total flux, it stays such that its change is equal to the source emf or constant.

Can anyone settle my confusion?

Any comments will be greatly appreciated!

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