Theoretical question about an electromagnet in an AC circuit

[Wattif]

TL;DR Summary

Can an inductor used as an electromagnet be in an AC circuit without
affecting the overall circuit

This may be a stupid question, but here is what I am asking.

Using a very simple circuit, say 120v AC water heating element rated at 1000 watts
meaning 120v AC hot leg on 1 terminal and a neutral on the other terminal.
That would give 8.3 amps of current, meaning the resistance would be 14.4 ohms.

Now after the resister the neutral line would show no voltage with 8.3 amps.
So here is the theoretical part, is there any way known where an inductor could
be used on the neutral line to use the amperage to create an electromagnet without
affecting overall voltage or amperage other than the resistance of the inductor of the
electromagnet.

You may ask why, because I theorize that if I can create magnetic
fields using waste current, or whatever you want to call it, the current that's been used
for the task at hand, then those magnetic fields may be able to be used for other purposes.
I understand why it should not work, but does it seem totally impossible?

 

[NascentOxygen]

There is no waste current. Anything added into the neutral line reduces the voltage available to the heater element, so there is no free lunch going begging here. You might decide you'll wind the electromagnet of very low resistance wire, but coiled wire around a magnetic core is an inductor and its reactance robs your heater element of some voltage, again.

 

[Baluncore]

A current, i, flowing through an inductor, L, generates a magnetic field. The energy, E, in the magnetic field is E = ½ · L · i²
That represents a loss of energy, radiated from the inductor circuit. Conservation of energy must hold. If energy is radiated, it must come from somewhere, so the circuit parameters must change to allow energy to flow through the inductor.

 

[tech99]

If the mains supply was DC, I think you are correct that a magnet can be obtained for nothing. Of course, the magnet, if zero resistance, stores energy but does not lose it.

 

[Baluncore]

If the mains supply was DC, I think you are correct that a magnet can be obtained for nothing.

Energy must be supplied initially to manufacture a magnet, or to increase the DC current flowing through an inductor.

Of course, the magnet, if zero resistance, stores energy but does not lose it.

Establishing a magnetic field in the magnetic circuit, and the nearby universe represents an initial energy investment during the change.
If zero resistance conductors are present, the magnetic field will be reflected perfectly. Those perfect conductors will prevent magnetic fields entering that superconducting space.
Where resistive conductors are present, even if far away, there will be induced eddy currents that must convert some of the changing magnetic field energy into heat. That heat energy is lost from the magnetic circuit.