Insulated inductor vs non insulated

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Im wondering what the difference would be for an inductor made of insulated copper wire and one without insulation in its effect of producing a magnetic field. Are there any cases when one would be used in place of the other?
 
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Bare copper wire would be slightly better at dissipating heat than insulated wire.

However, bare copper wire must be spaced so that adjacent turns of the wire do not touch each other while insulated wire can be wound so that the wires are touching. This is very necessary when hundreds or thousands of turns of wire must be used as in some or most transformers.

The insulation itself has no effect on the inductance of the coil but it can increase the losses of the coil at high frequencies.

Large inductors used in transmitters are sometimes wound with bare wires and the wires are sometimes even silver plated to get better conductivity and fewer losses. These coils are spaced so that adjacent turns do not touch each other.
 
Here is some additional information. If you need many close turns, use Formvar or enamel insulated magnet wire, or other coating suitable for max expected temperature. If you have a multilayer coil, and 100 turns ber layer, for example, and your L dI/dt is 10 volts per turn, you could have 2000 volts between touching turns. If the wire diameter is comparable to the skin depth at your operating frequency, then use Litz wire with insulated strands.
If your core is laminated transformer iron, the laminations need insulation (oxide or similar coating).