Ohmic heating
The only power consumed in a DC electromagnet is due to the resistance The electrical resistance of an object is a measure of its opposition to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material of the windings, and is dissipated as heat. Some large electromagnets require cooling water circulating through pipes in the windings to carry off the waste heat.
Since the magnetic field is proportional to the product NI, the number of turns in the windings N and the current I can be chosen to minimize heat losses, as long as their product is constant. Since the power dissipation, P = I2R, increases with the square of the current, the power lost in the windings can be minimized by reducing I and increasing the number of turns N proportionally. For this reason most electromagnets have windings with many turns of wire.
However, the limit to increasing N is that the larger number of windings takes up more room between the magnet's core pieces. If the area available for the windings is filled up, more turns require going to a smaller diameter of wire, which has higher resistance, which cancels the advantage of using more turns. So in large magnets there is a minimum amount of heat loss that can't be reduced. This increases with the square of the magnetic flux B2.
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