Editing Electromagnet (section)

===Ohmic heating===
[[Image:Current carrying busbars at the LNCMI.jpg|thumb|Large aluminum busbars carrying current into the electromagnets at the [[LNCMI]] (Laboratoire National des Champs Magnétiques Intenses) high field laboratory]]

The only power consumed in a [[direct current]] (DC) electromagnet under steady-state conditions is due to the [[Electrical resistance|resistance]] of the windings, and is dissipated as heat. Some large electromagnets require water cooling systems in the windings to carry off the [[waste heat]].

Since the magnetic field is proportional to the product <math>NI</math>, the number of turns in the windings <math>N</math> and the current <math>I</math> can be chosen to minimize heat losses, as long as their product is constant. Since the power dissipation, <math>P=I^2R</math>, increases with the square of the current but only increases approximately linearly with the number of windings, the power lost in the windings can be minimized by reducing <math>I</math> and proportionally increasing the number of turns <math>N</math>, or using thicker wire to reduce the resistance. For example, halving <math>I</math> and doubling <math>N</math> halves the power loss, as does doubling the area of the wire. In either case, increasing the amount of wire reduces the ohmic losses. For this reason, electromagnet windings often have a significant thickness.

However, the limit to increasing <math>N</math> or lowering the resistance is that the windings take up more space between the magnet's core pieces. If the area available for windings is filled up, adding more turns requires a smaller diameter of wire, which has higher resistance, and thus cancels the advantage of using more turns. So, in large magnets there is a minimum amount of heat loss that cannot be reduced. This increases with the square of the [[magnetic flux]], <math>B^2</math>.