Wikipedia:Reference desk/Archives/Science/2021 October 12

= October 12 =

Electromagnet: Loops vs current
Let's say I'm building an electromagnet, and I have a fixed amount of copper, and a fixed amount of power. What's better: More loops, higher voltage, lower current; or fewer loops, lower voltage, and higher current? What if I can vary the power, what's better fewer loops and higher current or vice versa? Ariel. (talk) 00:18, 12 October 2021 (UTC)


 * Suppose you have n windings. With a fixed amount of copper, the cross-sectional surface area of the wire goes with 1/n, so the resistance per unit of length goes proportional to n. The length of the wire goes with n, so the resistance goes with n2. I=sqrt(P/R), so with constant power, the current goes with 1/n. The magnetic field goes with I times n, so for a fixed amount of copper and a fixed power supply, the number of windings doesn't matter.
 * There are some other considerations. The current not only runs in the electromagnet, but also in the wires connecting it to the power supply. A higher current leads to more losses there and to difficulty switching it off (not more difficulty switching it off. The lower inductance of the coil with less windings compensates for the larger current. After all, the energy stored in the magnetic field is the same). Higher voltage requires better insulation between the wires in the coil. A longer wire means you have to cover a larger area with this thicker insulator, which takes volume and may pose a problem for cooling the electromagnet. PiusImpavidus (talk) 09:23, 12 October 2021 (UTC)