# Calculating electromagnet – magnetism vs heat

Im making an electromagnet that will be more or less permanently turned on so I need to avoid heating problems. I have studied this a bit and came to the conclusion that:

the lower the gauge (AWG) (the thicker the wire) and the more turns around the core => the greater current it can handle and the lower the heat.

with this in mind I would have taken something like 500 turns around a 10 mm diameter screw, with pretty thick copperwire awg 20 (0.5 mm) or something similliar would be okey?

What do you say? Is there a way of calculating these heatingproblems before I decide the dimension and number of turns of my copperwire?

• First calculation is power dissipation: $P = I^2R$. Aug 21, 2019 at 12:51
• ...the more turns around the core => the greater current it can handle and the lower the heat. More turns could actually mean reduced current capability when you wire the turns on top of one another. Then the "inside" turns cannot dissipate their heat as easily. Aug 21, 2019 at 12:55
• In this case, why not use a permanent magnet? Research how a magnetic base works to see a clever way to disrupt that magnetism. If electricity must be continuously spent, consider water-cooling. Mount the screw to a metal heat-block and pump coolant through it to a radiator. Aug 21, 2019 at 13:11
• yes that would be better but I need to be able to turn the magnets on and off and controll them with PWM from raspberry pi Aug 21, 2019 at 15:10

Just working through your example, a coil diameter of 10mm, wire thickness of 0.8128mm, means ~32.7mm per turn of wire length, so for 500 turns you have 16,350mm of wire length,

for that length and wire size, you end up with 0.55 Ohm for the entire length, of which the heat has to be spread over the surface area of your coil based on how many turns and how thick the wire is, from a quick cross check I am going to have to assume you where planning multiple layers for the coil (a single layer would be 40cm long), which will increase the total length, resistance, and drastically reduce how much surface area you have to dissipate that heat,

Now for how hot things will get, specific numbers get difficult without simulation, instead I would focus on what you can do to reduce the power for the same magnetism, or the other way, increase magnetism for the same dissipation

For single layer coils, doubling the coil diameter increases the length of each turn by double, and doubles the surface area, so you do not actually see any significant cooling providing you have the same amount of current flowing each time, in other words the coil diameter is mostly irrelevant,

Every time you increase the wires diameter by 1.414 times, it decreases the wires resistance by 2, but also increases the total length slightly, and increases the surface area of the coil by about the same amount. so for the same current, you end up with ~50% the original dissipation, and slightly more surface area to dissipate it over, this is all well and good, as long as it is a single layer,

When you stack multiple layers on top of one another, well lets say you just decided to increase the thickness of your wire by 1.414 and want to keep it the same length, so you make this coil 2 layers thick and add ~40% more turns to make up the same power dissipation of the original coil, the second layer has a wider diameter, so it is longer per turn, but unless your coil diameter for the first layer was about the same as the wire thickness, it will generally be only a fractional increase in diameter, leaving you with about the same total power dissipated with a slightly increased surface area from the larger diameter of the extra layer, and ~40% more magnetism

From this you can iterate the math forward to work out your relative power dissipation for different wire thicknesses, layer counts and coil diameters, in general thicker wire reduces the total dissipation, a larger coil diameter increases surface area, and layer count is a trade off between total dissipation and surface area,

The wire gauge does not affect how much power you need to produce a certain $$\H\$$ field through the core.

There is only a single fundamental way to generate more $$\H\$$ field through the core using the same power:

Reduce the resistivity of the volume that caries the magnetizing current.

Let's think about the implications of that statement for a bit:

• This volume is the infinite space around the core. The more of the universe you thus fill with your coil, the better. Costs and practicality aspects forbid extremes.

• Improving the filling ratio of the wire is better. Square or hexagonal wire can achieve higher filling factor than round wire. Depending on the target power dissipation, the conductive heat dissipation might not be enough however and volume for active cooling must be reserved.

• Using wire material with lower resistivity is better. Cool wire is better than warm wire. Superconducting wire would allow operation at zero power.