Ampere Turns

I have been trying to wrap my head around the puzzle that is ampere turns for electromagnets. The convention is that the more amps per turn of wire around a core the stronger the electromagnet. However the more turns you have the more resistance you have which drives down the amps. So if you were to lengthen the core and increase the gauge of the wire, you'd have room for more turns. But the increased turns drives up resistance so your amps are around the same as before but you now have more turns because you increased the length of the core. So hypothetically have you just created a stronger electromagnet without using more power because you're using the same amount of amps but you'd have a higher number of turns?

...confusing

there is no free lunch, for the strongest possible field with the least amount of copper you need a solenoid with an inside diameter of 1, a length of 2, and a thickness of 1 iirc.

how many turns don't matter, the variable is how much copper you can stuff in the core.
the field strength follows the square root of the watts lost in the core.

Njguy said:

I have been trying to wrap my head around the puzzle that is ampere turns for electromagnets. The convention is that the more amps per turn of wire around a core the stronger the electromagnet. However the more turns you have the more resistance you have which drives down the amps. So if you were to lengthen the core and increase the gauge of the wire, you'd have room for more turns. But the increased turns drives up resistance so your amps are around the same as before but you now have more turns because you increased the length of the core. So hypothetically have you just created a stronger electromagnet without using more power because you're using the same amount of amps but you'd have a higher number of turns?

...confusing

Click to expand...

Hi,


If you start with 10 turns with wire diameter 1 unit, then go to 20 turns with wire with twice the cross sectional area, you've got twice the ampere turns so you've increased the field strength. So you are right. But remember the fatter wires get farther apart too so you'll loose something there, but it will increase.

There's a limit to this process however, and that is that the size of the coil is going to get larger and larger one way or the other, and that is going to put more distance between the coil and the thing it has to pick up or just attract. For near fields the decrease acts like 1/d so the field decreases as the distance d gets larger by a factor of 1/d. This is eventually going to make adding more turns ether not do anything at all or maybe even decrease the field at some point. The time to stop adding 'layers' will be when the maximum field is created of course. It could also be that it tapers off, so that adding turns after a certain point doesnt add much to the field even though it doesnt decrease.

We could take a better look at this i guess if you like, but usually the coil actually built is never optimum anyway but is based on what voltage supply is available to power the thing. If you'd like to try this optimization process yourself, just start to factor in the 1/d issue in with the diameter and layers.

Hello again,


This has been corrected since earlier this morning.

Since we have to consider distance from all the wires to the 'object' to be attracted, we have to think about the shape of the coil as well as how many turns and how much current.

The force varies as:
F=K1*I^2*N^2/L^2 (B varies as 1/L but the force as 1/L^2)

and with a current of 1 ampere we get:
F=K1*N^2/L^2

so the force goes up with the square of the turns N but down with the square of the distance L. This means we need to know the shape of the coil also, or determine it. But if we determine it, it probably wont be the shape we really want since we probably want something with a flat face. We also have to know what size object we intend to attract, or a range of object shapes we might be using this with.

For a simplification into 1 dimension along the axis of the coil, we see that the distance increases with the wire diameter d, but the wire diameter d only changes by:
d=2*sqrt(A1*N/pi)

where A1 is the initial wire cross sectional area, and normalizing for that area, and L=2*d, so we get:
F=K1*N/(16*pi)

so yes the force does increase along the axis when the coil diameter is small compared to the length.

But next we'd have to check the result for when the coil diameter is not small compared to the length (next time). In this case the force probably varies as the square root of the number of turns N cubed (N^(3/2)) (for a square coil with simplification into 1 dimension along the axis).

We could also check other shapes like a pie shape on a point target with the point of the pie facing the target.

Keep in mind that this optimization is for when we increase the number of turns N and at the same time double the cross sectional area of the wire. We are using more turns but bigger wire for each increase in N.

"so the force goes up with the square of the turns N but down with the square of the distance L."

I see, I am assuming that this scenario only applies to a cylindrical type electromagnet where only one pole is being used to generate force upon the object and the other pole is shot off into space?? Would this scenario change with another core design like a horseshoe where both poles act upon the object?

Hi,


Yes that was for a long cylinder with one end doing all the work. Each wire contributes to the B at the point where the object is, but only once.
Given two poles, we'd probably get 2 times the force (B on both ends of the coil would be equal but opposite but the object doesnt know that they are opposite unless they are very close together) which really is significant if you think about picking up a car. With 2000 pounds of pull we wouldnt be able to pick up most cars, but with twice that we would be able to pick up quite a few. I havent actually worked this out yet though. We could look on the web to find the electromagnets that pick up cars and get a better idea what to expect most likely.