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# AC electromagnet optimization

## AC electromagnet optimization

(OP)
Hi!

I need some help in optimizing an electromagnet for my company. All the parameters (like material/dimension of the core etc) are constant, I am not allowed to change them. The only what can vary now is a diameter and number of windings of the wire inside. Details concerning the electromagnet:
- E-I shaped steel core with the gap of around 2 mm (between the E and I part).
- The area of the intersection of the E-shape is 3800 mm2.
- Material used for the coil itself is an 'enamel' copper wire.
- The magnet is supplied by 320 V, ~50 Hz AC.
- The power consumption should be around 1 A.
- The electromagnetic force should be as high as possible.

Does anybody here have any experience with the AC magnets? I cannot find too many resources concerning this problem on the web. I'll appreciate any help.

Cheers

Replies continue below

### RE: AC electromagnet optimization

A formula for a gapped core inductor is

L = 3.2 {(N^2)(A)}/{(1 x 10^8)(l)}

L = Inductance in Henries

N = Turns of wire

A = Area of the core in inches2

l = gap in inches

### RE: AC electromagnet optimization

(OP)

Could you please tell me how you derived that formula? The thing is that it does not take into consideration the frequency of the supply AC voltage, and I belive that it should, since the inductance depends strongly on it.

Cheers

### RE: AC electromagnet optimization

I found the formula years ago and I'm certain it's somewhat empirical  Inductance is proportional to the number of turns squared and the area of the core for all inductors.  The other numbers make the units correct.

In a gapped core inductor, the gap controls the inductance since the permiabilty of iron is, say, 1000 times the permiability of air.

The impedance of an inductor (XL) is

XL = 2 x pi x f x L

As a starting point, you want an XL of (from Ohms Law and your numbers)

XL = V/I = 320 Vrms/ 1 amp rms = 320 Ohms

L is then

L = 320/(2 x 3.14 x 50) = 1 Henry

You'll also have to make certain you don't magnetically saturate the iron core (target 10,000 Gauss)

B = ( Vrms x 10^8)/(4.44 x f x N A)

B flux density, Guass
f hertz
N Number of turns of wire
A Core area in cm^2

### RE: AC electromagnet optimization

Has anyone else tried to download this book?  I've tried three times and each time Adobe says there's an error when it tries to open it.

### RE: AC electromagnet optimization

Navigation appears a bit slow for a PDF of that size, but it otherwise appears to be OK.

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