# Electromagnet design

1. Nov 13, 2012

### MG_xy

Dear all,
I need realizing an electromagnet producing a magnetic field changing in direction with a given frequency (from 100 to 800kHz). Max intensity should be 400-500 Oe.
I need applying this magnetic field in a small region (10x 10 mm2) and I would prefer the electromagnet not so big because I have to use it in a bench experimental setup.
Do you have any suggestion for realizing it by myself? Or could you suggest me some commercial stuff?

Maria

2. Nov 13, 2012

### Carl Pugh

This may or may not work. However it should be easy/low cost to try.
Design an air core coil large enough to place your experiment in the center.
Calculate the inductance of the coil. Locate an AC (Make positive it's AC) capacitor that resonates with the coil at the desired frequency. If the capacitor is too small, remove turns from the coil. If the capacitor is too large, add turns to the coil.
Obtain an oscilloscope and a signal (function) generator.
With the signal generator, oscilloscope, coil and capacitor in parallel, tune the signal generator until there is a voltage peak.

This should give you a magnetic flux with a sine wave shape. If you have to have something other than a sine wave, this approach will not work.

It should be possible to calculate the magnetic field intensity from the voltage measured on the oscilloscope, the number of turns on the coil and the capacitance of the capacitor.

Good Luck

3. Nov 14, 2012

### Enthalpy

45mT at 800kHz makes already 23V per turn (rather 30V as it will be round), so you'll have very few turns...

Take 2 turns separated by 10mm, then you need about 360A...
Or 10 turns over 15mm, you need 300V and 54A approx.

A ferrite core wouldn't save voltage nor current but it would give more room to the windings. Alas, at 800kHz you won't increase the voltage so you can only increase the wire diameter, which is very inefficient because the current flows at the wire's surface only. It would require a diabolic Litz wire, home-made with great effort.

Can you have a few frequencies only and resonate with a selected capacitor? Of course, at this power and frequency, the selector is mechanical... But at least the amplifier would become less difficult.

Do you already have the amplifier? It's seriously difficult to build!

Naturally, your coil will work for very short periods and cool down between.

Unless you have very special operating conditions, it's unfeasible.

The least bad option for continuous operation would be a superconducting resonator, which works at one frequency only, and can't be a simple cavity at 800kHz. It takes niobium and liquid helium.

Did you check what happens to the thing put in this field?

4. Nov 14, 2012

### Carl Pugh

The requirements are not clear. Does this inductor have to operate in the range of 100 to 800 kHz? Or does it have to operate at only one frequency that may be chosen anywhere from 100 to 800 kHz?
Choosing 100 kHz, I have run through some calculations (and if no mistakes were made) it's not that difficult.
It would require a 20 watt, 100 kHz amplifier or oscillator.
The coil would require strong forced air cooling.
Everything else would be easy.
Again it is not clear if a sine wave magnetic field would be acceptable in this application.

5. Nov 15, 2012

### Enthalpy

100kHz is easier than 800kHz, and one single frequency even more, especially for the tuning capacitor, sure.

Though, how do you consider to make the coil's wire? At 100kHz and 300V it would have like 80 turns only, and the skin depth is just 0.4mm, so eddy current losses in the wire will be brutal. DC resistance just doesn't apply here.

From quick estimates, 20W would correspond to perfectly tuned Q>>100, and this Q from a small air coil at 100kHz would be very difficult.

6. Nov 15, 2012

### Carl Pugh

My calculations are rough. But if there are no mistakes, it appears that it is possible to meet 400 oersted at 100 kHz.

My calculation for skin depth is 0.00822 inch. (0.209 mm)
Doubling, 0.00822X2=0.0164 inch (0.418 mm)

#23 AWG film insulated copper wire, 0.0226 inch OD copper, 0.0243 inch OD over insulation, 20.3 ohm/1000 foot.

0.0226 is not that much larger than 0.0164 so am assuming since this is a rough calculation that skin effect can be ignored. I am guessing that actual loss would probably be less than 2 times loss calculated using DC resistance.

A single layer solenoid using #23 AWG, 1 inch diameter, 1 inch long, 38 turn would have an inductance of 24.9 microhenry.
This would resonate with a 0.1 capacitor at 100.9 kHz.

Using energy storage rather than Q, I come up with a requirement of 100 volt RMS and a power neglecting skin effect of 8 watt.

Again the calculations are rough and it is possible that mistakes have been made.

7. Nov 16, 2012

### Enthalpy

We agree on some values, but not on the losses even in DC.

1 Oe (100µT in vacuum) takes 80A/m in the coil. The D=L=25.4mm coil has an equivalent length around 35mm, so 400 Oe need 1100A*turns or 38 turns and 30A.

Already the DC resistance of the coil (3m and 0.57mm) would be 0.2 ohm which dissipates 180W.

Worse, AC losses don't result just from skin effect. Eddy currents in the wire are much worse.

You can represent the skin effect as an eddy current created by the induction that results from the wire alone. But if packing 38 turns, of which >10 are close to an other, each turn sees an induction much bigger than its own contribution, and since eddy current losses increase as the induction squared, eddy currents overshadow the skin effect by two magnitudes.

I put some formulas there, but they don't fit exactly a single-layer solenoid:
https://www.physicsforums.com/showpost.php?p=4149736&postcount=12
Phillips had an excellent application databook for ferrites long ago. If you own one, keep it. This effect was described, it's the only place where I've seen it - and in my measures.

8. Nov 16, 2012

### Carl Pugh

This coil may or may not work. I believe that the coil has to be built and tested before anyone can say positively whether it will work or not.

The following is from the book Physics, by Hausmann & Slack.
"The same expression may be used for a straight solenoid, but applies only to it's central portion."

H=4*Pi*N*I/(10*l)

H=Oersteds
Pi=3.14
N=Turns
I=amp
l=length in centimeters

For 400 Oersted this calculates to 21.3 amp peak, 15 amp RMS.

Ignoring skin effect, this calculates to 15 watt/in squared.
Assuming that skin effect doubles this, the coil will have 30 watt/in squared.

From experience, eddy losses are nowhere near two magnitudes of skin loss.

The coil could be made of high temperature wire and nomex and could operate at 220 degree C.

It may be possible to operate at 30 watt/in squared with lots of forced air cooling and below 220 degree C.

9. Nov 17, 2012

### Enthalpy

The present solenoid is short so the formula is off by about 1.4 here, doubling the power. Then it should be made clear if "400-500 Oe maximum intensity" means peak, or an adjustable RMS field.

Eddy currents in the wire is by far the predominant effect. This is experience at 100kHz without a magnetic core. Taking the DC losses, even doubled, gives a very incorrect estimate.

At least we're already far from the first figure of 20W, even with the 0.2 ohm DC resistance we seem to agree on.

Last edited: Nov 17, 2012
10. Nov 22, 2012

### Carl Pugh

Yes the 20 watt is much too low.

Have built transformers where the wire diameter was a little over twice the skin depth. Used twice the wire resistance to calculate the coil loss and assumed the loss due to proximity and skin depth was zero. The transformers were not returned, so always assumed this was a reasonable estimate.
Enthalpy’s statement “Taking the DC losses, even doubled, gives a very incorrect estimate” got me wondering if the two times resistance was a realistic estimate.

Had nearly everything on hand to build and test a coil similar to that discussed previously, so built a coil and tested it for proximity and skin depth effect. The 2 times resistance increase is a conservative estimate.

If anyone is interested, will provide details of coil and how it was tested.

My belief is that it may be possible to make a forced air cooled coil that will operate continuously at 400 Oe peak, 100 kHz.
The forced air cooling would have to be great.
The coil would have to have 220 degree C insulation.
The coil life at operating temperature could be as low as maybe 40 hours.
Again the coil would have to be built and tested before it could be guaranteed to work.