Electric magnet efficiency and dimensions?

What are you trying to achieve? "Efficiency" to do what? Perhaps to create a magnetic field of a given amount in the center? Is there a volume spec: ie: 10% variation inside a given cylindrical volume? Define the field you want FIRST.

For an air core magnet? I don't think there are any limits. (search for Bitter magnet... bizarre looking coils.)

George H.

For an air core magnet the resistive losses in the wire length will ultimately determine how big you can sensibly make one.

I haven't checked the algebra but for a solenoid this looks about right:

It is left as an exercise in optimisation to find S the length of wire, solenoid diameter a and length L that meets your requirements.

We were more concerned with getting very uniform fields over the entire flight tube and fringe fields than any considerations of efficiency.

I need efficiency using AA batteries So, to get the strongest field intensity concentrated near the center of the coil, would you recommend a thin, wide diameter, pancake shape, or a long skinny pencil shape with the same number of turns? I guess the pencil winding would have more turns for the same wire length, and therefore more amp-turns. I know little about magnetics. It seems like a work problem of force and distance and joules of energy. If you can figure out the work done in terms of joules, you can convert to watt-seconds and battery drain. I see some electric motors are about 75% efficient, so maybe that's a number to strive for?

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To get the maximum field in a given area, you ideally want the current to circle that area as closely as possible, so either the pancake or the pencil coils are about the worst. A core can do wonders to get the field where you want it.

Then there are matching issues with your power source: You could use many turns with a small current or few turns with a large current. The key point is that the power dissipated in the coil remains the same for a given value of ampere-turns and a given conductor volume. That's just one of the issues; There are more.

The remainder makes no sense at all. You haven't given us any pertinent information. What exactly are you trying to achieve? What is 'work done' in this context? How do you define 'efficiency'?

Jeroen Belleman

It's defined exclusively by the resistivity of copper and the amount of power dissipation you can live with (temp rise, cooling capability, etc.).

A superconductor can be made in any size, and always dissipates zero power and stores as much energy as its operating temperature and critical field allow.

A piece of resistance wire cannot produce much magnetic field without getting excessively hot, no matter the size.

So, conductivity is a direct proportion into it. And conductivity (or the lack thereof) makes heat, so the limit is how much heat you can remove for a given safe temp rise.

I'm taking your question to mean, "assuming some given geometry, how should the dimensions be scaled for a given maximum power dissipation and temp rise?" So that, a low power magnet can be small, dense enough to achieve that temp rise, and therefore will have some magnetic field strength corresponding to all that copper and current. Wereas a very large one is limited by its surface area (e.g., electromagnets handling cars in the scrap yard), and may be limited to a much lower H at its most intense point, without overheating.

What I'm not taking your question to mean is, whether the magnetic field is maximal strength for a given size, or anything. That's a matter of geometry, which requires hard questions answered by extensive computation, or simulation. Everything else is just scaling, and power tradeoffs.

The peak field intensity should scale down with increasing size, because power density goes as a 2/3 law (unless additional cooling is provided). Though field intensity is dropping, total energy storage (or putting it another way, the total volume of relatively intense field) scales up with size.

Tim

Neither. Pancake and pencil are the two extremes of shape that give worst case return on resources. The optimum is somewhere in between.

Pancake coil inner turn length 2pi.a, 2pi.(a+w), ...2pi.(a+(N-1)w) Total wire length 2pi.(Na + Nw(N-1)/2) Enclosed volume of coil pi.a^2.w

Solenoid coil turn length 2pi.N.a is less but the enclosed volume of magnetic field in a long thin one is much larger at pi.a^2.Nw

But if you wrap the solenoid coil back on itself to halve its length you can maintain a stronger field over half the internal volume. eg

Two layer solenoid coil 2pi.N/2(2a+w)

It would help if you described roughly what you are trying to do and why it has to be air cored. The only reason I can think of is to scan the field intensity rapidly or as a sensorhead for metal detectors.

You can get a much higher field strength by adding a soft iron core.

You want a dumpy not that far off cubic arrangement of the wire wrapped as tightly and uniformly as you can manage close packed onto its former. My instinct is that it is better fatter than taller but that is not based on anything more than memory of how our coils were made (and we were after uniformity and not concerned with efficiency at all).

For a given wire diameter, number of turns and solenoid specification you can compute the field using the formulas given above close enough to choose the optimum length to diameter geometry.

If you are not happy doing the mathematics you might well be better off making a few coils each with say 60 turns and testing them.

ie 1x60 2x30 3x20 4x15 5x12 6x10 10x6 12x5 etc.

If you start with 6x10 and work outwards from there you may only need to make three or four coils to find the optimum.

(snips to the point; apologies to Martin Brown)

To achieve what, exactly?

It depends on the geometry of your test volume.

of

Pencil winding = long, axially symmetrical field, constant strength ove r most of its length. That what you want?

Pancake coil windings farther from the center make weaker contributions t o the central field. Wasteful of space, too.

How much volume really matters, and how is it shaped? I like triaxial Hel mholtz coils for (very roughly) cubical test volumes.

It depends on how you define "efficient". Helmholtz coils give you a smal l constant-field volume but trades that for a large inconstant field outsid e the coils.

OTOH with triaxial coil sets you can adjust the field vector at will.

Tesla would wind coils on soft iron rings with slots in them to get stron g fields in small places. As has been pointed out, pole pieces are really g ood at concentrating fields.

BTW do you want constant or time-varying field? If the latter, whatever's in your test volume will likely have mu different from the free space valu e, and will present a load to the coil(s). If it's any sort of magnetic the setup becomes a transformer, albeit one with a shorted secondary.

I mention that because transformers are the most efficient electrical dev ices I know of, but shorted turn secondaries mean you have to limit the pri mary current.

Mark L. Fergerson

I'm trying to get the maximum force at a distance of 1/8 inch between a permanent disc magnet and and an electro magnet. The diameter of the permanent disc magnet is about 3/8 inch (neodymium type). I found winding an air core electro magnet to the same diameter as the permanent magnet gave usable results. But later found adding more wire of a larger size (less resistance) and making the coil somewhat wider than the diameter of the magnet improved the strength and also drew less current from the battery due to the increased resistance. So, as you say, the optimum dimensions will be some compromise between the pancake and pencil shapes. Looks like it might be a cylindrical shape where the height is equal to the diameter and the diameter is somewhat greater than the permanent magnet diameter?

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This Wiki page may help you (and the links)

Turns out doing the integrals analytically is somewhat tricky but my back of the envelope crude algebra yields a rough heuristic for multilayer solenoid coil with N turns and n layers of n ~ Nw/a.

Tables of typical self inductance for various length to diameter ratios of a simple solenoid are online at:

Hope that helps.

Ahh, Well the force goes as the gradient of the field. For a single turn (or thin) coil you can calculate the field on axis (form freshman physics). And then take a derivative to find the gradient. I think the maximum force is at about 1/2 the radius of the coil. (I'm too lazy to redo the math.) So you could try scaling your coil size for that. If you want a constant force you can run Helmholtz coils in opposition, and then you get a pretty uniform gradient between them.

So again you want a big field gradient, not just a big field per se, (Of course a bigger field will have a bigger gradient, all other things being equal.)

George H.

NOT available.

Works from here (or follow the links from the other page)

You really should invest in a working computer you know.