Calculating the Uniform B Field in an AC Helmholtz Coil: What's the Formula?

[artis]

What would be the formula to calculate the right spacing distance between the coils in order to get a uniform homogeneous B field in the middle of the coils and how to determine the B field strength?

I can only find bits and pieces on google about these sort of formulas but their intended for DC current and static B field , I am more interested in RF AC B field , so I assume I would need to determine by calculation the turns and wire size (litz or tubular) etc, can you please help me out ? thanks.

 

[BvU]

Hi,

In my memory, B is calculated from the current in the coils; in what way would the AC issue make a difference ?

 

[artis]

But the formula changes due to there being no iron to guide the filed but air instead ?
I am confused because I find different formulas online and I am not sure which one specifically applies to my case?

 

[BvU]

Iron ? Who mentioned iron ? What are we talking about ?

not sure which one specifically applies to my case

Of course. First and foremost because you are the only one who can know the specifcs of your case. Second because it takes some sleuthing to find out what the network stuff ignores and what not.

Did you notice I asked a question in post #2 ?

But the formula changes

To avoid misunderstandings, it is a good idea to accompany such a statement with a complete quote and a reference. What formula ? What is different with AC compared to DC ?

 

[berkeman]

I am more interested in RF AC B field

What frequency range? What volume do you want to fill with this RF field? How strong of an AC B field do you want to generate? Do you have a shielded room where you want to do this? Depending on the frequencies, volume and power, you will likely need to be careful not to violate FCC-type rules against causing harmful RF interference for nearby RF devices.

https://en.wikipedia.org/wiki/Helmholtz_coil

 

[artis]

Yes BvU, I should have been more careful with my explanation, surely the AC case doesn't differ from the DC only in that in AC the B field and current in the coil changes direction periodically and there are some added losses due to that which depend on the frequency etc.

Ok, my setup is this , I need to fill a space with an RF AC B field , I am still making the setup once it will be finished I will be able to measure the capacitance and inductance of my system and determine the frequency range necessary, I will have the ability to change capacitance within a given range.

The dimensions are as follows, I need to have a homogeneous B field within a space of 7cm horizontal distance and 24cm vertical , the element is circular and 24cm is the outer diameter so it should be covered nicely by the field since the coils are also circular. well basically imagine a cylinder 24cm in diameter and 7cm long and I need this cylinder to be covered with a homogeneous B field, as for the strength for my experiment the stronger the better but I am looking forward to the formulas to understand what results I can practically achieve.

PS. no worries about RF interference because I will use a mesh cage that will enclose the device once running.

 

[BvU]

but I am looking forward to the formulas

You are looking forward to what ? I concluded you had loads of formulas but couldn't make up your mind which one to use ?

But the formula changes

To avoid misunderstandings, it is a good idea to accompany such a statement with a complete quote and a reference. What formula ?

So -- again -- : what formula ?

I will use a mesh cage that will enclose the device

I'm unsure whether this then should be a really big cage in order not to deform the shape of the field too much. Anyone ?

If your 'element' under scrutiny contains iron, it is certain to deform the magetic field shape. No way it can remain uniform.

the capacitance and inductance of my system

Not clear to me if you are referring to your Helmholts coils or to $C$ and $L$ of the system you want to investigate.

Accel has some interesting equipment on offer, but you'll need a hefty budget ! https://www.edn.com/design/analog/4441240/4/High-Frequency-Helmholtz-Coils-Generate-Magnetic-Fields is another link to edn

 

[berkeman]

Ok, my setup is this , I need to fill a space with an RF AC B field

I still don't think you've told us what RF frequency range. That is very imporatant. And most likely, at RF frequencies you will have an AC EM field, not a B-field. Depending on your application and frequency range, it may be better to use an antenna with gain to generate the RF and anechoic absorbers to stop it after it propagates through your sample volume. That is similar to how TEM cells work. Are you familiar with TEM cells?

 

[berkeman]

Are you familiar with TEM cells?

Check out these compact TEM cells to see how close they are to what you are trying to do...

https://www.emcfastpass.com/test-equipment/shop/gtem-tem-cells/compact-tem-cell-tbtc1/

 

[artis]

I do apologize for the lack of certain key aspects here , the reason is because I don't want to speculate or put forward things that I haven't yet tested or seen or understood properly. I have actually done a few experiments with regards to my topic and concluded the results this will be just one of them, I plan to do a few interesting topics here on PF after I'm done with all of this and will have the necessary information to back my claims.The reason I couldn't specify a certain frequency or range of frequencies is because the device that I'm making itself will be a LC resonator which should in theory produce an RF frequency output the exact frequency will be determined by the L and C components ofcourse and since I haven't measured those yet I don't know the specific output frequency, the LC circuit will work as a generator so my idea is to use its output to power the Helmholtz coils so that they would then produce the necessary homogeneous B field in the region I said earlier which would then in turn induce current in my LC circuit. The power source for my LC will be a mechanical input , I know this sounds weird but I will show the idea when it's done if I will manage to build the device and make it work.Berkeman , no I am not familiar with TEM cells I am looking at them now trying to understand the idea.
Basically all I want to know as for now is whether I could make a sufficiently strong B field which is also homogeneous in the region the dimensions of which I specified in post #6, the strength of the field as I said ideally should be as high as possible but I should get decent results from anything above 0.2 to 0.5 Tesla which I feel is rather high for a helmholtz coil that is why I am looking for advice how to better make those coils in order to have low enough inductance and high enough current at high frequencies in order to produce a strong enough B field.

 

[BvU]

0.2 to 0.5 Tesla

Did you try plugging this in in the simplest of Helmholtz coil formulas to see what order of magnitude current you need to achieve such a huge field ? And then at high frequencies ? You work at CERN or Fermilab ? (*)

Read your story but can't find any argument to require the field is strictly homogeneous; in combination with you mentioning iron, I wonder what this 24 x 5 cm disk is supposed to contain

(*) Browsed a few of your other threads and am pretty convinced you don't -- but you might well end up doing good work there: no lack of curiosity and enterprising courage! Best of luck !

 

[artis]

I do realize that the problem is that at such high frequencies there aren't any materials that can help to "guide" the B field unlike at lower frequencies where we use laminated iron or ferrites to do the job so making a strong field out of Helmholtz coils that stand in "mid air" is not so easy, maybe there are other options here?

Judging by your last sentence you are probably thinking this must be one of those amateur tin foil hat ideas? And I'm not saying it isn't but before I get to conclusions I first need to calculate and make the thing.

 

[BvU]

Did you try plugging this in in the simplest of Helmholtz coil formulas to see what order of magnitude current you need to achieve such a huge field ?

Read your story but can't find any argument to require the field is strictly homogeneous; in combination with you mentioning iron, I wonder what this 24 x 5 cm disk is supposed to contain

I don't understand the combination 'Helmholtz' and 'guide the B field' ?

you are probably thinking

I'm pretty bad at telepathy, but in this one you are too: as long as you don't turn angry on me, all I want is to help -- see avatar

 

[berkeman]

The reason I couldn't specify a certain frequency or range of frequencies is because the device that I'm making itself will be a LC resonator which should in theory produce an RF frequency output the exact frequency will be determined by the L and C components ofcourse and since I haven't measured those yet I don't know the specific output frequency,

Well there's a big difference between a frequency of a few kHz and a few 100MHz in terms of what the fields will look like for devices of your dimensions.

the LC circuit will work as a generator so my idea is to use its output to power the Helmholtz coils so that they would then produce the necessary homogeneous B field in the region I said earlier which would then in turn induce current in my LC circuit.

It sounds like you should be thinking more in terms of two coupled inductors (your outer coil and your inner LC device). That will be a better model instead of a Helmholtz coil generating an AC field. Do you know how to model coupled inductors?

The power source for my LC will be a mechanical input

And how is the RF generated then? A mechanical input will not generate any RF content, unless it's connected to a generator that powers an RF oscillator circuit.

https://i.stack.imgur.com/TV16E.png

 

[artis]

The frequency will be closer to Mhz region that Khz for sure , my capacitance is very small in the order of picoFarads.

BvU well with guiding I meant to say that for a coil that has air as the medium through which B field permeates the B field strength will fall off faster than for a coil with laminated iron for example as the flux guide since air is rather bad at magnetic permeability compared to a laminated iron core , I do realize that at such high frequencies air is the only option otherwise I would have an inductive heater and my iron would melt if enough power would be applied to the RF correct?

Ok How about this version, can I make the B field homogeneous on a flat surface area near the coil because I don't need the field to actually be homogeneous all throughout the cylinder just at the ends and one more thing the field can be reversed from each coil as it can loop back through the middle. I'm sorry I specified the dimensions of my whole physical assembly I should have said that the field needs to specifically be homogeneous a few cm off the coil through a flat 2d surface what happens "further down the line" doesn't matter . I added a simple picture illustrating the idea, so being more specific the field only needs to be strong and homogeneous through the end surfaces which can be placed near the actual coils.

before I start calculating numbers in formulas is this even sound or do I have no chance of doing this at the Mhz frequencies with reasonable B field strengths?

 

[rude man]

Depending on the frequencies, volume and power, you will likely need to be careful not to violate FCC-type rules against causing harmful RF interference for nearby RF devices.

Once a ham, always a ham, eh b?

 

[BvU]

or do I have no chance of doing this at the Mhz frequencies with reasonable B field strengths

Did you already estimate the order of magnitude of the RF currents you need to generate 0.2 - 0.5 T in, say, 0.5 m Helmholtz coils ?

 

[artis]

I plugged in some numbers and basically we are talking about tens of thousands of Amps. Although I am not sure whether the formula I used takes into account of what happens when one adds a cap in series with the coils forming a series LC circuit , by matching the cap one can achieve resonance at given frequencies and cancel out the otherwise high impedance the coils would show to a high frequency current, what then?

If say my inductance instead of being few K ohms drops to a few ohms and I have say two loops for each coil and I run them parallel , in theory how could I calculate the necessary voltage and current for driving the coils and B field output?

 

[BvU]

tens of thousands of Amps

We're moving into the area of superconducting magnets ... and hefty budgets !

in theory how could I calculate

Did you check the accel link from #7 ?

 

[artis]

yup I did check it out.
Well in theory I could do without a complex RF amp because my LC circuit is producing the output frequency which I could feed back into the coils, the thing is that the strength of that output depends on the strength of the B field of the coils so I may need at least two stages, the first one producing the output to feed the second one's Helmholtz coils which could then produce a more powerful field for even powerful output in the second stage.

Well before superconducting I could simply use small copper heating pipes as wires and run ordinary water through them which is a rather simple setup an cheap and that way I could probably run hundreds of amps the problem would probably be to set it all up so that the field is uniform and inductance kept to a minimum.

Well anyways I've been told my aluminum parts have been made by a friend in a metal shop so I should be able to start piecing this thing together.

 

[Vanadium 50]

Stop right now. It's evident that you do not have the experience to handle this much current safely.

 

[rude man]

Habve you looked at the voltage you need to develop large current at megahertz frequencies? What is your inductance and what is 2 pi f L?

 

[BvU]

Stop right now. It's evident that you do not have the experience to handle this much current safely.

Tut tut, we're not yet at the point of blowing up things . Just considering and looking at the physics ramifications.

Just like with the train rails, we can calculate how much current a standard issue copper water pipe can carry without evaporating. From that we get a number of turns and an intrinsic resisitance, etc. etc.

The physics is fun and instructive !

 

[artis]

rude man I assume you are asking about the Helmholtz coils inductance and reactance? I did some quick google calculations about inductance of such coils (put in my approximate design specifics like diameter etc) the answer is about 1.9uH. although I couldn't find how to calculate the capacitance such coils would have.

For the test setup to see if all works I will firstly build the LC circuit and measure it's capacitance and inductance then I think I could try to match my coils with that in order to get maximum efficiency so that my LC circuit could drive the coils themselves.

 

[berkeman]

For the test setup to see if all works

I don't think you've said yet what you are going to use to drive the RF signal into the coil. You said something about a mechanical source, but that didn't make sense.

 

[artis]

I'm just moving ahead slowly and because PF is extra "sanitized" these days I don't want to say everything and even with as little as I said now Vanadium managed to say I should stop.
I may not know all the formulae involved but I am fairly familiar with electric safety and its not my first year going around wires and voltages but it is complicated to express one's experience through a bunch of posts.
One thing is for sure if I had listened to every one who said I shouldn't do this or that in my life I would probably been bored to death or living in a homeless shelter by now.

I will continue on with this and the only thing that will stop me is science itself (if the damn thing doesn't work in the end) Well I guess I will just have to go through papers and find the formulas for calculating the inductance and capacitance of the coils etc.

As I said I will explain in detail (I understand your curiosity of what drives the RF signal into the coils) but i want to do that in a separate thread once all is done so that I have some diagrams and a simple but detailed text so that anyone who reads can express and opinion or give feedback. After all my previous thread got closed for me dealing with too many subjects in one thread so here I'm just trying to deal with how to make functioning Helmholtz coils.

 

[berkeman]

Thread closed for Moderation for a bit...

Thread will remain closed. I'm in an extended PM discussion with the OP.