I am building a square, single-frame Helmholtz coil device for tracking the drift of an EMF meter between calibrations. I need some help figuring out resistors for controlling the circuit so that I can get 3 different magnetic field outputs in the center of the coil. Keep in mind, I'm not trying to calibrate the meter, I just want to qualitatively track whether it is losing calibration over the course of a year.

The coil gizmo I've built is self-contained and portable. The coil lives in the bottom of a large, flat wooden box. The controls live on the lid of the box, and I have designed the lid, complete with controls, to be separated from the coil so that they do not interfere with the magnetic field (within reason).

I have the following components:
- A square coil wrapped around a wood frame that is 18 inches long per side, consisting of 9 turns of a single strand of (approx.)16 gauge speaker wire (so, about 72 linear feet of wire)
- I twisted together the two wire tails that come off the coil (to control induction), and these two lead wires will attach to the transformer circuit
- The control box is driven by a 3 A transformer (AC) with a 12 or 24 V output and a polarized plug
- A 3 Amp fuse will be installed between the transformer and the coil
- On the other side of the coil, a 3-way switch will be installed to select one of 3 resistors that will help control the strength of the magnetic field
- A 1 Amp voltmeter will be installed (after the 3-way switch) on either end of yet another resistor to monitor voltage

Today, I hooked up the power cord to the transformer, and hooked the coil wires directly to the output on the transformer (I used 24 V output). I set my EMF meter in the middle of the coil, donned safety glasses, grabbed a fire extinguisher, and switched the circuit on. I achieved a magnetic field in the middle of the coil of approximately 3200 milligauss . I switched everything off before the smoke escaped. I call that a success.

I tried it again with the 12 V output and got about 3000 milligauss. Not much of a difference.

Now I'm stuck. I am having a hell of a time with the math for calculating the resistors I need to get the magnetic field outputs I want. Math has never been my strong point, and I am completely befuddled by the Helmholtz formula. So, I am hoping someone here can help me figure out what resistors I'll need to get the approximate magnetic field I want.

What I'm hoping to achieve, using resistors connected to the 3-way switch, is the following output:
- 1 setting of approximately 10 milligauss
- 1 setting of approximately 200 milligauss
- 1 setting of approximately 500 milligauss

By "approximately", I mean within 50 to 100 milligauss.

FINALLY, The Questions:
I understand that my power output using 12 V transformer setup is 36 Watts, and that it's 72 Watts as a 24 V transformer. How in the heck do I calculate what resistors I need?

I know there's a 4th resistor in the circuit for the voltmeter that needs to be factored in (I have the formula RL = Rs +Rn where RL = all resistors together, and Rs = the sensor (voltmeter) resistor, and Rn = whichever resistor is selected with the 3-way switch).

In addition, I'm pretty sure these are huge power resistors, and I'd like them to be within +/- 2% accurate --what's a good source for these things?

Any kind of specific suggestions you folks can offer along with reference formulae would be appreciated. I really just need to get this monster built.

Thanks!
Maxine

 

The coil current you had in the setup was probably only limited by the effective circuit resistance, which is likely quite low. The Helmholtz coil inductive reactance would not be substantial at mains frequency.

The Helmholtz-coil field will be (notionally) directly proportional to current.

Your first task would be to measure the current (Ix) that gave you (say) the 3000mG, using a multimeter on AC range and the transformer connected at 12V. The low path resistance probably meant that the transformer was under heavy load - if not overloaded - possibly causing the output to drop well below the nominal 12V or 24V.

Having found the current you'll need about a sixth of that value to give you your maximum value of 500mG - i.e. Ix/6

So the total resistance for 500mG would be

R_500mG=Vac/(Ix/6)=6Vac/Ix

Similarly

R_200mG=Vac/(Ix/15)=15Vac/Ix

And

R_10mG=Vac/(Ix/300)=300Vac/Ix

Say, by way of example you find Ix=5A.

Then...

R_500mG=1.2Vac=14.4Ω with 12V supply or 28.8Ω with 24V supply

R_200mG=3Vac=36Ω with 12V supply or 72Ω with 24V supply

R_10mG=60Vac=720Ω with 12V supply or 1440Ω with 24V supply.

The coil resistance will probably be less than 1 ohm, so it shouldn't change the required external series R values by that much - say 0.4 Ω.

You then need to rate the resistors so that they don't overheat.

You would use Power=Vac^2/R

So if you actually had found you required R=14Ω with 12V ac then you would need a minimum rating of ~10.3Watts. You might try a 15Ω 10W in that situation. If you used 28.8Ω with 24V ac then you'd need a 20Watt minimum rating.

Having worked out the required series R values and their ratings, you then have to source them from a supplier. Power resistors are sometimes harder to get - depends where you live of course.

 

An objection I would have with measuring the current with the transformer seriously overloaded would be the risk of damaging something while you are taking the current measurement. Also the current waveform might be seriously distorted.

You might do better to insert some resistance in series with the coil to prevent this. Even if you can get hold of a 10Ω 20W resistor to place in series as a starting point and use the 12V tap on the transformer, then you could take a current measurement and another field flux density measurement in relative safety.

These two numbers will then give you the starting point for your required resistance calculations.

If the current is Ix and the flux density is Gx[mG] then for the 500mG resistance setting you would require

R_500mG=(Gx/500)*Vac/Ix

For the 200mG resistance ....

R_200mG=(Gx/200)*Vac/Ix

For the 10mG resistance ....

R_10mG=(Gx/10)*Vac/Ix

Hopefully your transformer is capable of delivering the necessary continuous current for the maximum case of 500mG.

 

Ah, this is helpful. I figured it was something along these lines. I don't necessarily need to achieve 500 mG. I could go with much lower outputs (10 mG, 100 mG and 250 mG) if 500 mG is not practical. I really just need three different points to measure. Also, thanks for the formulae, that is exactly what I needed.

I think I understand the concept here--my huge voltage input with low resistance will overload my transformer.

Based on that, does it make sense to do either of the following:

- Size down my wire gauge for the coil (maybe to 20 or 22 ga);
- Size down my input voltage (maybe to 6 V) and (maybe) increase my amps; or
- All of the above?

If I do that, are there any other formulae I need to consider?

 

What you need to know is the field as a function of current. You can of course use the classic formula for such coils, but, as you're doing, you really want to measure the relationship. The ideal tools here, assuming you can get them, are an AC ammeter (a digital multimeter should work fine, as I assume you're using line-frequency voltages), a 24 VAC transformer (or thereabouts; it sounds like you already have one), and a Variac. The Variac will drive the transformer and the transformer drives the coils. As you increase the Variac's output, you can plot the measured field as a function of current. Of course, you start at 0 current and work up. The Variac helps you avoid putting too much current through the coils.

Once you know the required currents, then you'll need to find the requisite resistors to use with the transformer you'll use. These can be calculated by knowing the coil resistance (use a 4-wire measurement).

 

Holy moly. I have a multimeter (and yes, I'm dealing with 60 Hz here). However, a Variac (which I had never heard of before) is not really in my budget, especially since this is a one-off thingumy. Looks like Variacs range from $13 (if you get lucky on eBay) to $400.

Is there any kind of trick that would work besides a Variac?

 

Actually, the first answer seems to be the answer.

 

If you're an EE working for a company, they shouldn't balk at supplying a Variac. And it's possible there's already one somewhere in your company, unless it's a small company.

Another option might (I repeat, might) be to use a lamp dimmer to supply the current. The problem is that the current will definitely not be a sinusoid and you won't get correct current readings unless you have a meter that can read RMS amperes. And a decent meter can cost more than a Variac. If you have access to a digital scope, then you could look at the waveform and measure the current. You'd probably use a shunt resistor on the secondary low-voltage side and use the scope to measure the voltage across the resistor and convert it to a current. It's not hard, but there are some subtleties and ask for help before trying it. It's definitely NOT something a beginner should try on the high-voltage side.

Another option is a big pot or rheostat that can handle the power to drop the voltage across. But it's unlikely you have access to one of those. One place to check for both a Variac or a rheostat is the physics or EE department of a local school -- they might be willing to loan you one in exchange for something.

If you could borrow a Variac, it probably wouldn't take more than 15 to 30 minutes to have the data you want, including hooking it up.

 

This is a rather independent project. Also, please note I'm a complete noob, not an EE, but I am trying to figure this out and make a useful tool without burning the house down.

I just looked at some of my random vintage electronic gizmos, and I might actually have something that might be useful, though I'm not sure of it's actual functionality or usefulness in this case (it's a Daven Company Power Output Meter)?

Here's a link to exactly what I have:http://cgi.ebay.com.sg/ws/eBayISAPI.dll?ViewItem&item=280626335376#ht_500wt_922

Mine has one missing ceramic insulator on the upper left, and I can see through the side mesh that some of the ceramic or asbestos has come off of some of the windings on the impedance resistors.

I also have an Eico Push-Pull Oscilliscope, and I think the only thing wrong with it is that it has one bad wire that I can solder back on. I presume that's what you're referring to.

Of course, neither of these gizmos have been tested, so any advice on checking either of these for functionality before I attempt to use them would be appreciated. So I don't burn the house down.

As I mentioned, I'd be willing to re-wind my Helmholtz coil using a finer gauge of wire, if that will prevent me from having to spend a truckload of money on power relays. And/or I can find a different transformer with a lower voltage. I may have some resources at the local university, but I'm trying to figure this out on my own as much as possible.

Thanks.

 

Another cheap option might be to "set" currents in the coil by using 12V automotive lamps connected in series / parallel configuration - rather than power resistors.

A single 15W 12 V lamp would limit the current to about 1.25A. Two lamps in parallel would give you 2.5A. You could use lower wattage types to give the lower current conditions.

Just a thought, but possibly a simple cheap solution.

You really do have some vintage equipment in your toolkit! Do you have access to those old fashioned power rheostats with the slider tap bar on top?

Someonesdad's suggestion of the Variac option is a good one.

 

SOP would normally dictate that an experiment like this be initiated at the lowest voltage available and then work your way up. We very rarely begin with the highest available source and work our way down. This is just a logical order of progression for testing nearly every electromechanical device or machine.

It could be argued that there are devices such as induction motors, certain electronics circuits, etc that, when operated at a lower voltage than which it was designed, could cause damage. This isn't one of them though.

 

Dang -- t_n_k's suggestion is a good one because local stores will provide you with a bazillion different types of bulbs and you shouldn't break the bank finding a suitable bulb. Bulbs are good loads.

You have to give us an idea of the power levels of your coil setup. Tell me the voltage and current you're running the coil at and the no-load voltage output of your transformer. I have one or two World War 2 power rheostats that I've had for over 40 years and never used (and they're gorgeously made -- you probably can't buy stuff like them today) -- I'd be willing to send it to you if you pay the postage. They came of a beautiful sealed unit that was a PPI (radar display) for outdoor use on a ship's bridge. The thing was built like a tank. I'm still using the some of the hundreds of brass screws I took out of that thing.

 

Of course, neither of these gizmos have been tested, so any advice on checking either of these for functionality before I attempt to use them would be appreciated. So I don't burn the house down.

As I mentioned, I'd be willing to re-wind my Helmholtz coil using a finer gauge of wire, if that will prevent me from having to spend a truckload of money on power relays. And/or I can find a different transformer with a lower voltage. I may have some resources at the local university, but I'm trying to figure this out on my own as much as possible.

Thanks.

The Variac is useful for powering up old equipment to make sure nothing starts burning.

One thing I forgot. You can make some decent low-resistance resistors yourself. Go to Harbor Freight and buy some of the 0.041" diameter stainless steel safety wire (it usually comes in a 1 pound roll for $5-$10). Get a smaller diameter if possible. The 0.041" wire has a resistance of 0.1 ohms per 119 mm (last time I measured some). You can wind the wire around an insulator. A good one would be a threaded wooden or nylon dowel because the threads keep the wire from shorting. Nichrome or Chromel wire is even better (so is Monel), but a lot more expensive. Plain steel wire is good too, but I don't like to use it if I can help it because it rusts.

 

I could try the light bulb thing. I have quite a few of those lying around.

I wish I had a power rheostat, but no luck unless the Daven product is a power rheostat by design. I picked up the equipment cheap because I love the look of it. Dials and gauges are also high on the list of nifty things.

I'm seriously considering re-winding the coil using smaller gauge wire as well. Hmmm...

 

Oops, I missed some of the other posts. Thanks for the additional input.

The transformer is designed to run 12 or 24 V at 3 A. Clearly, I don't have enough resistance on the thing. Which is why I'm considering re-winding the coil. It's a pretty easy task (I figured out how to do it easily). I just need more fine wire.

I presume this would increase the resistance of the circuit and make life easier for the transformer. But the lightbulbs or a hand-wound resistor sound like good tricks also.

I would love to have followed SOP, but I admit to completely flailing my way through this project. There aren't a lot of easy access documents on how to build a coil like this from scratch. It's not the kind of thing I would normally pick as a "first AC project", that's for sure.

I'll post some photos when I'm done re-winding the coil and building the project box.

 

Well, kudos for tackling the project at all. That's how we all learn -- we get interested in something and try to make it work. Bulldog perseverance (to a point!), curiosity, initiative, and learning to find good mentors all lead to knowledge you can't get any other way.

You can estimate the resistance of the coil if you know the material and wire diameter. I'll assume you're using copper wire and know how to use a copper wire table to get the resistance per unit length. If not, a quick web search will turn it up.

 

I will definitely check that out. Thanks for the kudos!

So, if I'm calculating this right--using the 3 amp transformer, to avoid damaging it, my minimum resistance in the coil should be:
At 12 V, 4 ohms
At 24 V, 8 ohms

Is that right? If so, this might be the breakthrough I'm looking for. I was worried that putting too much resistance in the coil would damage the transformer or light a fire. I had it backwards, apparently. Too little resistance on a circuit damages the transformer. OOPS.

So, according to http://en.wikipedia.org/wiki/American_wire_gauge
1000 feet of 22 ga copper wire has about 16 ohms resistance. If I need, say, 4 ohms resistance, I could use 250 feet of wire. On my coil, which is about 1.5 feet per side (6 feet in circumference), that's about 42 winds around the circumference.

Did I get that right? If yes, EUREKA!!

 

Did I get that right? If yes, EUREKA!!

Have you calculated what flux density this will give you or will you accept whatever it turns out to be?

Anyway - Sounds fine.

That's a reminder of a nice segue ... believe it or not there is a type of wire known as Eureka Wire - used for making wire wound resistors!

 

Ha ha!! How appropriate. But yes, I'm pretty much willing to take what I can get, then modulate it down with resistors to make three different field strengths. This, I decided a few weeks ago, would be easier than trying to design a circuit to a very specific field quantity.

I just need it to stay the same every time I turn it on so I can check my instrument.

Now that I have some kind of clue, my goal is to get the resistance high enough to get the wattage low enough so I can buy cheaper resistors.

I hope i'm on the right track!

 

I hope i'm on the right track!

Just make sure it's not a railroad track.

Oh, one glitch in your scheme is that when your line voltage varies, the current in your coil will also vary. Don't be surprised by variations of a few percent -- they're common. And most engineers design their stuff to handle 10% or so variations (or they should).

Years ago I had problems with line variations when I was making some finicky UV measurements from UV fluorescent tubes. I found an old ferroresonant transformer on ebay for $20 or so that completely solved my problems.