# Experimental approach to calculate magnetic field of magnetic coil

Discussion in 'The Projects Forum' started by cupcake, Nov 9, 2011.

1. ### cupcake Thread Starter Member

Sep 20, 2010
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0
Hi, I have made some TMS (transcranial magnetic stimulation) coils, using a copper wire, and I have calculated the inductance using some kind of formulas, and I could calculate the magnetic flux of the coils using faraday's law, but I think the results won't be so accurate, hence, is there a way to calculate the magnetic flux of a coil using experimental approach, like for example a circuit design to test or some kind equipments and tools?

thanks

2. ### wayneh Expert

Sep 9, 2010
12,093
3,032
You can buy a Gauss meter for this purpose. It would be easy to build something to detect the field, but not so easy to have your measurement be calibrated.

Aug 27, 2009
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4. ### t_n_k AAC Fanatic!

Mar 6, 2009
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If practical - One experimental approach might be to wind a small air cored 'search' coil of known physical dimensions and turns. This could be connected to a DMM on AC voltage range to measure the induced AC voltage. The TMS coil would then need to be excited with a low voltage AC source - perhaps from the secondary of a mains transformer with some secondary current series limiting resistance. The search coil would then be placed at various positions/orientations in relation to the excited TMS coil and the maximum DMM readings recorded. The voltage induced in the search coil can be translated back to the magnetic flux density at the point of observation, using the search coil's physical parameters. The search coil signal may require some amplification - an added complication.

One can purchase Hall Effect sensors which may be a simpler (and probably relatively inexpensive) alternative to that proposed above.

If you can hire or borrow a Gauss meter then all the better.

5. ### wayneh Expert

Sep 9, 2010
12,093
3,032
Well, it's called a LAW for a reason. The calculation will be accurate if interpreted correctly.

But I assume you're trying to estimate or control "dosage" into the load, a human head. I think this will be difficult because of all the variables; the magnetic permeability of the subject, the distance between the coils, the air and hair gap between the coil and the skin, how well the coils are aligned on, and perpendicular to, an axis line and so on.

Are you following someone else's work in this area? Folks here are good with circuits but direct experience with this particular technology might not be in the toolbox around here. And there's no substitute for experience.

6. ### cupcake Thread Starter Member

Sep 20, 2010
73
0
Thank you all for your kind replies. I didn't have Gauss Meter, that's the problem, but I guessed I could try to find one.

I would like to obtain this kind of graph, by measuring the magnetic flux of the coil.

where, model 1,2 etc is the different types of coils.

7. ### cupcake Thread Starter Member

Sep 20, 2010
73
0
This sounds so complicated, but doable. By the way, how to measure the resistance of the coil? I'm provided by the formula to calculate the inductance of the coil (knowing its turn, diameter, permeability etc), but not the formula to calculate the resistance. Someone told me briefly, that I have to measure it, by building a simple circuit (forgot consists of what components), and measure the output signal (?) not really sure though.

8. ### cupcake Thread Starter Member

Sep 20, 2010
73
0
Right now, I'm trying to do the "easy" part first, like building the coils and measure it magnetic flux density, I'm leaving the implementation and testing with the human head later. I want to match my hand calculation with the experimental result, but, don't know how to proceed from there.

9. ### wayneh Expert

Sep 9, 2010
12,093
3,032
If you used standard copper "magnet" wire, you can calculate the resistance from the length you used and a value from a table. I can hunt a link for you if needed. If you wound the coil without measuring the length, you can estimate the length from the geometry.

The resistance is probably quite low, a few ohms or less, maybe in the mΩ range if you used low gauge wire. A cheap multimeter won't help you much in that range. I imagine an expensive meter might. Another way is to run current through it, say 100mA, by using a power source and a current-limiting resistor. Then measure the voltage drop, which would be 100mV for each ohm if you were at 100mA. (There's no need to control the current, just measure it.) Even a cheap meter can measure 10mV fairly precisely, which would take you down to measuring tenths of ohms.

10. ### cupcake Thread Starter Member

Sep 20, 2010
73
0
but, how to calculate? I tried to google it, looking for a formula to calculate the resistance of the copper wire, but could not find it. I'm using normal copper wire, not sure what you meant by "magnet" copper wire.

11. ### cupcake Thread Starter Member

Sep 20, 2010
73
0
anyone knows how to calculate the inductance for butterfly coil (tms)???? I managed to find a formula for circular coil and flat circular coil, but could not find butterfly.

12. ### wayneh Expert

Sep 9, 2010
12,093
3,032
Go see here, for instance.

Copper wire has 0.01724 Ω per square mm, per linear foot. The diameter can be calculated from the AWG gauge:
bare wire diameter in inches = (0.0050) x (1.1229322)^(36-AWG)