How to calculate required current and specifications for a “wet coil” to generate x Tesla of magnetic field?

A water management project requires a "wet coil" (coil will be submerged in aqueous media) designed to generate a steady-state electromagnetic field of adjustable magnetic magnetic flux density at the center. The coil will be helical with a hollow core (wound on a nylon perforated cylinder used as former). The inner diameter of the coil needs to be between 6 and 12 centimeters, say 8 cm to put a number to it.

I would like to understand how to compute the number of turns needed, and the current that must be driven through the coil, to generate a specific magnetic flux density.

In this context the required range is from 0.1 Tesla to 1 Tesla, but I would rather understand the method than the result. Also, if there are any suggested commercial resources / products to look at, for both coils and drivers, pointers would be very helpful.

My background is oriented more towards banal analog and digital electronics and software, than electromagnetic phenomena or applied physics. Though I did learn basic electricity and magnetism 2 decades ago, that's all very rusty. Hence, I apologize if my question leaves too many gaps, please let me know and I will amend the question accordingly.

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2 Answers

Here is an approximation of what you are trying to do. The magnetic field inside a solenoid is given by (from Wikipedia) $B={\mu}nI$ where ${\mu}$ is the permeability of the medium (presumably water in your case), $n$ is the number of turns per unit axial length, and $I$ is the current. The maximum value of $n$ is determined by the thickness of the wire you are using. This vendor sells magnet wire as thick as 12 gauge, which for a single layer wrapping yields $n=468$. The permeability of water is very close to that of vacuum, so use ${\mu}=4{\pi}{\cdot}10^{-7}$ $H{\cdot}m^{-1}$.

Achieving your minimum desired field of 0.1 Tesla requires a 170 Amp current which is probably well beyond the safe operating range for 12 gauge wire. Now this is an engineering problem. You could look for a thicker wire and also wrap multiple layers to reduce the required current. If the water is flowing that will help keep the wire cool, but being submerged demands careful consideration of electrical isolation. Here are some epoxies for potting electronics, though I suspect there are many other options available. Hopefully the links provided help illuminate what keywords to use in your research.

Once you have an idea of what kind of wire to use (and its resistance), and also the max current you'd like to run, you can use $P=I^2R$ to estimate the power you will need. Then you can start shopping for a DC power supply.

A 1 Tesla field is huge!

To the senior members: I apologize in advance if it was in bad taste to link to vendors.

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So if I understand this right, the one reasonable option might be a 5 to 10 layer winding? Would that not also affect flux density adversely, compared to a single-ply winding? – Anindo Ghosh Nov 28 '12 at 7:00
You will certainly need to use multiple layers. In the ideal case, a safe 9Amp load on 12AWG will demand almost 20 layers just to get 0.1T. You need higher current and thicker wire. The toughest part will be figuring out if there is any wire available that can do what you need. Thicker wire can carry more current, but the added thickness reduces $n$, which increases the current you need. It might help to make a spreadsheet of various currents required for a range of standard wire gauges, then call around to see if any vendors have a wire that can satisfy your requirements. – xxx Nov 28 '12 at 15:11
Useful info: 1 2 – xxx Nov 28 '12 at 15:14
Thank you for all the help! Let's see how far this rolls, given the concerns. – Anindo Ghosh Nov 28 '12 at 16:31

A wise man once said: "A 1 Tesla field is huge!" You need to be considering using an iron core, with your water between the pole pieces. Varian is the first vendor to come to mind.

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Unfortunately the iron core is not an option, the processing plant design is not mine. – Anindo Ghosh Nov 28 '12 at 6:58
OK. Well, the equation B = unI is for a thin layer solenoid. See utc.edu/Faculty/Tatiana-Allen/magfield.html the field depends on the diameter of the coil, so each added layer is less effective. The integral of 1/d does not go to zero, so at least you -could- get one T with an arbitrarily large solenoid. This could be a fun homework for you: given a stated current per square cm capacity for copper wire, solve for the size of the solenoid needed to generate 1T. It will be HUGE. – Bobbi Bennett Nov 28 '12 at 20:07
And -then- (!) you have to question the stated current per square cm capacity of the copper. That will give you solution for size vs field, but the real limit is the highest temperature in the copper coil. So now you gotta solve for thermal conduction from a point source of heat inside a solid mass of copper to the outer surface, and use the resistivity of copper to give you a new current (per square cm cross section) limit. – Bobbi Bennett Nov 28 '12 at 20:16