# Relation between air-core and ferromagnetic solenoid -core magnetorquers and measurement of dipole moment

I am going to be using air coil magnetorquers for a satellite development project. These air coil magnetorquers come embedded in solar panels. I am currently using this magnetorquer , it's a solar panel with a magnetorquer embedded into it. The magnetorquers are going to be used to produce a magnetic moment ($m$) to desaturate the reaction wheels in space. I have a controller that will provide me with the $m$ that I require, but I need a way to experimentally verify that I am getting the correct $m$.

I am pretty familiar with the math behind the ferromagnetic magnetorquers, alot of information is provided by this link.

I mainly have two questions:

Firstly,I am working with the magnetorquers integrated with the solar panels, would the mathematics remain the same? I also know that for normal ferremagnetic magnetorquers , $m=nIA$ , where $m$ is the magnetic dipole moment, $I$ is the current through the magnetorquer and $A$ is the area of the magnetorquer. Are these equations still valid for the air coil magnetorquers?

Secondly, how would I be able to experimentally measure the magnetic dipole moment generated by the air coil? For the ferromagnetic coil magnetoquers, I found this research paper to measure the magnetic dipole moment for a normal ferromagnetic magnetorquer, but I don't know if it would work for an air coil magnetorquer. I am also worried about how the solar panel itself would interfere with the measurements.

Thanks.

• That's a very nice paper about the ferromagnetic rod magnetotorquer testing. I don't think that that the equation $m=nIA$ applies to a ferromagnetic rod - there's no place to but the permeability or dimensions of the rod. However I think is a good equation to use for your flat coil. I believe that the spec of 1.55$m^2$ in the data sheet represents the product $nA$. If the area of one turn of the PCB trace is roughly 9x9 cm${}^2$ then there are roughy 150 to 200 very narrow turns in the trace, which explains the high DC resistance. – uhoh Oct 16 '16 at 1:26
• Yeah, I tried using m=nIA to calculate n, the number of turns, and found that it is indeed 1. The datasheet specifies the max m at the max voltage. But in terms of measuring the actual m, would it be already to think of my air coil as a ferromagnetic rod that is pressed flat, and use the same paper that I linked to find m? – John Oct 16 '16 at 1:29
• No you definitely can't use that equation. It is a (fairly good) approximation for a uniformly magnetized rod of ferromagnetic material, with a permeability $/mu$. The detailed shape of the coil isn't even specified there - it assumes the coil magnetizes the permeable material uniformly. Here you have only a coil and no permeable material. You need math that applies to a flat coil in air. It will also have to be an approximation because this coil has multiple turns of different sizes, and their shape isn't even a perfect square. – uhoh Oct 16 '16 at 1:41
• So again the best way is to measure at large distance where you can call it a point dipole. – uhoh Oct 16 '16 at 1:41
• Ah, alright. I'll edit my question to make it more concise – John Oct 16 '16 at 5:04

As for the equation, the difference between an air core and a magnetic core is reflected in a missing term known as the magnetic permeability, $\mu$, which is a measure of how much the magnetic field is boosted by the presence of the core material.
• Yeah. My main concern is that they are two totally different types of magnetorquers. Unless I can assume that my current embedded magnetorquer to be a compressed version of the torque rod used in the research paper. Which would mean that I'd have to prop up the solar array on it's side and duplicate the same experiment. Which I am not sure if I can do. I can't really apply $m=nIA$ as well, as the no. of turns,$n$, is not provided in the datasheet. – John Oct 16 '16 at 17:17