Determination of a magnetic field for a project

[icesalmon]

Homework Statement

Determine the magnetic field equation(s) for the following diagram as a function of frequency, material.

Relevant Equations

This is a project I am working on for my undergraduate senior design course and I have talked to professors in my department who do research in this area and have essentially told me that it is too difficult for an undergraduate to complete. Bear with me, I apologize for anything I may be neglecting to mention.

The network is a 3-Dimensional circular cross section path made out of silicone tubing or a 3D printed material and will be set inside of a agarose hydrogel in an attempt to mimic the density of human muscle/tissue.

The object of this project is to guide a ferrofluid (Iron Oxide particles suspended in a viscous fluid, a diluted mixture of 15% glycerine to 85% water, to a predetermined location by using a magnetic field generated by a series of electromagnets made by, possibly, Coilcraft model number DO5022P-105ML (pictured below) the multi-colored squares on the top of this path are where I am thinking of placing these and perhaps controlling their strength using a frequency generator and a circuit of which I am also having an issue determining.

My main focus right now is that, given that these magnetic fields will need to penetrate an agarose polysaccharide gel and whatever material the path will be printed out of, how to determine the "tesla" value of the field at any given depth of this network. Apologies if I haven't been fully clear about any crucial details, hopefully I can provide that information if need be.

If this truly is too complicated, is there a way to design a custom series of magnetic fields in order to achieve this goal?

 

[mfb]

This could make a nice BSc thesis, or a MSc thesis with more work and experimental results.
You might get a reasonable approximation by just assuming everything apart from the magnets is like vacuum, and ignore the feedback of the ferrofluid. That would be a much easier system.

 

[icesalmon]

This could make a nice BSc thesis with more work and experimental results.

I agree! Would a reasonable thing to do just be use the magnetic field equation(s) generated by a conducting loop of wire (an inductor)?

 

[mfb]

You probably want to add the different coils, but that's basically what I suggested.

 

[icesalmon]

You probably want to add the different coils, but that's basically what I suggested.

I'm not sure if this would be sufficient. Any thoughts?

 

[mfb]

Hard to tell without l,z,R being defined, and you might want to generalize that to arbitrary coils (a formula where you can plug in the number of the coil).

 

[icesalmon]

Hard to tell without l,z,R being defined, and you might want to generalize that to arbitrary coils (a formula where you can plug in the number of the coil).

The value 'N' is this quantity (the number of coils in the device). As for the value of R, I, and z these are all values that I will either obtain from the data sheet for the device itself (pictured above) or will determine from the network (the depth 'z' from the coil itself and the value of the current ('I') will be determined as well. Although I am nervous to test this out as I do have some values i'd like to compare with (MRI machines, Earths Magnetic field etc.) so i'll plug in some numbers and see if my solutions are at least reasonable. Thank you!

 

[mfb]

The magnetic field won't be proportional to the number of coils if the coils are in different places.

The magnetic field depends on the position and I don't know where you take that into account because $l$ (lowercase L, not I), R and z are not defined.

Edit: I wasn't defined either but it is obviously the current in the coil.

 

[icesalmon]

Thanks for the response!

The magnetic field won't be proportional to the number of coils if the coils are in different places.

Is there a way to simultaneously control different coils as a ferrofluid passes through successive sections of the path pictured above? If I can turn these electromagnets on and off by feeding them with current, there must be a way to control the coils this way.

The magnetic field depends on the position and I don't know where you take that into account because $l$ (lowercase L, not I), R and z are not defined.

You mean the distance an object being influenced by the field is from the source of the field(Iron Oxide particles) ? I must have misread but I could have sworn that '$z$' was this variable.

EDIT: I'm sorry I never mentioned what each variable actually means!

'$N$' is the number of turns in a single coil with a circular cross section

'$l$' is the length of a single coil, not the unfurled wire itself but when wound up how "tall" would that cylindrical coil be (it's like the 'h' in the volume of a cylinder pi*R²*h)

'$z$' is the distance away from the coil

'$R$' is the radius of the circular cross section of the coil

"$I$' is the magnitude of the RMS current in the coil so i_peak/sqrt(2)

 

[mfb]

Is there a way to simultaneously control different coils as a ferrofluid passes through successive sections of the path pictured above? If I can turn these electromagnets on and off by feeding them with current, there must be a way to control the coils this way.

That's something you need to check in the hardware. For the calculation it is trivially true.

'$z$' is the distance away from the coil

The magnetic field is not a function of distance alone. You probably found a formula for a special case (along the symmetry axis?).

 

[icesalmon]

That's something you need to check in the hardware. For the calculation it is trivially true.
The magnetic field is not a function of distance alone. You probably found a formula for a special case (along the symmetry axis?).

I did find the equation posted above as a special case for a solenoid outside the coil. How can I go about deriving an equation for a solenoid in this case. If I'm ignoring the feedback of the ferrofluid and that I'm working in a vacuum. And what do you mean by 'adding the different coils'. What is this accounting for? The interference of the magnetic fields?

 

[mfb]

How can I go about deriving an equation for a solenoid in this case.

You can find equations in textbooks, and probably somewhere online as well.

And what do you mean by 'adding the different coils'.

If you have two coils, add their magnetic field (vectors).

These is all very basic preliminary work before it gets interesting. It won't get easier.