Why Don't NMR Magnet Designs Utilize the Fourth Maxwell Equation?

[Domenico94]

Hi everyone...I'm just looking nmr schemes, and magnets, and, at the same time, studying Physics II and electromagnetic fields at my faculty of electronics engineering. I know this may sound like a "dumb" question, and I don't want to sound like councited or similar stuff, but I was just asking myself, why, when people design magnets, especially for NMR (which requires a very strong magnetic field), they don't just exploit the 4 th maxwell equation, according to which the rotor of the magnetic field, is equal to the current density, plus the DERIVATIVE of the electric field, in time.
If we woud use an increasing electric field (in any way possible), with a quantity, say:
E(t) = (1,5)*t
The slope would be 1,5 which, at least IN THEORY, would be equal to the magnetic field created by the magnet.

So, my curiosity, was, of course it wouldn't work, because scientists would have thought to such a "naive" solution, but why doesn't it work? Does magnetic field in that case reach some level of "saturation", which we can not go beyond, or is it just for some other reason? Any answer is well accepted :)

 

[Orodruin]

The slope would be 1,5 which, at least IN THEORY, would be equal to the magnetic field created by the magnet.

This would be the curl of the magnetic field. How the magnetic field would look would depend on the boundary conditions. Furthermore, have you tried computing the charge buildup that would be required to create this electric field?
The easiest way of creating a strong stationary magnetic field is to use large stationary currents creating electromagnets.

 

[Domenico94]

This would be the curl of the magnetic field. How the magnetic field would look would depend on the boundary conditions. Furthermore, have you tried computing the charge buildup that would be required to create this electric field?
The easiest way of creating a strong stationary magnetic field is to use large stationary currents creating electromagnets.

with "charge buildup" you mean the voltage?

 

[Orodruin]

Yes.

And again remember that this only gives you the curl of the magnetic field, not the magnetic field itself.

 

[Domenico94]

If you consider a slope of 2, (by approximating 1,5 with 2), voltage would increase with this relation
E(t) = 2t (with t, obviosully, in seconds).
A NMR lasts 30 min, if I'm right, then 1800 seconds
At the end of the NMR, the Electric field, should be equal to
E(t) = 2 * 1800 = 3600 V/m.

The voltage is equal to the line integral of the electric field, and I don't know how to find it in this case, but I guess it could be something like 3600 o 7200 Volts, at is highest value, which I think could be obtained with a special transformator.
The point is : this surely, doesn't work, because engineers would have surely thought of this "naive solution". But then, WHY doesn't it work? What are the physical princples that don't allow doing that?

 

[Orodruin]

If you consider a slope of 2

The slope cannot be 2. The number 2 does not have the appropriate units. If you consider that you want a magnetic field of ca 1 T in a volume of ca 1 m, the appropriate units would give you a slope of ca 10¹⁷ volts per meter per second. This comes from basic dimensional analysis of the Maxwell equation.

Edit: Also, the rotation describes a change in the magnetic field with the spatial position. In NMR you usually want to have a constant magnetic field in the z-direction and add smaller gradients on top of that.

 

[Domenico94]

The slope cannot be 2. The number 2 does not have the appropriate units. If you consider that you want a magnetic field of ca 1 T in a volume of ca 1 m, the appropriate units would give you a slope of ca 10¹⁷ volts per meter per second. This comes from basic dimensional analysis of the Maxwell equation.

Edit: Also, the rotation describes a change in the magnetic field with the spatial position. In NMR you usually want to have a constant magnetic field in the z-direction and add smaller gradients on top of that.

Thanks for your reply, at first :) So, from what I'm seeing, if we apply an electric field that varies linearly with time, you would obtain a magnetic field, but that would be too weak to be used, correct?

 

[Orodruin]

Yes - and it would not be constant in space, which you generally want to have for NMR application (apart from the gradients).

In order to get any kind of magnetic field in the ballpark of what is used for an NMR in the fashion described, you would have to use electric potential differences of the order of 10²⁰ V. I do not see that you can put a patient in any kind of environment that is a good enough insulator for that not to discharge ... with the patient in the middle of it ... We are often deleting threads based on describing dangerous activities for voltages around 200 V ...

 

[Domenico94]

Oh ... I see :D I didn't consider all the stuff related to the rotor and Maxwell's equations then ahahah :D
By the way, I've seen on your profile page that you're a physicst, so I think you're the right person to ask this question : I'm at 2 year of bachelor of communication systems engineering (it's very similar to electronics engineering), but, as you may have noticed, I really want to work with medicine - related stuff one day, like CT scans or NMR, etc.
The problem with this is that this field is pretty much for people with a degree in physics (things like the quantum principles behind the NMR will never be studied in an engineering course). Then, what would you suggest to a person wanting to take this path? Maybe spending his time studying the physics subjects he doesn't know, in order to access the Master's degree in physics, and of course, having a master's degree in physics, or continuing with electronics engineering, and takind master's degree in Engineering?
The point in favour of engineering, is that an engineer may have better knowledge about stuff like signal processing, and electronics-related things, but I don't know how much it can help to improve CT scans, or NMR machines, compared to the work a physicist may do.

 

[Orodruin]

I think this depends a lot on where you are. In Sweden there is a special degree (called medical physics) for people doing essentially anything related to medical applications of physics such as NMR, dose calculations, nuclear medicine, CT scans, etc. I am not sure how it works in the states or anywhere else. I suggest you make a new post in the Academic Guidance forum regarding this issue if you want more to the point answers. Do not forget to specify your location, as this is often of importance.

 

[Domenico94]

No..I'm from Italy..but we have that degree in Medical Physics too. The problem is I would have to take a lot of physics courses (like quantum physics, nuclear physics, and so on), in order to access the master's degree in physics. The thing I'm undecided about is : would you suggest a person to take phyiscs after graduating, though it takes much more time? or would it better to continue with engineering (although I'm afraid an engineer there could study only signal processing, and similar stuff, but nothing more)?

 

[Orodruin]

I am sorry, but I do not have any clue about how the Italian system works or what would be required of you to work with NMR in Italy. Therefore, I would not feel comfortable trying to answer your questions about this in particular. The only thing I can advise you to do is to get as much information as you can before making a decision. Ask around and try to find out what different options would imply.

 

[Domenico94]

I am sorry, but I do not have any clue about how the Italian system works or what would be required of you to work with NMR in Italy. Therefore, I would not feel comfortable trying to answer your questions about this in particular. The only thing I can advise you to do is to get as much information as you can before making a decision. Ask around and try to find out what different options would imply.

Alright...Thank you for your previous answers anywayThank you very much!

 

[Domenico94]

Yes - and it would not be constant in space, which you generally want to have for NMR application (apart from the gradients).

In order to get any kind of magnetic field in the ballpark of what is used for an NMR in the fashion described, you would have to use electric potential differences of the order of 10²⁰ V. I do not see that you can put a patient in any kind of environment that is a good enough insulator for that not to discharge ... with the patient in the middle of it ... We are often deleting threads based on describing dangerous activities for voltages around 200 V ...

Hi :) I was just thinking about the calculations we were talking about the other day, and tried to think how you arrived to that number, although I wasn't able to reply the calculations...Can you explain the procedure you have to follow to obtain that result? You have to start from the Ampere - Maxwell's law, of course, but after that, what do you have to do? Thanks again :D

 

[Orodruin]

Just estimate the order of magnitude of the field you would like to obtain (roughly 1 T) and note that the typical length scale is roughly one meter. Everything else is natural constants and the derivative you want to estimate.

 

[Domenico94]

OK...thanks :)

 

[marcusl]

No..I'm from Italy..but we have that degree in Medical Physics too. The problem is I would have to take a lot of physics courses (like quantum physics, nuclear physics, and so on), in order to access the master's degree in physics. The thing I'm undecided about is : would you suggest a person to take phyiscs after graduating, though it takes much more time? or would it better to continue with engineering (although I'm afraid an engineer there could study only signal processing, and similar stuff, but nothing more)?

You wouldn't have much chance of entering a physics Master program (at least in the US) without mastering (excuse the pun) the undergrad physics curriculum and doing very well on the GRE exam. it's much easier to do that now than to start over after your undergrad education ends. It's also much easier for a physicist to pick up EE concepts through self-study than the other way around.

 

[Domenico94]

You wouldn't have much chance of entering a physics Master program (at least in the US) without mastering (excuse the pun) the undergrad physics curriculum and doing very well on the GRE exam. it's much easier to do that now than to start over after your undergrad education ends. It's also much easier for a physicist to pick up EE concepts through self-study than the other way around.

Yes...it s what I meant..physics is, on one side, much harder than engineering is, but, in the ither side, I m afraid an engineer would be cobdibd only to signal processing and stuff likr that. By the way, now I ve been reading stiries of people working with nmr, designing tje coils, etc. And their degree is on biomedical engineering. If I think that is close to what I study,( i study communication system engineering), would it be a good choice to study it rather than physics? Which are thw differences between medical physics and biomedical engineering?

 

[marcusl]

Sorry, I'm not familiar with the curricula in these fields. I suggest looking online into the degree programs at one of your favorite universities.