UHF/SHF Electromagnet Homework Solution

[JasonGodbout]

Homework Statement

I am making a prototype and I need an electromagnet with a wavelength of the order of centimeters. The magnetic field can be 10 mT or more.

The Attempt at a Solution

Microwave have magnetron in it, but they don't specify the magnetic field since it's not the purpose of the device. I would like something between an MRI (lol) and microelectronics.

 

[mfb]

An electromagnet is a magnet that can be controlled with current in a coil. It doesn't have a wavelength.
An electromagnetic wave has a wavelength, but with a wavelength of centimeters a peak magnetic field of 10 mT would be absolutely insane - gigawatts of power.

What exactly do you want to do?

 

[JasonGodbout]

An electromagnet is a magnet that can be controlled with current in a coil. It doesn't have a wavelength.
An electromagnetic wave has a wavelength, but with a wavelength of centimeters a peak magnetic field of 10 mT would be absolutely insane - gigawatts of power.

What exactly do you want to do?

I want to control a magnetic field with metamaterial design by PCB. That's why I need that order of wavelength. What magnetic field strength can I expect?

 

[berkeman]

with metamaterial design by PCB

Sorry, what does that mean? What metamaterial? And is PCB = Printed Circuit Board in this context?

 

[berkeman]

What metamaterial?

Like these?

https://en.wikipedia.org/wiki/Metamaterial

 

[JasonGodbout]

Like these?

https://en.wikipedia.org/wiki/Metamaterial

View attachment 235893

yes it's use to give a specific permeability for a given wavelength of the magnetic field in my project. (i'm a physics student)

 

[Yggdresil]

Warning: magnetrons in microwaves may or may not contain beryllium oxide, which could lead to chronic illness and death if breathed in. You also have concerns about high voltage. If you don’t know what you’re doing, don’t.

A magnetron in consumer microwaves probably operates in S-band, around 2.5 GHz. Although that isn’t the only frequency they use. I believe some might operate below L-band and others up in C-band(guesses here, all of it). You’d have to look at the spec sheet of whatever model.

Since you’re a physics student you should be able to roughly calculate the maximum magnetic field strength from the spec sheet. It’s probably on the order of $\mu T$ or even nT. That’s just an estimate, I don’t know.

Like was said earlier, you don’t sound like you want an electromagnet itself, but something more like a magnetron(which uses an electromagnetic as one part) so you can produce electromagnetic waves.

You haven’t really explained what you’re trying to do. Are you trying to measure the absorption properties of this “meta-material”, testing it like radar asorbing material would be tested?

Most of these kinds of tests would be done in an anechoic chamber. I don’t know if your university has one or not. Are you working with an advisor on this project? Have you asked them for some help/guidance?

 

[JasonGodbout]

Like was said earlier, you don’t sound like you want an electromagnet itself, but something more like a magnetron(which uses an electromagnetic as one part) so you can produce electromagnetic waves.

What I want to do is putting an electric AC current in the electromagnet so it can generate an AC magnetic field. I don't want to create an electromagnetic waves.

You haven’t really explained what you’re trying to do. Are you trying to measure the absorption properties of this “meta-material”, testing it like radar asorbing material would be tested?

I want to concentrate the magnetic field by folding the normal space in a mathematically equivalent space of smaller size using tensors. To do it with a negative permitivity it require an oscillating magnetic field.

Most of these kinds of tests would be done in an anechoic chamber. I don’t know if your university has one or not. Are you working with an advisor on this project? Have you asked them for some help/guidance?

I want to know if it's possible to do a simple version at home to have a proof of concept before asking Lab. time from one of my Professor.

 

[mfb]

What I want to do is putting an electric AC current in the electromagnet so it can generate an AC magnetic field. I don't want to create an electromagnetic waves.

Okay, so you need an electromagnet that can have a magnetic field up to 10 mT. Easy so far. What is the AC frequency you are looking at? Lower frequencies will be easier. How large is the volume where you want the magnetic field? Any space constraints for the electromagnet? Does the field have to be very uniform?

What is the purpose of this magnetic field?

I want to concentrate the magnetic field by folding the normal space in a mathematically equivalent space of smaller size using tensors. To do it with a negative permitivity it require an oscillating magnetic field.

I don't think that combination of words makes any sense.

What is the overall purpose of the device? This sounds like an x-y-question so far.

 

[JasonGodbout]

I don't think that combination of words makes any sense.

This is an exemple of optical transformation : https://arxiv.org/ftp/arxiv/papers/0905/0905.1484.pdf

I want to modify only the magnetic componant (permeability) sorry I wrote it to quickly on the last post.

What is the purpose of this magnetic field?

The magnetic field will induce an electric current in an array of split ring resonator. Which will generate a magnetic field that interact with the first one.

What is the AC frequency you are looking at? How large is the volume where you want the magnetic field?

To resonate I guess the wavelength have to be as large the magnetic field his. That is why I'm thinking centimeters. Also the split rings need to be around 1/100 of the wavelength.

Does the field have to be very uniform?

It would be easier.

What is the overall purpose of the device? This sounds like an x-y-question so far.

To concentrate the magnetic field, to make a displacement of the field or any geometric transformation.

 

[mfb]

To resonate I guess the wavelength have to be as large the magnetic field his. That is why I'm thinking centimeters. Also the split rings need to be around 1/100 of the wavelength.

An electromagnet doesn't have a wavelength.
I asked about a frequency, the answer should have units of Hz. If you want (speed of light)/(a few cm) as frequency then this will be far outside the DIY range.

To concentrate the magnetic field, to make a displacement of the field or any geometric transformation.

Concentrate which magnetic field? Displacement of what relative to what?

 

[Yggdresil]

This is an exemple of optical transformation : https://arxiv.org/ftp/arxiv/papers/0905/0905.1484.pdf

I want to modify only the magnetic componant (permeability) sorry I wrote it to quickly on the last post.

So I’m no expert on transformation optics by any stretch of the imagination, but what I think you’re saying here is that you want to test or create a single negative metamaterial, with $\mu r<0$. These are called electromagnetic metamaterials. So maybe that’s where your insistence on electromagnets comes from. These are not created with electromagnetics per say, but I don’t think that’s what you meant either.

The magnetic field will induce an electric current in an array of split ring resonator. Which will generate a magnetic field that interact with the first one.

A Split ring resonator is a type of structure in such metamaterials and will produce rotating currents which can enhance or interfere with the incident field.

To resonate I guess the wavelength have to be as large the magnetic field his. That is why I'm thinking centimeters. Also the split rings need to be around 1/100 of the wavelength.

This completely depends on the design of the EM metamaterial. They’re generally constructed to operate in a narrow bandwidth. Microwaves would you require you build the metamaterial on a millimeter scale, not centimeters.

It would be easier.To concentrate the magnetic field, to make a displacement of the field or any geometric transformation.

No idea what you’re trying to do here.

You have two issues that I see. One you need to build a device to generate the desired b-field at the desired frequency. Hooking up a signal generator to a feed horn probably wouldn’t do it for. Maybe a Helmholtz coil would work. I don’t know. Second, the harder problem is creating the metamaterial itself unless you already have it. Creating this at home would seem like an impossible DYI project, at least to me.Anyway, I’m bowing out as this is all way beyond my knowledge. Hopefully though this might clarify the actual question (if this is indeed what you’re trying to do) for the others who more knowledgeable so they can actually provide a good answer.

 

[berkeman]

his is an exemple of optical transformation : https://arxiv.org/ftp/arxiv/papers/0905/0905.1484.pdf

Were there any photographs that went along with that paper? A paper about optical illusions with no illustrations seems vacuous, IMO...

 

[Yggdresil]

Were there any photographs that went along with that paper? A paper about optical illusions with no illustrations seems vacuous, IMO...

Here’s were the arxiv paper was published: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.253902

 

[JasonGodbout]

Were there any photographs that went along with that paper? A paper about optical illusions with no illustrations seems vacuous, IMO...

It doesn't work at optical frequency they use those terms to help people understand the principle.

 

[Yggdresil]

It doesn't work at optical frequency they use those terms to help people understand the principle.

The paper does work at optical frequency, or any other frequency.

As far as I could tell last night it was a natural extension of Pendrys work:http://science.sciencemag.org/content/312/5781/1780

Which is why it got published.

 

[JasonGodbout]

The paper does work at optical frequency, or any other frequency.

As far as I could tell last night it was a natural extension of Pendrys work:http://science.sciencemag.org/content/312/5781/1780

Which is why it got published.

Ok It works in theory but due to loss in nano wire split ring resonator don't work in optical frequency. The size of split ring must be less than 1/10 for the wavelength to work. (70 nm for optic)

 

[Yggdresil]

Ok It works in theory but due to loss in nano wire split ring resonator don't work in optical frequency. The size of split ring must be less than 1/10 for the wavelength to work. (70 nm for optic)

If it hasn’t been built in practice that’s one thing, I don’t know, but those are engineering/material science problems, not physics problems. Which is vastly different then “the theory doesn’t really work for optical frequencys.”

I know optical cloaking has been done with classical lenses in lieu of metamaterials, and it’s a project you could DYI. http://www.rochester.edu/newscenter...ects-across-continuous-range-of-angles-70592/

You still need to explain what it is you’re trying to do. Was my guesss above correct?

 

[JasonGodbout]

You still need to explain what it is you’re trying to do. Was my guesss above correct?

Pendry and his team made the first metamaterial yes.
I don't want to make it invisible. I never found a paper online about what I'm trying to do. Because the transformations can be apply to all maxwell equations I want to apply it to an alternating magnetic field only.

 

[Yggdresil]

Pendry and his team made the first metamaterial yes.
I don't want to make it invisible. I never found a paper online about what I'm trying to do. Because the transformations can be apply to all maxwell equations I want to apply it to an alternating magnetic field only.

So you want to cloak the time varying b-field by changing its path geometry at some radio frequency and allow the time varying e-field to pass unmolested? I’m confused by the second part , since the form of Maxwells equations won’t change form with geometric transformations. A change in geometry requires you alter $\mu$ and $\epsilon$ to stay consistent, and altering the b-field portion of a wave without also altering the e-field would break Maxwells symmetry. So what you’re wanting to do sounds contrary to what little I know from the one lower division course I’ve taken on E&M.

 

[JasonGodbout]

So you want to cloak the time varying b-field by changing its path geometry at some radio frequency and allow the time varying e-field to pass unmolested? I’m confused by the second part , since the form of Maxwells equations won’t change form with geometric transformations. A change in geometry requires you alter $\mu$ and $\epsilon$ to stay consistent, and altering the b-field portion of a wave without also altering the e-field would break Maxwells symmetry. So what you’re wanting to do sounds contrary to what little I know from the one lower division course I’ve taken on E&M.

Your right I have to apply it for magnetic and electric component. The transformation I want to apply is like in this paper but to a magnetic field: https://arxiv.org/ftp/arxiv/papers/0811/0811.0458.pdf

 

[f95toli]

It is hard to understand what you are really asking; but if the question is "how can I create B field with a magnitude of 10 mT with a frequency of ~1 Ghz" the answer is "you can't".

Even if you use a resonator ( which how the oscillating B-field is created in e.g. electron spin resonance spectrometers) you would need an enormous amount of power even if the volume was very small; a quick back-of-the-envelope suggest about 10 kW in the best case scenario using a commercial ESR cavity (which BTW wouldn't be able to handle that much power)

.

 

[JasonGodbout]

It is hard to understand what you are really asking; but if the question is "how can I create B field with a magnitude of 10 mT with a frequency of ~1 Ghz" the answer is "you can't".

Even if you use a resonator ( which how the oscillating B-field is created in e.g. electron spin resonance spectrometers) you would need an enormous amount of power even if the volume was very small; a quick back-of-the-envelope suggest about 10 kW in the best case scenario using a commercial ESR cavity (which BTW wouldn't be able to handle that much power)

.

thanks