# Maximum magnetic field strength

Say I have an electromagnet, (that I know the dimentions, geometry, material characteristics, etc) that I am driving with a current that is oscilating at some frequecy how can I calculate the maximum strength of the magnetic field that it can create at that frequency?

and the equations need to be valid for extream ranges, all the way up to say 1.5Ghz

What would be even better though, would be some real instructions on how to use maxwells equations, I could figure what I need to know from them, but ive looked through about 12 electromagnetics books and none of them did a very descriptive job a explaining them. Or answering pratical questions like "where do you find the equations that define the magnatization or polarization properties of a material you want to work with?" and almost all of them follow the equations with the words "but if we are not dealing with very large field strengths or high frequencies these equations can then simplify to ..." and they give you all the nice information about how to use those simplified equations, and they leave you in the dark about how to do anything remotly practical with maxwells equations.

any help would be greatly appriciated

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Taking the second part of your questions

first, any magnetic material is non-linear at high field strengths, so that is why you are supplied with the "simplified" properties in the literature.

The building of practical magnets is more a matter of engineering, I think you may find out more from engineering texts than from physics books. Also a supplier of magnetic materials would better supply you with data on their line of materials.

You haven't given us any idea what you plan to do with the magnets so it's hard to make any concrete suggestions. ∈

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yeah, I know that the're nonlinear at high field strengths, thats why im not useing the watered down versions of those equations.

basically I want an electromagnet that changes polarity at a rate of at least 400Mhz and the highest field strength that the magnet can handle at those frequencies.
The higher the frequency and the higher the field strength the better (but frequecy is worth 4 times as much to me as the field strength).

I basically just want to be able to calculate the maximum field strength of an electromagnet at a given frequency, so that i can plug in different material characteristics and see which materials will work best.

btw, when I was asking for an explination about maxwells equations, I wasnt asking for specific applications, a completely general explination would be fine, like "to find the magnetic field strength, take this constant multiply it by the permiability equation for the material then multiply it by the current density in the conductor, and intigrate it over the surface of the conductor" (of course thats not correct, just an example), but somthing as simple as that would work

The only "material"

that will work at 400mhz is vacuum. Futhermore any practical material has a property called hysteresis which means it absorbs energy whenever the field changes, which causes heating propertional to frequency. To get high field strengths you may need to use water cooled copper tubing and fiberglass construction to hold the coils together, and forget about any core material.

Originally posted by warpexplorer
btw, when I was asking for an explination about maxwells equations, I wasnt asking for specific applications, a completely general explination would be fine, like "to find the magnetic field strength, take this constant multiply it by the permiability equation for the material then multiply it by the current density in the conductor, and intigrate it over the surface of the conductor" (of course thats not correct, just an example), but somthing as simple as that would work
You can see that the materials available won't work at 400Mhz, you just do the calculations for a vacuum.

would superconductors work well for what i want? say maybe a 0.5 T at 800Mhz?

will just the plain watered down equations work at high frequecies and field strengths if I dont have a core? :)

btw, thanks for you input :)

NO, superconductors won't work,

Originally posted by warpexplorer
would superconductors work well for what i want? say maybe a 0.5 T at 800Mhz?

will just the plain watered down equations work at high frequecies and field strengths if I dont have a core? :)

btw, thanks for you input :)
In a practical application at those frequencies you'll probably want to use a simple coil in a resonant cavity, otherwise you'll emit radio waves. You'll need a high power RF oscillator to generate the field strengths you want. You can find good information on that in radio engineering books.