Magnetic Field Question (saturating an iron plate)

In summary: I think it would be interesting to do some more experiments to determine the validity of this result.In summary, the field inside sample is a combination of the demagnetizing field and whatever applied field you may have. So these two fields together influence how big a field you need in order to magnetize the sample. With a plate geometry, the ## B ## field inside the material is approximately the applied field (## B=H_o ##) because the lines of flux for ## B ## are continuous. Even though ## H ## is effectively zero inside the material of the plate, (because of the demagnetizing field), I think in calculations like this one, you need to assume that the effective ## H ## in the
  • #1
lcvoth23
1
0
Homework Statement
How strong a magnetic field is necessary to magnetize an iron plate to its saturation magnetization for a field applied normal to the plate surface? Assume that iron has a relative permeability 200 and a saturation magnetization of 1700 emu/cm^3. If the field is applied in the plane of the plate, how large a field is required?
Relevant Equations
B = H + 4*pi*M
H (total) = Hd + H (applied)
I know that the field inside sample is a combination of the demagnetizing field and whatever applied field you may have. So these two fields together influence how big a field you need in order to magnetize the sample.
 
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  • #2
With a plate geometry, the ## B ## field inside the material is approximately the applied field (## B=H_o ##) because the lines of flux for ## B ## are continuous. Even though ## H ## is effectively zero inside the material of the plate, (because of the demagnetizing field), I think in calculations like this one, you need to assume that the effective ## H ## in the material is the applied ## B ##, even though it really is a bit of hand waving to make such an assumption. It is a very interesting problem, but I think it also brings to light some discrepancies that arise when working with ferromagnetic materials, and the assumption that these materials behave linearly. Anyway, I think what I have proposed above is about the best you can do with such a problem. @vanhees71 Might you have an input here?
 
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  • #3
A follow-on: I put some more effort into this one, and I believe I got a result that makes sense.
For very large ## \chi ##, ## H_{total} \approx 0 ##, but more precisely ## H_{total}=H_o+H_D ##, where ## H_D=-4 \pi M ##. Since ## M=\chi H_{total}=\chi (H_o-4 \pi M) ##, we get ## M=\frac{\chi H_o}{1+4 \pi \chi} ##. ## \\ ## For large ## \chi ##, ## M \approx \frac{H_o}{4 \pi} ##.
Since ## B=H_{total}+4 \pi M ##, we see for large ## \chi ## that ## H_{total} \approx 0 ## , and ## B \approx H_o ##.
One other item, is they give you ## \mu=200=1+4 \pi \chi ##, so from this you can compute ## \chi ##. ## \\ ## It appears this one does not suffer from the linearity difficulty that I originally thought. ## \\ ## For this latest result, ## H_{total}=\frac{H_o}{1+4 \pi \chi} ##. This result is much different from what I proposed in post 2, and it suggests that the iron in the plate will be very slow to develop a magnetization in response to the applied field ## H_o ##. Whether this actually happens in practice, I'm not completely sure.
 
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1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by the movement of electrically charged particles, such as electrons.

2. How is a magnetic field created?

A magnetic field is created by the movement of electrically charged particles. In the case of an iron plate, the iron atoms are made up of tiny magnets called dipoles. When these dipoles align in the same direction, a magnetic field is created.

3. How can an iron plate be saturated with a magnetic field?

To saturate an iron plate with a magnetic field, it needs to be exposed to a strong external magnetic field. This will cause the dipoles in the iron atoms to align in the same direction, increasing the overall strength of the magnetic field.

4. What happens when an iron plate is saturated with a magnetic field?

When an iron plate is saturated with a magnetic field, it reaches its maximum magnetic strength. This means that the dipoles in the iron atoms are all aligned in the same direction, creating a strong and stable magnetic field.

5. Can an iron plate's magnetic field be reversed?

Yes, an iron plate's magnetic field can be reversed by exposing it to a strong external magnetic field in the opposite direction. This will cause the dipoles in the iron atoms to realign in the opposite direction, reversing the direction of the magnetic field.

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