# Finding the magnetic field inside a material shell under external field

• DaniV
In summary, the conversation discusses the use of boundary conditions on both the a and b radius surfaces, as well as using superposition on them. The focus is on finding a suitable magnetization M from the magnetic material and determining H_{in} for the problem. The only known relations are µ_{0}*κ*H_{in}*r(hat)=B_{ext}sin(θ) and µ_{0}*κ*H_{in}*θ(hat)=B_{ext}cos(θ). The speaker also mentions working out a different answer that matches with results found on the internet, specifically for a cylindrical shell. However, there is a correction made that the Wikipedia result is for a spherical shell, not a cylindrical one.
DaniV
Homework Statement
A uniform external field B_{ext} = B_{ext}xˆ is applied to an infinitely long cylindrical shell with inside radius a, outside radius b, and relative permeability κ = µ/µ_{0}. The rest of space is vacuum. Show that the field inside the shell is screened to the value :
Bin = 4κb^{2}Bext /((κ + 1)^{2}b^{2} − (κ − 1)^{2}a^{2})
Relevant Equations
B=µ*H,
B=µ_{0}(H+M) when M is the magnetisation of the material
I know that we need to use some boundry condition both on the a radius surface and the b radius surface and somehowuse the superposition on them both, the boundry condition most be for the tangential and the radial part,
the only things I got is that i dont know how to produce a magnetisation M from the magnetic material, and how tofind some H_{in} that is suitable
to the problem?

the only relations that I suceed to produce its:
µ_{0}*κ*H_{in}*r(hat)=B_{ext}sin(θ)
µ_{0}*κ*H_{in}*θ(hat)=B_{ext}cos(θ)

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timetraveller123 said:
i worked out a different answer and it matches with answer i see over the internet
for example in wikipedia,
https://en.wikipedia.org/wiki/Electromagnetic_shielding
The Wikipedia result is for a spherical shell, not a cylindrical shell.

timetraveller123

edit:
sorry for the inconvenience caused yes the answer is correct
i worked it out again the method is almost exactly same as the spherical one

Last edited:
timetraveller123 said:
That's OK. I do that sort of thing all the time.

## 1. How is the magnetic field inside a material shell affected by an external magnetic field?

The presence of an external magnetic field can induce a magnetic field inside a material shell, depending on the properties of the material. The direction and strength of the induced field will depend on the orientation and strength of the external field.

## 2. What factors influence the strength of the magnetic field inside a material shell?

The strength of the magnetic field inside a material shell is influenced by the material's magnetic permeability, the orientation of the material with respect to the external field, and the strength of the external field.

## 3. Can the magnetic field inside a material shell be manipulated?

Yes, the magnetic field inside a material shell can be manipulated by changing the orientation of the material with respect to the external field or by changing the strength of the external field.

## 4. How does the thickness of the material shell affect the magnetic field inside?

The thickness of the material shell can impact the magnetic field inside by affecting the material's ability to conduct magnetic flux. Thicker shells may have a lower magnetic field inside due to increased resistance to flux.

## 5. How can the magnetic field inside a material shell be measured?

The magnetic field inside a material shell can be measured using a magnetic field sensor or a Hall effect sensor. These devices can detect and measure the strength and direction of the magnetic field inside the material.

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