- #1

DaniV

- 34

- 3

- 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 don`t 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 it`s:

µ_{0}*κ*H_{in}*r(hat)=B_{ext}sin(θ)

µ_{0}*κ*H_{in}*θ(hat)=B_{ext}cos(θ)

the only things I got is that i don`t 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 it`s:

µ_{0}*κ*H_{in}*r(hat)=B_{ext}sin(θ)

µ_{0}*κ*H_{in}*θ(hat)=B_{ext}cos(θ)