- #1

AmanWithoutAscarf

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- Homework Statement
- I'm trying to calculate the magnetic field inside and outside a uniformly distributed paramagnetic sphere. The sphere has a permeability of μ (mu) and is placed in a constant external magnetic field.

- Relevant Equations
- Equations related to electric and magnetic polarization

**I believe there is an elementary way to solve this problem using some analogies with relevant models.**

First, I consider an electric model of polarization in uniform field.

First, I consider an electric model of polarization in uniform field.

Here, there is a dielectric sphere oriented in uniform electric field ##

**E**_0##. We can find out the electric fields inside and outside by modeling the charge distribution within the sphere as a superposition of two oppositely charged spheres. This allows us to determine the constant internal field and the external field with ##

**p**##. Finally, using electric boundary conditions on the spherical surface, we can solve for ##

**p**## and get the sollution.

Illustration of model

**Let's take a look at the phenomenon of conducting shell in uniform magnetic field.**

The shell expells magnetic fields, so ##B_{in}=0##. Assuming the total external field is the superposition of ##B_0## and the additional field generated by a magnetic dipole ##m## (I know it is the result of some complex calculations with vector potential, but the assumption without mathematical proofs is still acceptable), we can use the boundary conditions again to find ##m## and the total external magnetic field after that.

**So, in case of the initial question**, I'm thinking of a model of a constant internal magnetic field (inspired by the model of electric polarization) and a superposition of the external field with a magnetic dipole (as the second model).

Is my assumption correct? And how can I get further calculation for magnetic field from that?

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