Magnetostatics boundary conditions.

In summary, the conversation discusses difficulties in solving magnetics problems and applying boundary conditions. The example of an infinitely long cylinder with a permanent magnetization is used to illustrate this. The individual is trying to solve for the magnetic field on the z-axis using Legendre polynomials, but is unsure about the tangential component at the center. They also question if they are going about it the right way and suggest using Ampere's law.
  • #1
0ddbio
31
0
I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice.

For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by:
[tex]\vec{M} = M_{0}r^{2}\hat{\phi}[/tex]

If I first find the bound current distributions I get that the surface bound current is 0, and the volume bound current is:
[tex]\frac{3M_{0}r}{a^{2}}\hat{k}[/tex]

So I was doing it with legendre polynomials matching boundary conditions.. I thought it would be best to solve first for the magnetic field on the z-axis, so that could be another boundary condition.
However when I try to find it I end up with a magnetic field along the z-axis with a [itex]\hat{\phi}[/itex] dependence only...
This doesn't make sense to me, how could it have a tangential component when it is at the center?

Am I going about this all wrong?
Thanks
 
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  • #2
Ok so the curl of M is the J(bound), the bound current per area.
So the integral of J*DA would be your current , and then can't you use amperes law to find the B field. Or am I crazy.
 

1. What are magnetostatics boundary conditions?

Magnetostatics boundary conditions are a set of equations that describe the behavior of magnetic fields at the interface between two different materials. These conditions help us understand how magnetic fields interact with different materials and can be used to solve problems related to the design and operation of magnetic devices.

2. Why are magnetostatics boundary conditions important?

Magnetostatics boundary conditions are important because they allow us to accurately model and predict the behavior of magnetic fields in practical applications. They help us understand how magnetic fields behave at the interface between different materials, which is crucial for designing efficient and effective magnetic devices.

3. What are the most commonly used magnetostatics boundary conditions?

The most commonly used magnetostatics boundary conditions are the continuity of magnetic flux density, the continuity of magnetic field intensity, and the continuity of tangential magnetic field. These conditions ensure that the magnetic field remains consistent and continuous at the interface between different materials.

4. Can magnetostatics boundary conditions be applied to all materials?

No, magnetostatics boundary conditions are only applicable to materials that are linear, isotropic, and have no magnetic charge. This means that the materials must have a constant magnetic permeability and behave the same way in all directions.

5. How are magnetostatics boundary conditions derived?

Magnetostatics boundary conditions are derived from Maxwell's equations, specifically the equation for the divergence of the magnetic field. By considering the behavior of magnetic fields at material interfaces, we can arrive at the equations for the continuity of magnetic flux density, magnetic field intensity, and tangential magnetic field.

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