Magnetostatic field: solution to Poisson's equation and Boundary Conditions

In summary, the conversation discusses the process of deriving boundary conditions for interfaces between ferromagnetic material and air. The first equation in (7), V_{in}=V_{out}, is still unclear and the person is seeking hints for understanding it. The continuity of the tangential component of H is mentioned, but it only leads to a different equation, \frac{\partial V_{in}}{\partial t}=\frac{\partial V_{out}}{\partial t}. Further clarification or hints are requested.
  • #1
wzy75
7
0
How to derive boundary conditions for interfaces between ferromagnetic material and air?
Please see the attached figure. Any hints will be greatly appreciated!
 

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  • #2
I can see how the second equation in (7) is derived from the continuity of normal component of B, but still cannot figure out how to derive the first equation in (7), i.e.
[tex]V_{in}=V_{out}[/tex].

From the continuity of tangential component of H, I only get
[tex]\frac{\partial V_{in}}{\partial t}=\frac{\partial V_{out}}{\partial t}[/tex],
which is different from
[tex]V_{in}=V_{out}[/tex].

I must have been missing something here. Could anybody give me some hints?
 

1. What is a magnetostatic field?

A magnetostatic field is a type of electromagnetic field that is generated by stationary electric charges and current distributions. It is characterized by its magnitude and direction at every point in space.

2. What is Poisson's equation and how is it related to the magnetostatic field?

Poisson's equation is a partial differential equation that describes the relationship between the electric potential and the distribution of electric charges in a given space. In the context of magnetostatics, it is used to find the magnetic field distribution by solving for the electric potential.

3. What are the boundary conditions for the magnetostatic field?

The boundary conditions for the magnetostatic field are the conditions that must be satisfied at the interface between different materials or at the boundary of a finite region. They include the continuity of the magnetic field and the discontinuity of the normal component of the magnetic field and the tangential component of the magnetic field.

4. How is the solution to Poisson's equation obtained for the magnetostatic field?

The solution to Poisson's equation for the magnetostatic field is obtained by applying the boundary conditions to the general solution of the equation. This involves using mathematical techniques such as separation of variables and Fourier transforms to solve the equation and find the appropriate constants.

5. What are the applications of the solution to Poisson's equation for the magnetostatic field?

The solution to Poisson's equation for the magnetostatic field has various practical applications, including the design of magnetic devices such as motors, generators, and transformers. It is also used in the study of magnetic phenomena in materials and in the development of magnetic sensors and imaging techniques.

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