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

AI Thread Summary
The discussion focuses on deriving boundary conditions for interfaces between ferromagnetic materials and air, specifically addressing the equations related to the continuity of magnetic fields. The user understands the derivation of the normal component of magnetic flux density (B) but struggles with the tangential component of magnetic field intensity (H) and its implications for voltage continuity. They note that their current understanding leads to a time derivative relationship rather than the required voltage equality. The request for hints indicates a need for clarification on the relationship between the magnetic fields and the voltages at the interface. The conversation emphasizes the importance of accurately applying boundary conditions in magnetostatic field problems.
wzy75
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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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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.
V_{in}=V_{out}.

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

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