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

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SUMMARY

This discussion focuses on deriving boundary conditions for interfaces between ferromagnetic materials and air in the context of magnetostatic fields and Poisson's equation. The user seeks clarification on how to derive the equation V_{in}=V_{out} from the continuity of the tangential component of H, which leads to the equation \frac{\partial V_{in}}{\partial t}=\frac{\partial V_{out}}{\partial t}. The conversation highlights the importance of understanding the relationship between magnetic fields and potentials at material boundaries.

PREREQUISITES
  • Understanding of Poisson's equation in magnetostatics
  • Familiarity with boundary conditions in electromagnetic theory
  • Knowledge of ferromagnetic materials and their properties
  • Basic concepts of magnetic field components (B and H)
NEXT STEPS
  • Study the derivation of boundary conditions for electromagnetic fields
  • Learn about the mathematical formulation of Poisson's equation in magnetostatics
  • Explore the properties of ferromagnetic materials and their impact on magnetic fields
  • Investigate the continuity conditions for magnetic field components at material interfaces
USEFUL FOR

This discussion is beneficial for physicists, electrical engineers, and students studying electromagnetism, particularly those focusing on magnetostatic fields and boundary conditions in magnetic materials.

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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