[Q]One question about Magnetic boundary conditions.

[good_phy]

Hi.

You know that $$B_{1n} = B_{2n}$$ as one of the boundary condition when

magnetic field is go across from material 1 to material 2, n means direction perpendicular to

the boundary surface.

I wander this theorem is right in non-uniform field which is function of space variable r.

I read prove of this theorem that using limit so i thought this theorem is right only for close

observation point to boundary.


Please assist me.

Thank you

 

[Meir Achuz]

B1n and B2n are the fields just at the interface, but not away from it.
That is what is meant by "boundary condition".

 

[astrokreng]

for your question about magnetic boundary conditions. The statement B_{1n} = B_{2n} is a simplified version of the general boundary condition for magnetic fields, which is known as the continuity equation. This equation states that the normal component of the magnetic field remains constant across a boundary between two materials. This is true even in non-uniform fields, as long as the direction of the field is perpendicular to the boundary surface.

The proof of this theorem does involve taking limits, but this is necessary to account for the behavior of the field at the boundary itself. However, this theorem is valid for all observation points, not just those close to the boundary. In fact, it is a fundamental principle in electromagnetism and has been extensively tested and validated through experiments.

I hope this helps to clarify any confusion. If you have any further questions, please don't hesitate to ask. Thank you for your interest in magnetic boundary conditions.