In deriving the boundary conditions for $H$ at the boundary between two media, my lecturer stated that "since there is no conduction (free) current on the Surface... the tangential components of H are continuous at the surface interface".

Now I couldn't understand why there might or might not be a conduction current, so it is difficult for me to see where this continuity condition might not apply. Maybe the difficulty lies partly in my shaky understanding of bound and free current densities and surface current densities. I think

  • bound current density, or magnetization current, is analogous to bound charge in electrostatics. I.e. it pertains to the (possibly ficticious) little current loops within a material that result in little magnetic dipoles

  • If there is are bound/magnetization currents, there will be surface current from the internal dipoles and fictitious current loops; which is like the effective surface charge due to separation of charges within a material in electrostatics.

  • now when it comes to electrostatics, the concept of free charge is easy. It is like putting some charge on a conducting sphere, and it sits on the surface. But I don't understand what a free current might be? I suppose the current in a circuit is a free current, but for this you have to apply and electric field to make current flow. Perhaps it is the case that you always need an electric field for there to be a free current (link to electric and magnetic fields being connected in special relativity?) and thus a H, although you can have a B field without an electric field because B accounts for the material and possible net magnetic dipoles from the material? I any case, I cannot imagine having a free current on a surface, which is what was used in motivating the continuity of tangential components of H. Also, I cannot imagine having a lump of material which has some free current in it, or indeed a free surface current. I can only imagine this for something like a loop of conducting material, as in a circuit. Where might one find a free current or surface current in a lump of material?

Thank you in advance.


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