What is the role of surface currents in Ampere's Law with H fields?

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Discussion Overview

The discussion centers on the application of Ampere's Law in the context of the auxiliary field H, specifically regarding the treatment of surface currents in relation to free currents. Participants are examining the implications of surface currents when considering Amperian loops that intersect boundaries between different materials.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant references Griffiths Electrodynamics, questioning the omission of surface currents in the derivation of Ampere's Law as it applies to the field H.
  • Another participant asserts that H is defined to include only free currents, implying that bound currents are not relevant in this context.
  • A different participant challenges the inclusion of bound currents by questioning why they would be considered if only free currents are mentioned.
  • Another participant argues that surface currents, whether bound or free, do not intersect the Amperian loop since they are located on the surface.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of surface currents in the context of Ampere's Law with H. There is no consensus on whether surface currents should be included in the analysis.

Contextual Notes

The discussion highlights potential ambiguities regarding the definitions of free and bound currents, as well as the treatment of surface currents in the context of Ampere's Law. The implications of these definitions on the application of the law remain unresolved.

McLaren Rulez
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I'm using Griffiths Electrodynamics and I can't figure out something. For reference, this is on page 269 of the third edition.

In the derivation for Ampere's law as it applies to the auxillary field H (i.e integral of H over a loop = free current passing through), there seems to be no word on the surface currents. If I had an Amperian loop that cut through the boundary between two surfaces, shouldn't we also include the bound surface current Kb along with whatever free current passes through that loop?

Thank you, in advance.
 
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H is introduced so that Ampere's law with H includes only free currents.
 
You said, free currents. So why include bound currents?
 
Bounded or not, surface current is on the surface, it does not cut through the surface, right? So the surface current whether it is bounded or free don't cut through the surface ( or the current don't string the Amperian loop.).
 

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