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For the case of charge, it seems clear that in a perfect conductor the free charge refers to the excess charge that has been dumped into the conductor, while the bound charge refers to the charge that is set up to cancel the electric field within the conductor. Please correct me if I am wrong.

For the case of current, it is harder for me to understand. How do you disentangle the two concepts?

The reason I ask this is really in order to determine what the appropriate boundary conditions should be on a conducting surface. Say if you have an electromagnetic wave hitting the surface. Should there be free or bound charge? Should there be free or bound current?

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  • $\begingroup$ I would suspect that free current is the current in vacuum tubes, composed of free electrons. In conductors the current is carried by the electrons in the fermi level , which are bound to the lattice. for the latter hyperphysics.phy-astr.gsu.edu/hbase/Solids/band.html $\endgroup$ – anna v Sep 11 '18 at 4:13
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The bound charge-current response to the external field is what gives rise to the dielectric medium behaviour. In the Maxwell equations on a medium this response is accounted for by the dielectric constant so these charges and currents are taken out of the equations' right hand side.

For the case of reflection off an interface only the dielectric constant needs to be taken into account. In the linear regime there is no crosstalk from any currents or charges due to any other origin.

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