- #1
nonequilibrium
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Hello,
I'm reading Griffiths' Introduction to Electrodynamics and I got quite confused in 9.4.1 page 392 (but the question is general, for anyone who does not have that book):
It's about EM-waves in conductors. I will quote a paragraph:
What is the definition of bound (or free) current? I can't find a decent one online, and the book (chapter 6) seems to keep it to something like "bound current is the current you can't directly control", but that is not only too vague for me (there are situations where I'm caught in a limbo), the above paragraph seems to contradict that! I say this because of how he blames the existence of the free current on the fact that you cannot independently control the flow of (all) charge, yet that was his definition of bound current, so this should not concern free current.
Even more so: as he states that E is proportional to the free current, he implies that the bound current is zero (because E is proportional to all the current, in an Ohmic material). But that seems impossible, because if so, then the magnetic permeability of conductors would have to be equal to [tex]\mu_0[/tex], because there's nothing they're keeping track off (e.g. the magnetic permeability of an isolator is simply a way to easily add the (simplified) contribution due to bound current, but if the bound current is always zero, there is no need for an adapted constant, so [tex]\mu_{\textrm{conductor}} = \mu_0[/tex]).
I'm hoping I'm just misunderstanding the concepts, cause at the moment I'm not getting it. If I put an EM wave in a (uncharged) conductor, I would think the magnetic permeability and electric permittivity of the conductor take care of any subsequently induced currents, so that there is no talk of [tex]\rho_f[/tex] or [tex]\vec J_f[/tex]. Where am I wrong?
I'm reading Griffiths' Introduction to Electrodynamics and I got quite confused in 9.4.1 page 392 (but the question is general, for anyone who does not have that book):
It's about EM-waves in conductors. I will quote a paragraph:
In Sect. 9.3 I stipulated that the free charge density [tex]\rho_f[/tex] and the free current density [tex]\vec J_f[/tex] are zero, and everything that followed was predicated on that assumption. Such a restriction is perfectly reasonable when you're talking about wave propagation through a vacuum or through insulating materials such as glass or (pure) water. But in the case of conductors we do not independently control the flow of charge, and in general [tex]\vec J_f[/tex] is certainly not zero. In fact, according to Ohm's law, the (free) current density in a conductor is proportional to the electric field: [tex]\vec J_f = \sigma \vec E.[/tex]
What is the definition of bound (or free) current? I can't find a decent one online, and the book (chapter 6) seems to keep it to something like "bound current is the current you can't directly control", but that is not only too vague for me (there are situations where I'm caught in a limbo), the above paragraph seems to contradict that! I say this because of how he blames the existence of the free current on the fact that you cannot independently control the flow of (all) charge, yet that was his definition of bound current, so this should not concern free current.
Even more so: as he states that E is proportional to the free current, he implies that the bound current is zero (because E is proportional to all the current, in an Ohmic material). But that seems impossible, because if so, then the magnetic permeability of conductors would have to be equal to [tex]\mu_0[/tex], because there's nothing they're keeping track off (e.g. the magnetic permeability of an isolator is simply a way to easily add the (simplified) contribution due to bound current, but if the bound current is always zero, there is no need for an adapted constant, so [tex]\mu_{\textrm{conductor}} = \mu_0[/tex]).
I'm hoping I'm just misunderstanding the concepts, cause at the moment I'm not getting it. If I put an EM wave in a (uncharged) conductor, I would think the magnetic permeability and electric permittivity of the conductor take care of any subsequently induced currents, so that there is no talk of [tex]\rho_f[/tex] or [tex]\vec J_f[/tex]. Where am I wrong?