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Classical Electromagnetism: Question on Ampere's Law and Displacement Current 
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#1
Aug1108, 11:16 PM

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Hi, just out of curiosity...
Ampere's Law describes that an electric current produces a magnetic field. When corrected with Maxwell's displacement current, it describes that a magnetic field is also created by a timevarying electric field. Does this mean that an electric current produces the magnetic field purely BECAUSE of the changes in electric field associated with moving charges. Or is electric current one of two distinct ways (the other being changing electric field) to produce magnetic field. A little confused on the matter. Thanks. 


#2
Aug1208, 02:39 AM

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Ampere's circuital law does not say that an electric current produces a magnetic field. That is the BiotSavart law. I don't see how a changing electric field (without considering the current flow) can induce a Bfield.



#3
Aug1208, 07:10 AM

P: 37

Thanks for the reply.
But doesn't Maxwell's Theory of Light explain that changing electric fields induce magnetic fields due to Ampere's Law / BiotSavart Law. In vacuum for instance, there is no electric current, so why is it that a changing electric field without current flow can't produce magnetic field? 


#4
Aug1208, 08:24 AM

P: 1,036

Classical Electromagnetism: Question on Ampere's Law and Displacement Current
Good question. All we really can say from Maxwell's equations is that under time varying conditions, electric and magnetic fields cannot exist independently. It is futile to even attempt to ascertain which one comes first. Which is the cause and which is the effect is an endless vicious circle. In his 1905 paper "On The Electrodynamics Of Moving Bodies", Einstein states that "questions as to which one (electric or magnetic field) is the "seat" (root, fundamental, canonical, principle, basis) no longer have any point." The parentheses are mine.



#5
Aug1208, 10:04 PM

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#6
Aug1208, 10:15 PM

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#7
Aug1308, 12:00 AM

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imagine a simple two parallel plate capacitor with axial leads and a steady (DC) current flowing in one lead (and out the other lead). between the plates of the capacitor there is no current, but there is a magnetic field induced. 


#8
Aug1308, 02:02 AM

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#9
Aug1308, 08:59 AM

P: 367

The laws of Ampere and Biot and Savart both say that current induces the magnetic field; I would call it a matter of convenience in choosing which law to invoke for a specific problem. Note that you may consider either law as an axiom to EM theory from which you can derive the other. 


#10
Aug1308, 09:27 AM

P: 367

It is the timevarying realignment of dipole moments, when immersed in a timevarying electric field, that gives rise to the displacement current. Thus we can see the displacement current as a movement of real charge; the charge, however, is a bound charge as opposed to a free charge. Now in freespace, the polarization vector is identically zero, thus (taking the freespace permittivity to be unity) D=E. Clearly then, what is called the displacement current has nothing to do with an actual current, but is a pure timevarying electric field. But seeing that we have already named Maxwell's correction to the Ampere law as the displacement current, we might as well keep calling it that (or so some would argue). Really, its a matter of taste. 


#11
Aug1408, 12:26 AM

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1. Is every timevarying Efield would be associated with a displacement current D? 2. Are there any cases whereby you have a varying Efield but no associated displacement current? 3. If the answer to 2 is yes, then would there be a B field induced? These are just yes/no questions. I don't see how you have answered them. 


#12
Aug1408, 03:23 AM

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Anyway, here's what Wikipedia says:



#13
Aug1408, 08:00 AM

P: 367

1) Well first off D is not the displacement current, it is the electric displacement (sometimes called the flux density). The timederivative of D is the displacement current. In principle, there is nothing wrong with talking about the Dfield in freespace, but since it is equivalent to the Efield ( [tex]D=\epsilon_0E[/tex] ), there really is no point. As I said before, whether you wish to call the timederivative of the electric field in freespace a displacement current or not is really just a matter of taste. 2) See above. 3) As you Wikipedia article states, a timevarying electric field induces a timevarying magnetic field and viceversa. This is the mechanism by which light propagates. 


#14
Aug1408, 09:08 AM

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Thanks, got it. Should have read your post more closely. I was just trying to be sure I understood it correctly.



#15
Aug1408, 10:59 AM

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#16
Aug1508, 01:39 AM

P: 37

Hi everyone, thanks for all the input, even though it has kind of deviated from the intention of my original question.
Perhaps the questions I really should have asked are : 1. Does the movement of charges directly result in a displacement current (varying Efield)? 3. Can an electric current induce a magnetic field if there was NO consideration/existence of a displacement current? Ultimately, from cabraham's post, I assume it becomes pointless to question whether moving charges induce a timevarying magnetic field which then induces a time varying E field (Faraday's), or moving charges have a timevarying electric field which then induce a B field (MaxwellAmpere). Thanks. 


#17
Aug1508, 10:09 AM

P: 367

Well now your line of questioning is getting a bit more complex. It comes from the upperlevel idea that "there is really no such thing as magnetostatics." What this means is that what is usually taught as "magnetostatics" should strictly be called magnetoquasistatics. This, as you have said, is because a steady current is really a movement of charge which follows from it timevariances in the fields. But, we can often neglect these effects since they would add only the smallest of corrections (which is good because it is so much easier to write "magnetostatics").
To answer your questions: 1) Yes, the movement of charge implies modification in the electric field, but for a steady current, this can often be neglected. Note, however, that an AC current will induces an AC Bfield by Ampere's law which, in turn, will induce an AC Efield by Faraday's which, inturn, will induce an AC Bfield by Maxwell's correction to Ampere's law which, inturn, will ................ 3) Sure. This is just Ampere's law without Maxwell's correction. 


#18
Aug1508, 11:57 PM

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