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Reply-To: "fred bartoli"
From: "fred bartoli"
Subject: Re: Current distribution at DC non-uniform?
Date: Wed, 11 Dec 2002 13:47:53 +0100
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NNTP-Posting-Date: 11 Dec 2002 13:48:51 MET
John Larkin a écrit dans le
message : email@example.com...
> On Tue, 10 Dec 2002 09:57:36 -0800, "Christopher R. Carlen"
> >It would seem from the right hand rule for the force on a moving charged
> >particle do to the magnetic field, that even at DC there would be a
> >non-uniform distribution of charge in a cylindrical conductor.
> >For instance, if conventional current flows in the positive z direction
> >in a cylindrical coordinate system, then the electron drift velocity is
> >ue_vec = -z_hat |ue|
> >The magnetic field would be
> >H_vec = phi_hat |H|
> >And so the force on an electron would be
> >Fe_vec = -q ue_vec H_vec
> >Fe_vec = -r_hat |Fe|
> >where the vector magnitudes are not of issue, but the directions are.
> >We see that the electrons should be getting pushed toward the center of
> >the conductor, which would leave a positive charge density toward the
> >outer surface of the conductor.
> >If this is not what happens, I wish to learn why not.
> >The reason I am interested in this, is that for calculating the magnetic
> >field inside a conductor at DC, one usually assumes uniform current
> >distribution. But this makes me wonder if the assumption is valid.
> >I haven't yet gotten to the point where I can calculate the skin depth
> >of current, which comes in the chapter on time varying fields. I will
> >be getting into this in about a week. But at this point, I want to
> >understand what is wrong with the above argument for a non-uniform
> >current density radially in a conductor at DC.
> >Thanks for comments.
> Never thought about that, but it makes sense. The magnetic field
> created by the current causes Hall effect curvature of the carriers
> towards the center. In ordinary conductors at practical currents, the
> effect should be very weak.
Once, challenged by a somewhat pretentious freshout that stated it was
impossible to find an analytical form to the skin effect in round
conductors, I did it (with the nice help of mathematica as I'm certainly not
the king of Bessels functions) and have been puzzled by the result.
I found the classical asymptotic behaviour at DC and high frequency, but
also unexpectedly found a *minimum* resistance that wasn't, as one could
intuitively expect, at DC value, but just before the skin effect corner
I did verify over and over again the calculations and came to the conclusion
it was right (or maybe I didn't find the catch). Unfortunatly the effect is
so weak (under 1% IIRC) and in a zone were the inductive behaviour is
already strong enough that this makes such measurements difficults and
really impossible with home equipments. So I couldn't test the results
against reality, but if it were verified the result is simply a surprise (at
least for me) : the best transfert efficiency for a straight wire would not
be at DC but at an optimal "high" frequency.
This result not being my main interest, I didn't pushed further and stayed
with the question as "why can it be possible ?". Maybe Chris just gave the
I'll try to find the results and post them on a.b.s.e.
To Chris : IIRC you have available a copy of mathematica. Tell me if you
want me to send you a copy of the notebook files.
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