From: John Larkin
Subject: Re: Current distribution at DC non-uniform?
Date: Tue, 10 Dec 2002 11:27:46 -0800
Organization: Posted via Supernews, http://www.supernews.com
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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.