From: "Christopher R. Carlen"
Subject: Current distribution at DC non-uniform?
Date: Tue, 10 Dec 2002 09:57:36 -0800
Organization: Sandia National Laboratories, Albuquerque, NM USA
NNTP-Posting-Date: Tue, 10 Dec 2002 16:55:49 +0000 (UTC)
User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.1) Gecko/20020826
X-Accept-Language: en-us, en
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.
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA