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About surface charges

From: Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>
Date: Sat, 16 Feb 2002 13:55:23 -0500

This is for those who do not have the Chabay and Sherwood
textbook (C&S). Please correct me, or elaborate, if necessary.
I want to reproduce the argument they use in support of the
idea of surface charges.

Imagine two insulated conducting spheres separated by a
distance L. A mysterious device takes electrons from the
sphere A (on the left) and delivers them to the sphere B
(on the right). The device tries to keep the DOP between
A and B constant; this happens after charges of equal
magnitude Q are accumulated on the spheres.

The two insulated spheres form a dipole. We know how to
calculate potentials in various points. Next suppose that A and
B are connected by a very thin wire and a current starts flowing
in the circuit (a loop containing the working device, the two
spheres and the wire). The DOP is essentially the same as
before. It means that the rate at which charges are separated
by the device I equal to the current, for example, 0.1 A.

We know that the electric field E exists in every segment of
our wire. This field is always directed along the wire axis.
According to C&S that field is produced by static charges
residing on metallic surfaces. In electrostatics, as we know,
surface charges distribute themselves to produce E=0 inside
conductors. But this is no longer correct when a current is
flowing. In electrodynamics, the distribution of static charges
is such as to produce a nonzero field along the wires. The
very convincing argument (?) supporting the idea of surface
charges is as follows. A and B are constantly recharged by
the device while a current is flowing through the wire W
whose shape was chosen to make the argument convincing.

AAA BBB
WWWWAA + AA device BB - BBWWWW
W AAA BBB W
W W
W W
W W
W W
W W
WWWWWWWWWWWWWWWWWwWWWWWWWWW W
W W
W W
W W
W W
W W
WWWWWWWWWWWWWWWWWvWWWWWWWWW W
W W
W W
W W
W W
W W
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW

Suppose the opposite is true; the electric charges responsible
for the electric field are not distributed over the wire surface.
The charges responsible for E inside the wire reside only near
the battery terminals at A and B. In that case the values of E
could be calculated at any point as due to an AB dipole. We are
asked to do this at points below the dipole; these points are
indicated by the lower case w and v in my illustration. Convince
yourself that vectors E, at w and at v, are horizontal and directed
to the right. But this is nonsense, how can a steady state current
be flowing toward the bend from both directions?

This paradoxical situation does not exist if we assume that static
charges are distributed (like rings) along the circuit loop. The
concentration of "positive rings" is high near A. The concentration
of negative rings is high near B And there is a gradual transition
along the wire. No mathematical expression for surface charge
density is given; I suppose it can be calculated theoretically by
somebody. Note that in a long straight wire E would be zero if
the distribution of Q were uniform. Is the argument convincing?

Please share what you know about surface charges so we can
learn together more quickly. No other textbook I am familiar
with discusses surface charges. Why is it so?
P.S.
I just received the URL of archives from Bob Schimanda. Was I
the only one who saw parts of Bob's message with HTML tags,
etc. (as shown below)? Fortunately, the URLs are ready to click
on That what I am about to do now.
Ludwik Kowalski

Bob's message contained this:

Here is an abstract from a recent AJP article, along with citations back
to the 60's :

http://ojps.aip.org/vsearch/servlet/VerityServlet?KEY=AJPIAS&CURRENT=&ONLI
NE=&smode=strresults&sort=journ&maxdisp=50&docnum=&origquery=&threshold=0&
abscall=&logid=&allprl=&possible1=surface+charge&possible1zone=article&boo
l1=and&possible2=&possible2zone=article&fromyear=&frommonth=&fromday=&toye
ar=&tomonth=&today=&fromvolume=&tovolume=&fromissue=&toissue=&SMODE=&possi
ble3=&possible3zone=&bool3=&OUTLOG=NO&key=DISPLAY&docID=9&page=1&chapter=0

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

--Boundary_(ID_dL5bWOs6TjrbGjzgwUWFNA)
Content-type: text/html; charset=iso-8859-1
Content-transfer-encoding: QUOTED-PRINTABLE

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; charset=3Diso-8=
859-1">
<META content=3D"MSHTML 5.50.4913.1100" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>I don't see the following important =
contribution=20
included in the citations listed below:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>"In what frame is a current-carrying=
conductor=20
neutral?", P.C. Peters, AJP,Vol 53 #12, ppg 1165-1169, Dec 1985.</FON=
T></DIV>
<DIV><FONT face=3DArial size=3D2>(I think the only one that takes the=
Hall effect=20
forces [on the carriers] into account.)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV>Bob Sciamanda (W3NLV)<BR>Physics, Edinboro Univ of PA (em)<BR><A=
=20
href=3D"mailto:trebor@velocity.net";>trebor@velocity.net</A><BR><A=
=20
href=3D"http://www.velocity.net/~trebor";>http://www.velocity.net/~tre=
bor</A></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BOR=
DER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV=20
style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black">=
<B>From:</B>=20
<A title=3Dtrebor@VELOCITY.NET href=3D"mailto:trebor@VELOCITY.NET";>=
Bob=20
Sciamanda</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>To:</B> <A title=3DPHYS-L@lists.=
nau.edu=20
href=3D"mailto:PHYS-L@lists.nau.edu";>PHYS-L@lists.nau.edu</A> </DIV=

<DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Saturday, February 16,=
2002 12:48=20
PM</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Subject:</B> Re: Equipotential l=
ines</DIV>
<DIV><BR></DIV>
<DIV><FONT face=3DArial size=3D2>
<DIV>Ludwik wrote:</DIV>
<DIV>>>Joseph Bellina wrote:</DIV>
<DIV> </DIV>
<DIV>> >If you search the archives of AJP you will find artic=
les=20
on<BR>> >the role of surface charges. This is a very carefull=
y=20
written<BR>> >insightful text and deserves your careful readi=
ng.</DIV>
<DIV> </DIV>
<DIV>>Can you post the specific URL Jopseph? I am not yet very<B=
R>>good=20
in searching for things in archives.</DIV>
<DIV> </DIV>
<DIV>Ludwik:</DIV>
<DIV>Here is an abstract from a recent AJP article, along with cita=
tions back=20
to the 60's :<BR></FONT><BR> <A=20
href=3D"http://ojps.aip.org/vsearch/servlet/VerityServlet?KEY=3DAJP=
IAS&CURRENT=3D&ONLINE=3D&smode=3Dstrresults&sort=3Djo=
urn&maxdisp=3D50&docnum=3D&origquery=3D&threshold=
=3D0&abscall=3D&logid=3D&allprl=3D&possible1=3Dsurfac=
e+charge&possible1zone=3Darticle&bool1=3Dand&possible2=
=3D&possible2zone=3Darticle&fromyear=3D&frommonth=3D&=
=66romday=3D&toyear=3D&tomonth=3D&today=3D&fromvolume=
=3D&tovolume=3D&fromissue=3D&toissue=3D&SMODE=3D&=
possible3=3D&possible3zone=3D&bool3=3D&OUTLOG=3DNO&ke=
y=3DDISPLAY&docID=3D9&page=3D1&chapter=3D0">http://ojps.a=
ip.org/vsearch/servlet/VerityServlet?KEY=3DAJPIAS&CURRENT=3D&=
ONLINE=3D&smode=3Dstrresults&sort=3Djourn&maxdisp=3D50&am=
p;docnum=3D&origquery=3D&threshold=3D0&abscall=3D&log=
id=3D&allprl=3D&possible1=3Dsurface+charge&possible1zone=
=3Darticle&bool1=3Dand&possible2=3D&possible2zone=3Dartic=
le&fromyear=3D&frommonth=3D&fromday=3D&toyear=3D&=
tomonth=3D&today=3D&fromvolume=3D&tovolume=3D&fromiss=
ue=3D&toissue=3D&SMODE=3D&possible3=3D&possible3zone=
=3D&bool3=3D&OUTLOG=3DNO&key=3DDISPLAY&docID=3D9&=
page=3D1&chapter=3D0</A></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV>Bob Sciamanda (W3NLV)<BR>Physics, Edinboro Univ of PA (em)<BR>=
<A=20
href=3D"mailto:trebor@velocity.net";>trebor@velocity.net</A><BR><A=
=20
href=3D"http://www.velocity.net/~trebor";>http://www.velocity.net/~t=
rebor</A></DIV></DIV></BLOCKQUOTE></BODY></HTML>

--Boundary_(ID_dL5bWOs6TjrbGjzgwUWFNA)--

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