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Re: Charge Distribution around pointed areas



Hi Brian,
A non-rigorous heuristic view :

The potential of an isolated metallic sphere goes as Q/a , where Q is its
total charge & a is its radius.
If two such spheres are forced to the same potential (connect them with a
wire), then :
Q1/a1 = Q2/a2 . Now the surface charge density (Coulombs /square meter)
of each is sigma_i = Qi/ai^2
You should be able to show that this forces: sigma_2/sigma_1 = a1/a2.
Thus the smaller sphere has the larger surface charge DENSITY (and
therefore also the larger neighboring electric field strength).

Extrapolate this idealized geometry - consider that these two spheres are
parts of a single continuous conductor; they must then be at the same
potential, as above, and the "sharper" curvature will carry the larger
charge DENSITY and produce the larger neighboring electric field strength.

If I remember correctly, this argument can be found in Halliday & Resnick.
Hope this helps.

Bob

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

----- Original Message -----
From: Brian Rintoul <Brian_Rintoul@OCCDSB.ON.CA>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, November 14, 1999 8:30 PM
Subject: Charge Distribution around pointed areas


I'm about to start my first time teaching the unit on Electricity, for
the
Ontario grade 12A Physics course, which opens with electrostatics.

If a charged object is spherical, the charge is uniformly distributed
over
the surface, the reason for this distribution is quite clear. What
isn't
immediately apparent, this Biochemist is, why charge becomes
concentrated
around sharp pointed areas on a conductor's surface.

Explanation please.

\\\|///
[ @ @ ]
............o00o//(_)\\o00o...............
Brian Rintoul
Evening School Teacher (Ottawa Carleton District School Board, Tuesdays
and Thursdays)/Occasional Teacher (Ottawa Carleton District School
Board,
Ottawa Carleton Catholic School Board - M.F. McHugh School,
Fridays)/Ottawa Torah Institute (Mondays - Thursdays, Semester I)
e-mail: brian_rintoul@ocdsb.edu.on.ca

I thank whoever it was on this Listserv, or a chemistry Listserv I
subscribe to, that made the graphic I have only slightly altered. It
has
inspired both positive comments, and variations.