Re: Circumventing Earnshaw's Theorem

[Bob Sciamanda <trebor@VELOCITY.NET>]

For the record, this news report mis-represents Earnshaw's theorem; it
sounds like they are parroting the errors in the physics FAQ.  I pointed
out this FAQ error in the sci.physics list when this subject came up in
May (all replies were corroborating).  Following is a reprint of my
sci.physics May post:

The Physics FAQ quotes Earnshaw's Theorem as saying that it is impossible
to levitate an object in a gravitational field by using electric and
magnetic forces.  From my experience, this is not accurate, both because
the statement is not true, and because it is not Earnshaw's theorem.

Millikan's famous oil drop experiment (commonly repeated as a standard
undergrad physics experiment) levitates a charged oil drop in the earth's
gravitational field by means of an electrostatic field.

Earnshaw's theorem states that "a charge distribution cannot be in a
state of stable equilibrium under the action of electrostatic forces
alone"  (Electricity & Magnetism, O. Jefimenko, 1966, pg 203). This
theorem is valid within Maxwellian electrodynamics and is easily proven.

Other agreeing texts are: Static & Dynamic Electricity (2nd ed), W.
Smythe, pg 14;
The Physics of Electricity & Magnetism (2nd ed), W. Scott, 1966, pg 43.

The point is that if a non-electric force is added (eg. a gravitational
field) equilibrium IS possible.


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

"You have reached an imaginary number.  If you require a real number,
please rotate your telephone by 90 degrees, and try again."   Anonymous

----- Original Message -----
From: William Beaty <billb@ESKIMO.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Sunday, August 01, 1999 12:01 AM
Subject: Circumventing Earnshaw's Theorem


> Hey, SCIENCE NEWS has a brief article on a new form of passive magnetic
> levitation.  . . .