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                           PlanetPhysics
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The PlanetPhysics Newsletter

Edition # 3
Feb 8th, 2007
www.planetphysics.org

Contents:

*  Historical:     Works by Newton, Maxwell and J.J. Thomson
*  Mechanics:      Path Independence of Work
*  EM:             Gauss's Law
*  SR:             Spacetime Interval is Invariant...
*  Math:           Laplace Equation in Cylindrical Coordinates
*  Feedback:       Comments and Questions

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It has been just over a year since the first PlanetPhysics
newsletter came out and PlanetPhysics has started to grow.  To
see usage statistics over the last year, follow this link,
http://www.phys-x.org/usage/

We would like to give a special thanks to the Internet archive,
http://www.archive.org who has made some historical physics
works available online and in the public domain, so for your
convenience we have uploaded them into the books section on
PlanetPhysics.

Although, we have a substantial number of hits per day and now
have 253 users, we need more people to contribute content to
PlanetPhysics.  If you are a little rusty on LaTeX, let us know
in the forum and we will help you along or publish your notes for
you.  With spring just around the corner, we will be beginning
the Spring Topic shortly and you will find more info at the
top right corner of our homepage.  More than likely, the topic
will be Electrostatics, so get charged up and find your old
notes to help us.

Finally, we have paid a small amount of money for Google ads for
almost 2 months now.  In march we will go over the numbers and
see if it helped bring people to PlanetPhysics.

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** Works by Newton, Maxwell and J.J. Thomson **

These entire works have been added in the books section:

1)  "Newton's Principia Sections I. II. III."
    http://planetphysics.org/?op=getobj&from=books&id=3

2) "A Treatise on Electricity and Magnetism" by James Maxwell
    http://planetphysics.org/?op=getobj&from=books&id=2

3) "Elements of the Mathematical Theory of
    Electricity and Magnetism" by J.J. Thomson
    http://planetphysics.org/?op=getobj&from=books&id=1


** Path Independence of Work **

"...Therefore, from the final equation, it is clearly seen
that the work to move the object from position
$ \mathbf{r}_{1}$ to $ \mathbf{r}_{2}$ is only dependent
upon the potential energy at those positions, and not the
path taken. Note that in the above, the minus sign in front
of the integral has been dropped; this was done to show, in
the final result, the amount of work done by the system. That
is, if the potential energy at the final position is greater
than that at the initial, then $ W_{12}$ is positive,
and has done work."

http://planetphysics.org/?op=getobj&from=objects&id=200

** Gauss's Law **

"Gauss's law, one of Maxwell's equations, gives the relation
between the electric or gravitational flux flowing out a
closed surface and, respectively, the Electric Charge or mass
enclosed in the surface. It is applicable whenever the
inverse-square law holds, the most prominent examples being
electrostatics and Newtonian gravitation.

If the system in question lacks symmetry, then Gauss's law
is inapplicable, and integration using Coulomb's law
is necessary."

http://planetphysics.org/encyclopedia/GausssLaw.html

**spacetime interval is invariant for a Lorentz transformation**

"The spacetime interval between two events
$ E_1( x_1, y_1, z_1, t_1 ) $ and $ E_2( x_2, y_2, z_2, t_2 )$
is defined as $\displaystyle (\triangle s)^2 = c^2
\triangle t^2 - (\triangle x)^2 - (\triangle y)^2 -
(\triangle z)^2. $

If $ \triangle s$ is in reference frame $ S$,
then $ \triangle s'$ is in reference frame $ S'$
moving at a velocity $ u$ along the x-axis. Therefore, to
show that the spacetime interval is invariant under a
Lorentz transformation we must show

$\displaystyle (\triangle s)^2 = (\triangle s')^2 $"

** Laplace Equation in Cylindrical Coordinates **

"Solutions to the Laplace equation in cylindrical coordinates
have wide applicability from fluid mechanics to electrostatics.
Applying the method of separation of variables to Laplace's
partial differential equation and then enumerating the various
forms of solutions will lay down a foundation for solving
problems in this coordinate system. Finally, the use of Bessel
functions in the solution reminds us why they are synonymous
with the cylindrical domain."

http://planetphysics.org/encyclopedia/LaplaceEquationInCylindricalCoordinates.html

** Feedback and Comments **

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