### Assignment NP 2.01: A Matlab Example in Electrostatics

Graphics and description
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I began my matlab experience by prerusing through the "Getting
Started with Matlab" handout using the computer.  Next I followed
Professor Lockhart's writeup.  The writeup guided me through a problem of
two point charges. - Find the potential and the electric field and then
graph the results in various ways.  I then placed the commands into a file
called matlabex.m for which I could modify at the slightest whim and then
rerun the program to see the results of the changes.  Through the
combination of using the help command (similar to the man command in
UNIX), and the trying out modifications in my program I learned my
interesting things.

Diverging for a moment, I will compare the Lockhart program results
using Matlab and the Dancing Gaussian from Mathematica.  Both Mathematica
and Matlab have good and bad points.  Which one that you use depends upon
what you are doing.  Mathematica can easily do computation of functions
but Matlab is more user friendly in the area of adding finishing touches
to a graph and looking at it from different view points.  Anyways, each
program requires a different technique towards the common goal of finding
the best resulution of the spike of a given function.

Returning the to the topic at hand, I decided upon the mesh graph
style to use for this next part.  Here I increased the resolution of the
potential function by increasing the x and y arrays used in creating the
meshgrid from 0.1 to 0.014.  This seemed to yield the best visual results.
To view the graph refer to graph1.  I wanted a
better view and thus rotationed it from the default position of:
azmuthal angle = -37.5 and elevation = 30 to 30 and 0 (a side view).  To
view the graph refer to graph2.  Wow!  Notice
that the first graph shows the potential plane with a spike at the
positive charge and a dot due to the negative charge.  The second graph
(due to rotation) reveals not only a spike due to the positive change
but one can clearly see that there's a spike in the opposite direction
from the plane due to the negative charge.  The color changes also add
to an easier interpretation of the results.

I also went through the above process for the gradient of the
potential.  The graph is labeled the electric field but it's actually
the negative of the electric field to be more precise.  If you are
interested the first graph, graph3, is the
graph using the default settings.  Again, notice the spiking of the
electric field at the charge points. The last graph,
graph4, reveals not only a spike similar to
the potential but an added "bump" on each.  Something that I noticed in
both the graph of the potential and the electric field, one spike is
"longer" than the other.  Off hand that seems incorrect - a glich in the
program.  If I have more time before this is due, I'll put some thought
into it.  There must be more to it.

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