## Potential for an infinitesimal width infinite plane. Take III

Posted by peeterjoot on February 24, 2012

# Document generation experiment.

The File menu save as latex produced latex that couldn’t be compiled, but mouse selected, copy-as latex worked out fairly well.

Post processing done included:

\begin{itemize}

\item Adding in latex prologue.

\item Stripping out the text boxes.

\item Adding in equation environments.

\item Latex generation for math output in inline text sections was uniformly poor.

\end{itemize}

# Guts.

I’d like to attempt again to evaluate the potential for infinite plane distribution. The general form of our potential takes the form

We want to evaluate this with cylindrical coordinates , for a width , and radius , at distance from the plane.

With the assumption that we will take the limits , and . With , this does not converge. How about with ?

Performing the r’ integration (with ) we find

Attempting to let \textit{Mathematica} evaluate this takes a long time. Long enough that I aborted the attempt to evaluate it.

Instead, first evaluating the z’ integral we have

This second integral can then be evaluated in reasonable time:

Does this have a limit as ? No, the last term is clearly divergent for .

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