The problem: If two electrons are held at fixed points (5,0) and (-5,0), respectively, find the work done in moving a third electron from the origin to (3,0)(adsbygoogle = window.adsbygoogle || []).push({});

All equations:

Force of repulsion between two electrons:

\begin{equation}

\frac{1}{d^{2}}.

\end{equation}

\begin{equation}

W = \int_{a}^{b} \, f(x) dx

\end{equation}

"D" is the distance between the electrons

Attempt at a solution:

The distance between the electron at (-5,0) and the third electron is, 5+x where x is the position of the electron at any point on its journey to (3,0). The distance between the electron at (5,0) and the third electron is (5-x). I found the work by adding the two work equations like this:

\begin{equation}

\begin{split}

W&= \int_{0}^{3} \frac{1}{(5+x)^{2}} dx + \int_{0}^{3} \frac{1}{(5-x)^{2}} dx \\

& = -[-\frac{1}{5-x} |^{3}_{0}] + [-\frac{1}{5+x} |^{3}_{0}\\

&=\frac{3k}{8} ergs

\end{split}

\end{equation}

Book says the answer is

\begin{equation}

\frac{9k}{40}\, ergs

\end{equation}

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# Homework Help: Electron repulsion work problem.

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