- #1
B3NR4Y
Gold Member
- 170
- 1
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)
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}
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}