Solve for E
\left\{\begin{matrix}E=\frac{\sigma }{\epsilon }\text{, }&\epsilon \neq 0\\E\in \mathrm{R}\text{, }&\sigma =0\text{ and }\epsilon =0\end{matrix}\right.
Solve for ε
\left\{\begin{matrix}\epsilon =\frac{\sigma }{E}\text{, }&E\neq 0\\\epsilon \in \mathrm{R}\text{, }&\sigma =0\text{ and }E=0\end{matrix}\right.
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E\epsilon =\sigma
Swap sides so that all variable terms are on the left hand side.
\epsilon E=\sigma
The equation is in standard form.
\frac{\epsilon E}{\epsilon }=\frac{\sigma }{\epsilon }
Divide both sides by \epsilon .
E=\frac{\sigma }{\epsilon }
Dividing by \epsilon undoes the multiplication by \epsilon .
E\epsilon =\sigma
Swap sides so that all variable terms are on the left hand side.
\frac{E\epsilon }{E}=\frac{\sigma }{E}
Divide both sides by E.
\epsilon =\frac{\sigma }{E}
Dividing by E undoes the multiplication by E.
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