Answer
$\frac{E_2}{E_1} = \frac{1}{2}$
Work Step by Step
$\frac{\sigma_2}{\sigma_1} = 2$
We can find an expression for $E_1$:
$E_1 = \frac{J}{\sigma_1}$
$E_1 = \frac{I/A}{\sigma_1}$
$E_1 = \frac{I}{\sigma_1~A}$
We can find an expression for $E_2$:
$E_2 = \frac{J}{\sigma_2}$
$E_2 = \frac{I/A}{\sigma_2}$
$E_2 = \frac{I}{\sigma_2~A}$
We can find an expression for $\frac{E_2}{E_1}$:
$\frac{E_2}{E_1} = \frac{\frac{I}{\sigma_2~A}}{\frac{I}{\sigma_1~A}}$
$\frac{E_2}{E_1} = \frac{\sigma_1}{\sigma_2}$
$\frac{E_2}{E_1} = \frac{1}{2}$
