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The accompanying figure shows the cross section of a long wire whose center is at the origin. It has two conductors, a region 1, $r < r_1$, and a region 2, $r_1 < r < r_2$. The regions are isolated from one another by a thin insulator located at $r= r_1$. Each region has the same constant current density, only the direction of the current is region 1 is opposite to that of region 2.

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What is the ratio of $r_2 /r_1$ if the measured $\vec{B}$ field is found to be zero for all $r \geq r_2$?


$\cfrac{r_2}{r_1} = 2\sqrt{2}$


$\cfrac{r_2}{r_1} = \sqrt{2}$


$\cfrac{r_2}{r_1} = \sqrt{2 \pi}$


$\cfrac{r_2}{r_1} = 2$

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