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A magnetic field in air is measured to be

\[ \vec{B}=B_{0}\left(\frac{x}{x^{2}+y^{2}} \hat{y}-\frac{y}{x^{2}+y^{2}} \hat{x}\right) \]

What current distribution leads to this field ? [**Hint**: The algebra is trivial in cylindrical coordinates.]

- $\vec{J}=-\frac{B_{0} \hat{z}}{\mu_{0}}\left(\frac{1}{x^{2}+y^{2}}\right), r \neq 0$
- $\vec{J}=-\frac{B_{0} \hat{z}}{\mu_{0}}\left(\frac{2}{x^{2}+y^{2}}\right), r \neq 0$
- $\vec{J}=0, r \neq 0$
- $\vec{J}=\frac{B_{0} \hat{z}}{\mu_{0}}\left(\frac{1}{x^{2}+y^{2}}\right), r \neq 0$