A copper wire of length $10\text{m}$ and radius $\frac{10^{-2}}{\sqrt{\pi }}\text{m}$ has electrical resistance of $10\Omega$. The current density in the wire for an electric field strength of $10\text{V/m}$ is:

1. A
   $10^4{\text{A/m}}^2$
2. B
   $10^6{\text{A/m}}^2$
3. C
   $10^{-5}{\text{A/m}}^2$
4. D
   $10^5{\text{A/m}}^2$