Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct?
(where, r is the radial distance from the axis of the cylinder)

A. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{everywhere}}} \right)$$

B. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{everywhere}}} \right)$$

C. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{for }}r > R} \right)$$

D. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{for }}r > R} \right)$$

Answer: Option C