The current density \[\vec{j}\] inside a long, solid, cylindrical wire of radius a=12 mm is in the direction of the central axis, and its magnitude varies linearly with radial distance r from the axis according to\[J=\frac{{{J}_{0}}r}{a}\], where \[{{J}_{0}}=\frac{{{10}^{5}}}{4\pi }A/{{m}^{2}}.\] Find the magnitude of the magnetic field at in\[\mu T\]

• A. \[10\mu T\]
• B. \[4\mu T\]
• C. \[5\mu T\]
• D. \[3\mu T\]