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Magnetic Field from Non-Uniform Current Density

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A cylindrical conductor of radius R has a non-uniform current density given by J=krJ = kr, where kk is a constant and rr is the radial distance from the central axis. Determine the magnitude of the magnetic field at a distance of r=R2r = \frac{R}{2} from the axis.

A

μ0kR28\frac{\mu_0 k R^2}{8}

B

μ0kR212\frac{\mu_0 k R^2}{12}

C

μ0IπR\frac{\mu_0 I}{\pi R}

D

μ0I4πR\frac{\mu_0 I}{4\pi R}

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