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Magnetic Field from Non-Uniform Current

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A cylindrical conductor of radius RR carries a current with a non-uniform density given by J=krJ = kr, where kk is a constant and rr is the radial distance from the central axis. What is the magnitude of the magnetic field at a distance r<Rr < R from the axis?

A

μ0I2πr\frac{\mu_0 I}{2 \pi r}

B

μ0kr23\frac{\mu_0 k r^2}{3}

C

μ0kr34\frac{\mu_0 k r^3}{4}

D

μ0kr33\frac{\mu_0 k r^3}{3}

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