APFIVE Magnetic Field from Non-Uniform Current
A cylindrical conductor of radius $$R$$ carries a current with a non-uniform density given by $$J = kr$$, where $$k$$ is a constant and $$r$$ is the radial distance from the central axis. What is the magnitude of the magnetic field at a distance $$r < R$$ from the axis?
A
$$\frac{\mu_0 k r^3}{3}$$
B
$$\frac{\mu_0 k r^2}{3}$$
C
$$\frac{\mu_0 I}{2 \pi r}$$
D
$$\frac{\mu_0 k r^3}{4}$$
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