APFIVE Magnetic Field from Non-Uniform Current Density
A cylindrical conductor of radius R has a non-uniform current density given by $$J = kr$$, where $$k$$ is a constant and $$r$$ is the radial distance from the central axis. Determine the magnitude of the magnetic field at a distance of $$r = \frac{R}{2}$$ from the axis.
A
$$\frac{\mu_0 I}{4\pi R}$$
B
$$\frac{\mu_0 k R^2}{12}$$
C
$$\frac{\mu_0 I}{\pi R}$$
D
$$\frac{\mu_0 k R^2}{8}$$
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