9.2 Exercise 10

Consider a wire of a circular cross-section with a radius of $R = 3.00 \text{mm}$. The magnitude of the current density is modeled as $J = c r^{2} = 5.00 \times 10^{6} \frac{\text{A}}{\text{m}^{4}} r^{2}$. What is the current through the inner section of the wire from the center to $r = 0.5 R$?