A long coaxial cable consists of a solid cylindrical inner conductor of radius \(a = 2.0 \text{ mm}\) and a concentric cylindrical outer conductor of inner radius \(b = 4.0 \text{ mm}\) and outer radius \(c = 8.0 \text{ mm}\). The inner conductor carries current directed out of the page with a non-uniform volume current density \(J(r) = C r\), where \(C = 6.0 \times 10^7 \text{ A/m}^3\) and \(r\) is the radial distance from the central axis. The outer conductor carries a uniformly distributed total current of \(2.5 \text{ A}\) directed into the page. What is the magnitude of the magnetic field at the inner boundary of the outer conductor (\(r = 4.0 \text{ mm}\))?