Consider a wire of a circular cross$-$section with a radius of R $=3\mathrm{.}06$mm$.$The magnitude of the current density is modeled as J $=$cr$2=5\mathrm{.}2510^6$A$/$m$^4$r$^2.$What is the current $($in A$)$through the inner section of the wire from the center to r $=0\mathrm{.}5$R$?$