An $18$ gauge copper wire $($diameter $1\mathrm{.}02$ mmmm$)$ carries a current with a current density of $4\mathrm{.}101064\mathrm{.}10106$ A$/$m$2$A$/$m$2.$ The density of free electrons for copper is $8\mathrm{.}510288\mathrm{.}51028$ electrons per cubic meter.