Problem $4.$ Consider a cylindrical conductive wire with radius $a=0\mathrm{.}4mm$ and length $L=10m.$ The conductivity of the material is $=4000\frac{S}{m}.$ We apply a $50$ V voltage across the wire. Assume a uniform electric field vec$(E)$ within the wire.

$($a$)$ Calculate the magnitude of vec$(E)$ within the wire. $($Q$43)$

$($b$)$ Calculate the magnitude of current density vec$(J)$ within the wire. Express the results in SI unit. $($Q$44,$ Q$45)$

$($c$)$ Calculate the absolute value of current flowing through the wire. Express the results in SI unit. $($Q$46,$ Q$47)$

$($d$)$ Calculate the resistance of the conductive wire. Express the results in SI unit. $($Q$48,$ Q$49)$