A straight cylindrical wire lying along the x axis has a length of $0\mathrm{.}500$ m and a diameter of $0\mathrm{.}200$ mm$.$ It is made of a material that obeys Ohm's law with a resistivity $=4\mathrm{.}00$ x $10-8$ m$.$ Suppose that a potential of $4\mathrm{.}00$ V is maintained at x $=0$ and that at x $=0\mathrm{.}500$ m$,$ V $=0.$ Determine $($a$)$ the electric field of the wire, $($b$)$ its resistance, $($c$)$ the electric current that passes through the wire and $($d$)$ the current density J of the wire. Express the direction of the electric field and current. $($e$)$ Show that E $=$J$.$