The electron beam emerging from a certain high$-$energy electron accelerator has a circular cross section of radius $1\mathrm{.}45$ mm$.$

$($a$)$ The beam current is $8\mathrm{.}45$A$.$ Find the current density in the beam assuming it is uniform throughout.

A$/$m$2$

$($b$)$ The speed of the electrons is so close to the speed of light that their speed can be taken as $300$ Mm$/$s with negligible error. Find the electron density in the beam.

m$-3$

$($c$)$ Over what time interval does Avogadro's number of electrons emerge from the accelerator?

s