An electron beam has an aperture `1.0 mm^(2)`. A total of `6.0xx10^(16)` electrons go through any perpendicular cross section per second. Find(a) the current and (b) the current density in the beam.

Explanation

(a) The total charge crossing a perpendicular cross section in one second is
`q=ne`
`6.0xx10^(16)xx1.6xx10^(-19)C`
`=9.6xx10^(-3)C.
The current is
`i=q/t`
`=(9.6xx10^(-3)C)/(1 s)=9.6xx10^(-3)A`.
As the charge is negative, the current is opposite to the direction of motion of the beam.
(b) The current density is
`j=i/s=(9.6xx10^(-3)A)/(1.0mm^(2))=9.6xx10^(3)A m^(-2).`