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An electorn beam has an aperture 1.0 mm^...

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

Text Solution

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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)/(1s)=9.6xx10^(-3)A`
As the charge is negative , the current is opposite to be 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)/(1.0xx10^(-6)m^(2))`
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