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Current and Avogadro's Number

by Ithryndil
Tags: avogadro, current, number
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Ithryndil
#1
Sep18-08, 06:23 PM
P: 142
1. The problem statement, all variables and given/known data

The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.20 mm.
(a) The beam current is 7.75 ľA. Find the current density in the beam assuming it is uniform throughout.
correct check mark A/m2

(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.
correct check mark m-3

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



2. Relevant equations

[tex]J=I/A[/tex]
[tex]I_{avg} = nqv_{d}A



3. The attempt at a solution

Part a and b are straight forward.

For part a I have: 1.71 A/m^2

For part b I have: 3.565 x 10^10 m^-3

I am having issues with part c. I know I need to figure out how many electrons are leaving the wire per second and then from there it should be a straight division problem using the 6.022 x 10^23 for Avogradro's number.
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LowlyPion
#2
Sep18-08, 07:50 PM
HW Helper
P: 5,343
Quote Quote by Ithryndil View Post
1. The problem statement, all variables and given/known data

The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.20 mm.
(a) The beam current is 7.75 ľA. Find the current density in the beam assuming it is uniform throughout.
correct check mark A/m2

(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.
correct check mark m-3

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

2. Relevant equations

[tex]J=I/A[/tex]
[tex]I_{avg} = nqv_{d}A[/tex]

3. The attempt at a solution

Part a and b are straight forward.

For part a I have: 1.71 A/m^2

For part b I have: 3.565 x 10^10 m^-3

I am having issues with part c. I know I need to figure out how many electrons are leaving the wire per second and then from there it should be a straight division problem using the 6.022 x 10^23 for Avogradro's number.
Think of it as a bucket. How long to fill'er up.

So what's the definition of an ampere?
Ithryndil
#3
Sep18-08, 08:02 PM
P: 142
Right...an ampere is a coulomb per second. So we take the current which is a coulomb per second and divide it by the elementary charge to get the number of electrons per second. Afterwards it's a simple division of avogadro's number by the aforementioned number...far easier than I anticipated. Sometimes your mind can just be clouded.


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