Calculating the force between two electrons in a wire

AI Thread Summary
The discussion revolves around calculating the force between two extra electrons in an infinite line charge (wire) with a given electric field. The user successfully determined the linear charge density (lambda0) using the electric field equation. They calculated the spacing between electrons, finding it to be approximately 2.9E-14 meters per electron. Using Coulomb's law, they then computed the force between the two electrons to be about 0.28 Newtons. The user expressed gratitude for the assistance received, as their professor's hints were unclear.
helixkirby
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Homework Statement



An infinite line charge (wire) has lambda = lambda0. It produces an electric field of magnitude 5E4 N/C at a distance of 2m. Determine the typical force between two adjacent extra electrons in the wire

Homework Equations


E_line = lambda/(2pi*r*epsilon0)

The Attempt at a Solution


I managed to find lambda0 using the above equation, but now I'm stuck trying to find the force between the two electrons, how do I find thelectricity e spacing between them given the linear charge density, can anyone help me?
 
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What are the units of λ?
 
gneill said:
What are the units of λ?
C/m
 
helixkirby said:
C/m
Right. So how many electron charges make up a Coulomb?
 
gneill said:
Right. So how many electron charges make up a Coulomb?

1/1.6E-19 = 6.25E18 electrons
 
So how many electrons per meter for your value of λ?
 
gneill said:
So how many electrons per meter for your value of λ?
epsilon0 * 5E4 *4pi*6.25E18 electrons per meter I believe
 
Okay. What's the result of the calculation? What does it tell you about the meters per electron?
 
gneill said:
Okay. What's the result of the calculation? What does it tell you about the meters per electron?
I finally got it, I inverted the calculation to get the meters per electron which was about 2.9E-14 m per electron, then used this with coulomb's law to get .28N, thank you so much, my professor was giving me cryptic hints when I emailed him.
 
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