Calculating the force between two electrons in a wire

[helixkirby]

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?

 

[gneill]

What are the units of λ?

 

[helixkirby]

What are the units of λ?

C/m

 

[gneill]

C/m

Right. So how many electron charges make up a Coulomb?

 

[helixkirby]

Right. So how many electron charges make up a Coulomb?

1/1.6E-19 = 6.25E18 electrons

 

[gneill]

So how many electrons per meter for your value of λ?

 

[helixkirby]

So how many electrons per meter for your value of λ?

epsilon0 * 5E4 *4pi*6.25E18 electrons per meter I believe

 

[gneill]

Okay. What's the result of the calculation? What does it tell you about the meters per electron?

 

[helixkirby]

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.