Calculating the force between two electrons in a wire

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Homework Help Overview

The discussion revolves around calculating the force between two electrons in an infinite line charge (wire) setup, specifically focusing on the electric field produced by the wire and the implications of linear charge density.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine the force between two adjacent electrons after calculating the linear charge density using the electric field equation. Participants question the units of linear charge density and explore how many electrons correspond to a Coulomb, leading to discussions about electron spacing.

Discussion Status

Participants are actively engaging in calculations and clarifying concepts related to charge density and electron distribution. Some guidance has been provided regarding the relationship between charge and the number of electrons, and the original poster has made progress in their calculations.

Contextual Notes

There is an emphasis on understanding the relationship between linear charge density and the number of electrons per meter, as well as the implications of these calculations for determining the force between electrons.

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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