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Units for Coulomb's law

  1. Aug 31, 2004 #1
    Here's my question:
    Starting from Coulomb's law, show that e^2/(4*pi*epsilon_0) has dimensions of energy times distance.

    Coulombs law is F=(1/(4*pi*episilon_0))*(q1*q2/r^2)
    I understand how to convert the units for e^2/(4*pi*epsilon_0), where e is the charge of the electron, to ev * nm.
    Could someone explain how I can use this in conjunction with Coulomb's law to answer the question above? :surprised
     
  2. jcsd
  3. Aug 31, 2004 #2

    Doc Al

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    Staff: Mentor

    Start with Coulomb's law:
    [tex]F = \frac{1}{4 \pi \epsilon_0} e^2/r^2[/tex]
    Now rearrange it to solve for [itex]\frac{1}{4 \pi \epsilon_0} e^2[/itex].
    Does that help?
     
  4. Aug 31, 2004 #3
    When I do that, I get units of Newtons * (nanometers)^2 Is there any way that I can convert this into units of energy * distance?
     
  5. Aug 31, 2004 #4

    Doc Al

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    Staff: Mentor

    You may be better off thinking in terms of dimensions instead of specific units.

    Another hint: Energy has dimension of Force x Distance.
     
  6. Sep 2, 2004 #5
    Thanks for helping! I figured out two more dimensional analysis type problems on my own!
    I guess sometimes it's easier to work with dimensions than actual units? :smile:
     
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