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Electrostatics - line charges

  1. Feb 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A line charge has density λ and extends along the x axis from -a to +a. Find the electric potential at a point r on the x-axis (r>a). Use your result to find the E-field at r.


    2. Relevant equations
    [tex]V = \frac{1}{4\pi \epsilon _0}\int\frac{dq}{r} [/tex]


    3. The attempt at a solution
    I've said so far:
    dQ = λdx = Qdx/2a

    Then I made the substitution into the above equation, and integrated wrt x with limits ±a, leaving me with [tex]\frac{Q}{4\pi \epsilon _0 r}[/tex].

    However I'm not sure I made the correct integration here. I also believe that the answer for V should have λ in it somewhere. Have I gone wrong somewhere?

    I haven't actually gotten round to looking at the E-field yet - I'll get there once this is completed!

    Any pointers would be appreciated.

    Thanks
     
    Last edited: Feb 20, 2007
  2. jcsd
  3. Feb 20, 2007 #2
    Is this correct? I've spent my morning researching this, and I can't seem to find anything to compare it to - I'm a little confused as to what to do when the point is somewhere on the same line. Are my limits correct?
     
  4. Feb 20, 2007 #3
    You could find the Electric field using gauss's law and then use E=-dV/dr to solve for V.
     
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