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[symbolic] Linear uniform charge density (E field at a point)

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Center a rod of length L at (0,0) with the length going horizontally.

    Take a point P at (0,y).

    Find the electric field at P.

    2. Relevant equations
    [tex]E= \int k*dQ/R^{2}[/tex]

    3. The attempt at a solution
    I am integrating from -L/2 to L/2
    Since Q=lambda*L, I guess differentially dQ=lambda*dL.

    Substituting that into the integral, it becomes:
    [tex]k*\lambda \int dL/R^{2}[/tex]
    from -L/2 to L/2 of course.

    R is pretty messy so I'll just write what I came up with for [tex]R^{2}[/tex]:

    So... Doesn't this seem pretty reasonable? I just want to be double sure that this is OK.
  2. jcsd
  3. Nov 29, 2009 #2


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    Homework Helper

    There may be a confusion with L, used in two different ways here.
    I suggest you change dQ=lambda*dL to dQ=lambda*dx, where x is a distance along the x axis. This x runs from -L/2 to L/2.
    I think you'll find that R² = x² + y².
    Looks like one of those trig substitution integrals.
  4. Nov 29, 2009 #3
    Thankfully for this particular problem I get to do the integration by software... kinda. Turns out to involve arctangent and a relative mess of symbols.

    Thanks for the suggestion about variables, it is definitely more clear that way.
  5. Nov 29, 2009 #4


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    Looks like the substitution x = y*tan A really simplifies it!
    And the A is a real angle in the problem.
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