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Potential and intensity of magnetic field

  1. May 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Very thin wire bent into the shape of a quarter-circle with the radius R is uniformly charged with electric charge q.
    Calculate the potential and intensity of the electric field at point A, which lies on a line perpendicular to the plane of the semicircle and is passing through the center of its curvature at a distance a from the center. The wire is in the vacuum.

    2. Relevant equations
    I am integrating through the length of the conductor, where all the variables seem to be the constants. Is it correct?
    How would it look like if I took into account the changing of the angle?

    3. The attempt at a solution
    see the picture

    --
    this is my first post, greetings to all of you and thanks for the help
    Lukas
     

    Attached Files:

  2. jcsd
  3. May 18, 2016 #2

    Simon Bridge

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    Welcome to PF.
    Yes.
    You mean if you take θ anticlockwise about the axis, from one end of the wire?
    Try it and see: dx = R.dθ and the limits of integration are 0 - π/2 ...
     
  4. May 18, 2016 #3
    Thx a lot for your reply.

    Yes...mainly "dx = R.dθ" made the trick, thx again. (the result is the same :) )

    Now everything is ready for the second question:
    I need to calculate the intensity, I was thinking of using the equation "(vector)E = - grad θ" which gives me the partial derivations by x,y,z.
    But θ doesn't contain x,y or z, so I would stay only with constants and therefore 0...what am I missing?
     
    Last edited: May 18, 2016
  5. May 18, 2016 #4

    Simon Bridge

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    ##\vec E = -\nabla \phi## ... ;) where ##\phi## is the electric potential. I used ##\theta## for the angle.
    How to write equations: https://www.physicsforums.com/help/latexhelp/

    You have only worked out the electric potential at a specific point.
    ##\phi## is not the same everywhere... therefore it has a gradient someplace.
    But it may be easier to do the vector calculus for the electric field directly: exploit the symmetry.
     
  6. May 19, 2016 #5
    I really like the logic behind, it recommends me LibreOffice and its writing of the equations.

    Thx for the guidance, it is clearer now, hope I will do the calculations correctly.
     
  7. May 19, 2016 #6

    Simon Bridge

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    It's a typsetting markup script called LaTeX - and it's pretty much the academic standard ... you can use it for Libre Office too, though, as you've noticed, there is a limited Tex support already built in.
    http://extensions.libreoffice.org/extension-center/texmaths-1

    No worries - it can help to explicitly lay out the axes ... I used cartesian with the charges in the positive quadrant of the x-y plane and A on the z axis.
     
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