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Work Done line Integral question - Electrostatics - help please

  1. May 4, 2015 #1
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    Can anyone please tell me where I am going wrong? I am getting the incorrect answer for the Word Done should be: WD = q(3x^2-6y) ...

    Apologies for not changing it into the format on here - but for my revision I have pretty much done that myself.
     
    Last edited: May 4, 2015
  2. jcsd
  3. May 4, 2015 #2

    BvU

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    You showed that ##\vec E## as given is curl free. Well done.
    Then you worked out that ##\displaystyle q\int_{(0,0,0)}^{(x_1, y_1,0)} \vec E\cdot \vec{dl} = q\left(3x_1^2y_1 - y_1^3\right )## (small omission of the ##^2## ).

    To check it, you could verify that ##V = -\nabla\cdot E## is satisfied if ##-V(x,y,z) = 3x^2y - y^3## and then you can immediately see that W.D. is what you found (when you fix the missing square) and not q(3x2-6y).

    You could double check with another path: from (0,0,0) to (0, y1, 0) and then to ( x1, 0, 0) which givves the very same result.

    Have some faith and if we're both wrong don't hesitate to inform me with another post ! I love (:wink:) to be corrected when I'm wrong.

    (happens all the time :cry: )
    -
     
  4. May 4, 2015 #3
    Thanks - I guess I was just doubting myself! Really appreciate you helping me out like that. Sam.
     
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