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Electric Field due to a charged line; With y as function of theta

  1. Feb 16, 2014 #1
    Well the main problem here its once a i get the integral i do not how to put dy as function of thetha and then integrate ; at the end that's what i get

    Ex=integral (dE*cos[itex]\theta[/itex])=([itex]\lambda[/itex]/4[itex]\pi[/itex][itex]\epsilon[/itex])
    times the integral of cos([itex]\theta[/itex])dy/x^2+y^2

    where i can easily find the cosine and do the integral but i'm asked to express strictly "y" as function of thetha so as cos(θ)=x/√x^2+y^2 so 1/√x^2+y^2=cos^2(θ)/x^2

    and i know that y=x*tan(θ) but i dont how to get "dy" graphically nor analytically;
     

    Attached Files:

  2. jcsd
  3. Feb 16, 2014 #2

    Simon Bridge

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    Why not do the integral in terms of dy?
     
  4. Feb 16, 2014 #3
    Well the professor asked us for bring both methods in terms of y as function of theta & theta as function of y;

    I already did in terms of dy. making the substitution of cosine(θ) = x/√x^2+y^2 and then integrating.

    but now i need the other method. y in terms of "θ"
     
  5. Feb 17, 2014 #4

    Simon Bridge

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    OK - so complete: $$y=x\tan\theta\\ \implies \frac{dy}{d\theta}=\cdots$$ ... then multiply both sides by ##d\theta##.

    Then substitute these values for y and dy into:
    $$E_x=\frac{\lambda}{4\pi\epsilon_0}\int \frac{\cos\theta\; dy}{x^2+y^2}$$ ... with appropriate limits.

    note: I wrote all that out so you'd get an example of LaTeX, since I noticed you struggling with typing out the math there.
    To figure out how I did it - just hit the "quote" button attached to this post.
    The equations all appear between dollar or hash marks.
     
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