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Can you integrate a vector?

  1. Feb 5, 2005 #1

    mad

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    Hello, I just wanted to know if you can integrate a vector, and if so, how.
    Here is a problem: A charged piece of metal of linear density 2 * 10^-6 * x , between x=2 and x=5.
    I found its charge by integrating.. and it is 21 micro C.

    Now that's what I want to know: calculate the electric field at x=0
    I know that [tex] \vec{E} = \int{} d \vec{E} [/tex]

    but in my physics book, it says I have to decompose it in [tex] E_x [/tex] or [tex] {E_y}[/tex] and integrate. But since I hate working without vectors, do you think there's a way to integrate without decomposing it in x and y, like something like this..:
    [tex] \vec{E} = \int{} \frac{k dq }{r^2} \vec{u}[/tex] = [tex] \vec{E} = \int{} \frac{k \lambda dx }{x^2} \vec{u}[/tex]

    Is there a way to do this? My teacher hasn't started this topic yet, I'm just curious.
    Thanks a lot !
     
    Last edited: Feb 5, 2005
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  3. Feb 5, 2005 #2

    dextercioby

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    What is the direction of the unit vector [itex] \vec{u} [/itex] ?

    Daniel.
     
  4. Feb 5, 2005 #3

    mad

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    It is -i , since they ask the electric field at x=0 . Is there a reason you are asking this?
     
  5. Feb 5, 2005 #4

    dextercioby

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    Yes,i wanted to know whether it was constant or not.If it is,then u can take it outta the integral and compute the "scalar" integral (which yields the component of [itex] \vec{E} [/itex] along the direction of [itex] \vec{u} [/itex])...

    Daniel.
     
  6. Feb 5, 2005 #5

    mad

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    [tex] k \lambda \vec{i} \int \frac{dx}{x^2} [/tex]

    You mean this? We have just started integrals in math., so I may have confused some things.
     
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