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Polar to rectangular coordinates

  1. Sep 26, 2012 #1

    perplexabot

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    Hello all.
    I am trying to change:
    E = (1/r) ar

    To rectangular coordinate system. Where ar is a unit vector.

    So I know r = √(x^2 + y^2)
    i also think ar = ax+ay, where ax and ay are unit vectors along the x axis and y axis respectively.

    So that would give me: E = (1/√(x^2 + y^2)) (ax + ay) = ax/√(x^2 + y^2) + ay/√(x^2 + y^2)... Which is wrong.

    The correct answer is: (x ax)/(x^2 + y^2) + (y ay)/(x^2 + y^2)

    So what am I doing wrong? Thank you.
     
  2. jcsd
  3. Sep 26, 2012 #2
    Yeah, adding two unit vectors doesn't usually give you another unit vector. This is the big issue.
     
  4. Sep 26, 2012 #3

    perplexabot

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    Oh, that makes a lot of sense. Thank you. So I would have to divide by the magnitude of their sums. I will try and figure that out.
     
  5. Sep 26, 2012 #4

    perplexabot

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    Ok, I tried figuring this out but with negative outcome. Here is what I did:

    ar = (ax + ay) / |ax + ay| = (ax + ay) / √(x^2 + y^2)

    So: E = 1/r ar = (1 / √(x^2 + y^2)) * [(ax + ay) / √(x^2 + y^2)] = (ax + ay) / (x^2 + y^2)

    Still, this is wrong. What did I muck up this time?
     
  6. Sep 27, 2012 #5

    arildno

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    Dearly Missed

    [(ax + ay) / √(x^2 + y^2)]
    This is again an incorrect decomposition of the unit vector ar.
     
  7. Sep 27, 2012 #6

    perplexabot

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    Ok thanks. I will give it one last try tomorrow (maybe even tonight). But if I can't do it please direct me towards the right path.

    Is this part correct: ar = (ax + ay) / |ax + ay|
    ?
     
  8. Sep 27, 2012 #7

    arildno

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    No.
    You need to learn how to decompose vectors correctly.

    We have:
    ar=(x*(ax)+y*(ay))/r
     
  9. Sep 27, 2012 #8

    perplexabot

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    Thank you.
     
  10. Sep 27, 2012 #9

    perplexabot

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    So you multiply x with ax so that ax points in the direction of x, am I right? Same with y and ay?
     
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