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What the hell is wrong with this?

  1. Feb 16, 2010 #1
    What the hell is wrong with this?! :)

    I just can't spot the mistake! Please see if you can.
     
  2. jcsd
  3. Feb 16, 2010 #2
    Re: What the hell is wrong with this?! :)

    Sorry, I forgot the attachment.
     

    Attached Files:

  4. Feb 17, 2010 #3
    Re: What the hell is wrong with this?! :)

    In your first equation, both the dz parts have the wrong sign. Remember, you are going anti-clockwise, so the first dz-part moves in the negative z-direction, so it should be negative, not positive. The same (or rather, opposite) goes for the other dz-part at x=0.

    EDIT: Don't be fooled by the way the arrows are drawed. If E_z is positive in the second term, then it points backward in comparison to the direction of the path, and will therefore contribute negatively, hence the correct expression is -E_z*dz

    Torquil
     
  5. Feb 17, 2010 #4
    Re: What the hell is wrong with this?! :)

    But I don't think the signs are wrong. It follows from the properties of dot products. Please check the attachment.
     

    Attached Files:

  6. Feb 17, 2010 #5

    Ich

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    Re: What the hell is wrong with this?! :)

    Sorry, LucasGB, this may sound stupid, but yes, please check the attachment.
     
  7. Feb 17, 2010 #6
    Re: What the hell is wrong with this?! :)

    LOL. Oh my God, these subscripts are driving me crazy!

    In the last equation, the second term in the sum must be (E2z)(dz).

    I truly hope that's the only obvious mistake we're talking about.
     
  8. Feb 17, 2010 #7
    Re: What the hell is wrong with this?! :)

    No I'm pretty sure the signs are wrong. In your second calculation the error manifests itself like this:

    Notice how you have defined your angles. Your first and second equation is correct. But when you write it in terms of the components E_x and E_z you are using the wrong sign for both the E_z's.

    E.g. the second term: You have defined the theta angle to be the angle between E_2 and -dz. Therefore |E_2|cos(theta) is -E_{2z}, not E_{2z}. The opposite goes for the other E_z part.

    You get the component E_z of a vector E by doing |E|cos(theta) where theta is the angle between the vector and the "positively pointing" z-axis. Your are assuming the opposite for the two parts that are related to z-components.

    Torquil
     
  9. Feb 17, 2010 #8
    Re: What the hell is wrong with this?! :)

    That's perfect. I can totally see it now. Thank you very much, torquil, you're the man!

    I just learned something new!
     
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