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Adding Electric Fields

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Have two electric fields.

    [tex]\hat{x} E_1 e^{i(kz- \omega t)}[/tex]
    [tex]\hat{x} E_2 e^{i(-kz- \omega t)}[/tex]

    Where E_1, E_2 are real.

    Sum them such that the result can be expressed as one magnitude and exponential, e.g., |E|e^(iq), Where E is real.

    I have no clue how I would begin to simplify this. Any ideas? It's from an undergraduate text.
     
  2. jcsd
  3. Jun 19, 2011 #2

    vela

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    Factor out the common factor of e-iωt. Use Euler's formula, e=cos θ + i sin θ.
     
  4. Jun 19, 2011 #3
    Sure.. but that's trivial detail and not key step.

    [tex]e^{-i \omega t}[(E_1 + E_2) cos(kz) + i(E_1 - E_2) sin(kz)][/tex]
     
  5. Jun 19, 2011 #4

    vela

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    Well, the rest is even more trivial, so I have no idea where you're getting stuck.
     
  6. Jun 19, 2011 #5
    Perhaps wording is unclear. Here is answer. Looks little complex for name of trivial, so long that I attach rather than typeset in latex =].

    Disregard the unit vector.
     

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  7. Jun 19, 2011 #6
    So now, how do you calculate the absolute value of a complex number? And its argument? That's just converting from cartesian to polar coordinates in the complex plane (if we ignore the factor e^(-iωt) which you can set apart).

    (The only non-trivial part apart from that conversion will be using the identity sin² φ + cos² φ = 1).
     
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