1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Working w/ Complex representation E-field

  1. Mar 3, 2012 #1
    Often a time varying E-field is represented in complex format. I have a simple E-field (uniform in space) given by

    [itex]\vec{E}(t)=E_o\cos(\omega t)\cdot\hat{k}[/itex]
    or equivalently, the real part of

    [itex]\vec{E}(t)=E_o e^{\omega t}\cdot\hat{k}[/itex].

    We know the potential is the negative gradient of the E-field.
    If we want to calculate the potential of a field represented in the complex notation, do we need first convert to the "real" representation of and then take the gradient?

    In other words how do we deal with all the calculations when the field is represented in the complex format.

    Thanks
     
  2. jcsd
  3. Mar 5, 2012 #2

    Philip Wood

    User Avatar
    Gold Member

    You have this the wrong way round. The E-field component in a particular direction is minus the gradient in that direction of the potential.

    The answer to your question – suitably modified! – is that eiwt can be left in unmodified. It is a time-dependent factor; the gradient operation is a spatial one.
     
  4. Mar 5, 2012 #3
    Even when you come across time operators, such as in Maxwell's equations, you can stick with complex notation. The imaginary numbers behave very nicely and you still get the right answer in the end.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Working w/ Complex representation E-field
  1. Attenuation of E-field (Replies: 5)

Loading...