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Homework Help: Need help on an E&M problem

  1. Sep 26, 2005 #1
    I'm given this:

    A vector field is given in cylindrical coordinates as:

    F=(A)(s)(PhiHat) + (B)(z)(zhat)

    Where A and B are constants. Could F be an electrostatic field ? Why or why not ?

    I kind of feel stupid asking this because I feel like I should know, but, I'm currently braindead after having just spent hours doing the previous 29 problems.

    Thanks,
    Dan
     
  2. jcsd
  3. Sep 26, 2005 #2

    an electrostatic field should be curl-less.

    so... take the curl and see if it's zero or not.
     
  4. Sep 26, 2005 #3
    i guess i should provide some justification for my answer so that you'll believe me! :tongue:

    an electrostatic field can be written in terms of a scalar potential:

    [tex]
    \mathbf{E} = -\nabla V.
    [/tex]


    and it is a mathematical fact that
    [tex]
    \nabla \times \nabla V = 0
    [/tex]

    for any V.


    So if the curl is strictly zero, this implies that E can be expressed in terms of a scalar potential (and not have a vector potential term), and this is enough to determine if E is a static field or not.
     
  5. Sep 26, 2005 #4
    Duh. I knew I was just being stupid. I had to do a couple similar problems earlier. Gah. Thanks a bunch :) Too many hours doing homework...
     
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