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Displacement current in Maxwell equations

  1. Oct 21, 2009 #1
    Does anyone know how to solve or at least how to begin solving the following problem?:

    Prove that displacement current in the Maxwell equations can be neglected if characteristic time τ of changing electromagnetic field in the system satisfies to the following condition: τ >> L/c where L is the characteristic size of this system and c is light speed. (Hint: time derivative of some variable y can be approximated as ratio of its characteristic value to characteristic time, dy/dτ ≈ y/τ the similar approximation can be also used for spatial derivatives).
     
    Last edited: Oct 21, 2009
  2. jcsd
  3. Oct 21, 2009 #2
    Can you write down the relevant Maxwell equation, then change all derivatives in length and time to simple division by their charactersitic values?
     
  4. Oct 21, 2009 #3
    I believe I can use the following relation:
    img981.png


    Defining the current density of J as the displacement current, by differentiating D with respect to time
    ab93b5aac5ffa87badaa48f32c50715a.png


    (dD/dt)We get:
    8df256232f07aa711d287438280647be.png


    With B and E being defined as:
    57619c6a86c79e56ac806faf21502c90.png
    9cab6787646062d6e658cd1e83ad468f.png


    So instead of differentiating to time I can now simply divide by time? However, I don't quite see where light speed comes in and how I could prove the displacement current actually being neglectable.
     
    Last edited by a moderator: Apr 24, 2017
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