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J(dot)E = Work/Volume

  1. Aug 14, 2011 #1
    Hey guys,
    So I know I'm missing something really stupid, but I can't figure out what it is.
    I'm seeing the claim that the current density dotted with the Electric field is equal to Work per volume, or: J.E = W/V. Using dimensional analysis though, I keep getting an extra unit of seconds on the left hand side of the denominator:
    (Cm/m^3s)(N/C) = J/(m^3)
    Nm/sm^3 = J/m^3
    J/sm^3 = J/m^3

    What am I doing wrong?
  2. jcsd
  3. Aug 14, 2011 #2


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    I get the same answer as you using the fact that the electric field has dimensions of voltage / length. Then J*E becomes

    [C/(sm2)] * V/m

    = (C*J/C)*m-3s-1

    = Jm-3s-1

    Where exactly are you "seeing this claim?"
  4. Aug 15, 2011 #3
    W isn't "work" ,it's work/t(its dimension is J/s),you mistakes at this
  5. Aug 15, 2011 #4
    Yeah J dot E is power per unit volume. That's usually the starting point for deriving expressions for the poynting vector and the energy density in the field.
  6. Aug 15, 2011 #5
    Ahh Power/Volume. Thanks. I had seen this claim on a flashcard, I'm preparing for GRE's and got a bunch of flash cards sent from a school to help me. Must be a typo on their part then.

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