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Current density constant in time implies charge density linear in time?

  1. Mar 12, 2009 #1
    Does current density being constant in time and the charge density NOT being constant in time imply that the charge density has to be a linear function of time? i.e of the form
    [tex] p(r,t) = p(r,0) + \dot{p}(r,0)t }[/tex]
    Can this be derived using the continuity equation alone?
     
  2. jcsd
  3. Mar 13, 2009 #2

    clem

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    Science Advisor

    Yes. For j to be constant in time requires dp/dt to be constant in time.
     
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