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Why partial derivatives in continuity equation?

  1. Jun 14, 2012 #1
    Why is partial derivative with respect to time used in the continuity equation,
    [tex]
    \frac{\partial \rho}{\partial t} = - \nabla \vec{j}
    [/tex]
    If this equation is really derived from the equation,
    [tex]
    \frac{dq}{dt} = - \int\int \vec{j} \cdot d\vec{a}
    [/tex]
    Then should it be a total derivative with respect to time?
     
  2. jcsd
  3. Jun 14, 2012 #2
    Partial derivative is used because the charge density may also vary with distance.
     
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