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Ohms law implies specific condition for the charge density

  1. Aug 10, 2012 #1
    We have all seen Ohms law, J=σE. This approximations makes sense in simple electric fields in which the charges are accelerated in parallel.

    However as I will demonstrate, this implies a few conditions on the charge density (ρ) associated with the current density (J).

    Now, from the continuity equation, ∂ρ/∂t=-DivJ
    =-σDivE (using the approximation)
    =-σ(ρ/ε) (From maxwells equations)
    This is just a simple partial differential equation, solving...
    ρ=A(x,y,z)exp(-σt/ε)+B(x,y,z)
    This is a partial differential equation, so we have to allow the coefficients and constants as functions of position.

    This implies that at time 0 (when the electric field is set up), the charge density is A+b, after some time the charge density reduces to B(x,y,z).
    Has this been observed in ohmic resistors?

    I find this result quite strange, is this a physical result?
     
    Last edited: Aug 10, 2012
  2. jcsd
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