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Explain why the divergence of each of the functions must be zero

  1. Mar 6, 2007 #1
    1. The problem statement, all variables and given/known data
    the question is:
    Without doing any calculations, explain why the divergence of each of the functions must be zero(Hint: consider what electric field these functions physically correspond to)
    P.S: I make the unit vectors in bold.

    A1=x

    A2=ρ(1/ρ) with ρ>0

    A3=r(1/r2) with r>0

    2. Relevant equations
    I think we need to argue about the charge



    3. The attempt at a solution

    for A1 , the electric field of A! is a plane, which constant, so divergence is zero.

    for A2, it seems to be a line of charge but I don know how to argue for the divergence to be zero.

    Same for A3

    Can someone see what is going on?
    B
     
  2. jcsd
  3. Mar 6, 2007 #2
    Divergence shows the flux through some kind of area, so it indicates how much "stuff" flows in compared to out. This is basically going to be your argument for every single one, is that somehow as much stuff flows in as out.

    Are the vectors rho and r supposed to represent spherical and cylindrical coordinates?
     
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