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Homework Help: Finding charge density generating an Electric Field

  1. Jun 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that electrostatic field E = br
    where b is a constant
    is irrotational

    Find the charge density ρ(r) which can generate this electric field

    2. Relevant equations

    ∇ x E = 0 (following stoke theorem)

    ρ = ε0(div E) since: div E = [itex]\frac{ρ}{ε}[/itex]

    3. The attempt at a solution

    The first part (I'm assuming) will suffice as ∇ x E = 0

    The second part ρ = ε0(div E) = ε0(div br) = bε0(div r)

    The question is whether I can compute (div r) or not. Does "r" in this particular case equal to square root (x+y+z)2? I'm assuming I can't know data given, which is why I am tempted to leave the solution as it is.

  2. jcsd
  3. Jun 13, 2012 #2
    You cannot take the divergence of a scalar, so I suppose that r is actually the vector:

    [itex]\vec r=(x,y,z)[/itex]
  4. Jun 13, 2012 #3
    Ah good, that's what I was thinking. Thanks
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