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The curl of certain vector fields

  1. Jun 27, 2010 #1
    Given the two vector fields:

    \vec E and \vec B

    Where the first is the electric vector field
    and the second is the magnetic vector field, we
    have the following identity:

    curl(\vec E) = -\frac{\partial \vec B } { \partial t }

    and further that:

    curl(curl(\vec E)) = curl(-\frac{\partial \vec B } { \partial t })
    = -\frac{\partial curl(\vec B) } {\partial t }

    I tried to prove these by defining the vector fields:

    \vec E = C\frac{ \mathbf e_r } {p^2}


    \vec B = <0, 0, B>

    where C and B are constants. But I ended up with
    zero for curl(E), which cannot be right. So my reasoning
    is in error somewhere.

    Any insight appreciated.
  2. jcsd
  3. Jun 27, 2010 #2
    If p is your radial variable, then the electric field varies only radially and hence has curl zero, so that makes sense. Further, since you have a static magnetic field, its time derivative should also be zero, putting the two equal and satisfying Maxwell's equation.
  4. Jun 27, 2010 #3
    Hm, then in general how was the result reached that they are equal?
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