Divergence of B, circular current loop

  • Thread starter pobro44
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  • #1
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Homework Statement


[/B]
∇ * B = 0 and ∇ X B = Mu * J. This is proved to hold not only for infinite wires but for magnetostatics in general.

Magnetostatics = steady current

Closed wire loop with constant current is certainly a magnetostatics example.

Magnetic field on z axis above loop around origin is: B = (Mu* I * R^2)/(2 * (R^2 + z^2)^(3/2)) in z hat direction


Homework Equations



Partial derivative with respect to z gives a non zero answer. Divergence is not zero. I am missing something obvious but fail to see what.

The Attempt at a Solution

 

Answers and Replies

  • #2
TeethWhitener
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Divergence is not just the partial derivative along z. Really think about the meaning of ##\frac{\partial \mathbf{B}_x}{\partial x}## and ##\frac{\partial \mathbf{B}_y}{\partial y}##.
 
  • #3
rude man
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Can also use cylindrical coordinates to verify ∇⋅B = 0. Look up the formula for div in cylindrical coordinates and apply to the problem.
 

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