Divergence of B, circular current loop

[pobro44]

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

 

[TeethWhitener]

Divergence is not just the partial derivative along z. Really think about the meaning of $\frac{\partial \mathbf{B}_x}{\partial x}$ and $\frac{\partial \mathbf{B}_y}{\partial y}$.

 

[rude man]

Can also use cylindrical coordinates to verify ∇⋅B = 0. Look up the formula for div in cylindrical coordinates and apply to the problem.