Calculating the direction of magnetic field at a point above a loop of current

  • #1
I've uploaded my attempted solution here. The problem I'm having is highlighted at the bottom in red.

The issue I'm having is expressing the direction of H. I realize the cancellation that occurs at point (0,0,z), where the only the z-component of the H-field remains. I also realize that my final expression for [itex]\bar{H}[/itex] will be [itex]\hat{z}Hcos\phi[/itex], where [itex]cos\phi=\frac{r}{\sqrt{r^2+z^2}}[/itex]. I'm really just having a hard time resolving the geometry of these angles to where I can actually equate the two red phi's in the image.
 

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