Magnetic Dipoles on z-axis

1. Nov 26, 2012

mateomy

I'm given two magnetic dipoles on the z-axis with a separation of a distance L. I need to find the fields produced by the individual dipoles at a point on the x-axis in terms of x.

This problem is driving me nuts. I've drawn a diagram with the radial vector going from the z-point to the x-axis at a given point, P. The angle between the radial vector and the z-axis has been labelled as $\theta$. What I've done so far is calculate the vector potential ($\overrightarrow{A}$) and I think I'm confusing myself because I've produced two expressions; one for $\hat{y}$ and another for $\hat{z}$, but absolutely nothing for the x-component. My expression so far is:

For $\hat{y}$:
$$\frac{x}{r^3}$$

For $\hat{z}$:
$$\frac{1}{r^3}$$

*I've left out some constants

I'm not sure I've done that correctly, regardless I went to take the curl of these vector potential expressions $\nabla\times\overrightarrow{A}$, which only gave me expressions in the y and z directions. That doesn't seem right to me, but I wanted to take it to Physics Forums to get some advice. I'll show more detail if its found necessary, I'm mostly curious to see if the expressions for the vector potential make sense.

Thanks.

2. Nov 28, 2012

Tarti

I would not use the vector potential here. Just take the formula of a magnetic dipole, shift it by -L/2 and do the same for just another one at +L/2 to find the field by superposition.
Really, there is no difference to electric dipoles from the perspective of the fields.