- #1
RedDeer44
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For reference, this is from Griffiths, introduction to quantum mechanics electrodynamics, p253-255
When deriving the ideal magnetic dipole field strength, if we put the moment m at origin and make it parallel to the z-axis,
the book went from the vector potential A
$$
A= \frac{\mu_0}{4\pi}\frac{\vec{m}\times \hat{r}}{r^2}
$$
to
$$
A = \frac{\mu_0}{4\pi}\frac{m\sin{\theta}}{r^2}\hat{\phi}
$$
Can someone explain how the single ##\phi## component come about? This to me seems to indicate ##r## has non-zero ##\theta## component and zero ##\phi## component. But I thought ##r## is any point?
Also, for a point in spherical coordinates, is ##\phi## value defined when ##\theta = 0##? Or when ##r=0##?
When deriving the ideal magnetic dipole field strength, if we put the moment m at origin and make it parallel to the z-axis,
the book went from the vector potential A
$$
A= \frac{\mu_0}{4\pi}\frac{\vec{m}\times \hat{r}}{r^2}
$$
to
$$
A = \frac{\mu_0}{4\pi}\frac{m\sin{\theta}}{r^2}\hat{\phi}
$$
Can someone explain how the single ##\phi## component come about? This to me seems to indicate ##r## has non-zero ##\theta## component and zero ##\phi## component. But I thought ##r## is any point?
Also, for a point in spherical coordinates, is ##\phi## value defined when ##\theta = 0##? Or when ##r=0##?
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