This is an example from the book and it is not a homework. There is one part of the step I just don't get. This is the question on page 236 of Griffiths "Introduction to Electrodynamics":(adsbygoogle = window.adsbygoogle || []).push({});

Example 5.11

A spherical shell, of radius R, carrying a uniform surface charge [itex] \rho [/itex], is set spinning at angular velocity [itex]\omega[/itex]. Find vector magnetic potential it produces at a pointr.

The book setup so the point is on the z axis and let the sphere spin on axis in the xz plane where the axis of spin make an angle [itex]\psi[/itex] with the +ve z axis. The equation used is:

[tex]\vec A \;=\; \frac {\mu_0}{4\pi} \int_{s'} \frac {\rho \vec v }{\sqrt { R^2 +r^2 -2Rrcos \theta'}} dv' [/tex]

[tex] \vec v \;=\; \vec {\omega} \;X\; \vec r \;' \;\hbox { where }\; \vec {\omega} =\hat x [\omega \;sin (\psi)] + \hat z [\omega \;cos (\psi)] [/tex] (1)

I don't understand how the book arrive to (1)

My question is how do you go from a sphere spinning on the axis at direction of [itex]( \omega sin \psi, 0, \omega cos \psi )[/itex] to just a vector of [itex] \omega[/itex]?

Can anyone explain to me how they arrive the velocity vector [itex]\vec v[/itex]?

Thanks

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# Can someone explain why book use a vector to explain angular frequency of rotation?

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