Vector potential in spherical coordinates

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SUMMARY

The discussion focuses on the calculation of vector potential A in spherical coordinates, specifically addressing the expression A = ⅓μ0Rσ(ω x r) = ⅓μ0Rσωrsin(θ) θ^. The user seeks clarification on converting Cartesian coordinates to spherical coordinates, particularly in relation to the unit vector ##\hat \phi##. The conversation highlights the importance of understanding the geometric interpretation of these vectors, as well as the need to visualize their components in the xy-plane.

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in this problem i can solve v = ω x r = <0, -ωrsinψ, 0> in cartesian coordinates

but i don't understand A in sphericle coordinates why?

(inside) A = ⅓μ0Rσ(ω x r) = ⅓μ0Rσωrsin(θ) θ^

how to convert coordinate ?
 

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Look at figure 5.46. Unit vector ##\hat \phi## is in the xy-plane, perpendicular to the plane defined by ##\vec {r}'## and the z-axis in the direction of increasing ##\phi##. Make a drawing of it in the xy plane and find its x and y components. Hint: It has a positive y-component and a negative x-component.
 

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