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I am trying to formulate the Current Density for a Loop of wire with a diameter,d, current,I, and an cross-sectional Area of the wire ##\pi(d/2)^2##. With spherical coordinates (radial, azimuthal, polar)

##\bar j## = ##\frac{I}{\pi(d/2)^2}*cos \theta *sin \phi \hat x##

##+\frac{I}{\pi(d/2)^2}*sin \theta *sin \phi \hat y##

##+\frac{I}{\pi(d/2)^2}*cos \phi \hat z##

Charge Density, ##\rho=-grad . \bar j##

##\bar j## = ##\frac{I}{\pi(d/2)^2}*cos \theta *sin \phi \hat x##

##+\frac{I}{\pi(d/2)^2}*sin \theta *sin \phi \hat y##

##+\frac{I}{\pi(d/2)^2}*cos \phi \hat z##

Charge Density, ##\rho=-grad . \bar j##

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