Calculating flux without using divergence theorem

Re: Calculating flux without using divergence theorem

What you are doing, apparently, is projecting the surface of the sphere onto the xy-plane but once you have projected to the xy-plane, there is no longer a variable. You are using polar coordinates with r from 0 to R and from 0 to . Be careful to note that the both the "top" and "bottom" hemispheres project to the same disk in the xy-plane.

Personally, I would use the fact that the "vector differential of surface area" for a sphere of radius R is and integrate with from 0 to , from 0 to .

Re: Calculating flux without using divergence theorem

Calculating the flux in this case is straightforward given that is a sphere. We have that and

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