2-23a Divergence Theorem - Flux Through a Half Sphere

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For a vector function A= a=:::.
a) find pA·ds over the surface of a hemispherical region that is the top half of a sphere of radius 3 centered at the origin with its flat base coinciding with the xy-plane,
b) V ·A, and
c) verify the divergence theorem.
Problem Source: Fundamentals-Engineering-Electromagnetics-David-Cheng
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you have a calm voice and elaborated solution which helped me a lot to understand quicker. thank you so much💙

paulinetagalog
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6:28 forgot the negative!, but this section works out to zero so does not affect the overall problem just note the - from -z direction should still be in there, also I often say phi hat in this video when I mean theta hat!, please look at what I'm pointing at for clarification

redSTEM
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Why did we not use normal vector when finding the flux?

PG-