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henryc09
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Homework Statement
Consider the following vector field in cylindrical polar components:
F(r) = rz^2 r^ + rz^2 theta^
By directly solving a surface integral, evaluate the flux of F across a cylinder
of radius R, height h, centred on the z axis, and with basis lying on the
z = 0 plane.
Using the formula derived in the previous question, evaluate the divergence
∇ · F. Verify the divergence theorem by integrating ∇ · F over the volume
of the cylinder above.
Homework Equations
The Attempt at a Solution
I think I can do the second part (I can definitely work out the divergence of F) although I'm not 100% on that. I really don't know how to go about doing the surface integral. Do you need to do the integral over each side of the cylinder? I'm not really sure how to go about doing it over any side though to be honest. Any help would be appreciated.