Vector Calculus: Integral Theorems

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Homework Statement

Question 3 part b and c

Homework Equations

Divergence and Stokes Theorems. Knowledge of parametrization ect ect

The Attempt at a Solution

I got the B field by using curl. However any attempt to resolve the flux through the top hemisphere or even the sphere as a whole just gives me a horrible mess filled with cos's, sines and exponentials.

I used divergence theorem and calculated that the flux = 0. This cannot be write otherwise there would be no need for part c. Stokes theorem is the one that gives me the horrible mess.

My lecturer says that I have to use the right theorem, and ds will produce 1 easy component to calculate. I've tried everything but literally it's impossible.

Can someone shine the light on what theorem to use?

I tried to just do a line integral since the sphere is bounded by x^2 + y^2 = 1... Again I get a horrible mess that I cannot integrate.

I would show my proper attempt but your latex reference is too longwinded and difficult to use. It would be better if you reprogrammed it to work like the equation editor on Microsoft Word.

 

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Don't worry I got it.