Gauss's Theorem, Cylindrical Coordinates Consider a cylinder Z with radius a and height b given by Z={(x,y,z):x^(2)+y^(2)

Question

Gauss's Theorem, Cylindrical Coordinates Consider a cylinder

Z

with radius

a

and height

b

given by

Z={(x,y,z):x^(2)+y^(2)<=a^(2) and 0<=z<=b}

and the vector field

vec(F)(vec(r))=(xz,yz,z^(2))^(T)

. At which point within the cylinder is the source density of

vec(F)

highest? Calculate the flux of the vector field through the surface of

Z

. Hint: Use Gauss's theorem to convert the desired surface integral into a volume integral and use cylindrical coordinates to solve it.

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