Problem 1

The region lies between the spheres and and within the cone with ; its boundary is the closed surface, , oriented outward. Find the flux of out of .

Problem 2

Let and

(a). Find the Flux of out of the Rectangular Solid

(b). For what Values of is the Flux Largest?

(c). What is that Largest Flux?

Problem 3

Use the Divergence Theorem to calculate the flux of the vector field and through the surface given by the sphere of radius centred at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically.

with giving the interior of a sphere

Problem 4

Consider the flux integral . is the surface of the box with faces , , , , , and closed and oriented outward, and .

(a). Evaluate the Flux Integral Using the Divergence Theorem

(b). Directly Evaluate the Flux Integral