# Vector Calculus : Flux and Gauss's Law

(a) Consider a vector function with the properly ... = 0 everywhere on two closed surfaces S1 und S2 and in the volume V enclosed by them (see the figure). Show that the flux ol F through S1, equals the flux of F through S2. In calculating the fluxes, choose the direction of the normals as indicated by the arrows in the figure.

(h) Given the electrostatic field of a point charge q situated at r= 0.

....

where r =x2 + y2 + z2, show by direct calculation that....

(c) Prove Gauss' law for the field of a single point charge given in (b) [Hint : It is easy to calculatw the flux of E over a sphere centered at r = 0.]

(d) How would you extend this proof to cover the case of an arbitrary charge distribution?

Please see the attached file for the fully formatted problems.

Â© BrainMass Inc. brainmass.com November 24, 2022, 12:00 pm ad1c9bdddfhttps://brainmass.com/math/vector-calculus/vector-calculus-flux-and-gauss-s-law-35377

#### Solution Summary

Flux and Gauss's Law are investigated. The solution is detailed and well presented.