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