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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?

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Solution Summary

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