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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
The electric field at a point P(x, y, z) due to a point charge q located at the origin is given by the inverse square field
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where r = xi + yj + zk.
(a) Suppose S is a closed surface, Sa is a sphere x2 + y2 + z2 = a2 lying completely within S, and D is the region bounded between S and Sa. See FIGURE 9.16.7. Show that the outward flux of E for the region D is zero.
(b) Use the result of part (a) to prove Gauss' law:

that is, the outward flux of the electric field E through any closed surface (for which the divergence theorem applies) containing the origin is 4Ï€q.

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