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Unformatted text preview: a about the origin is 4 . Use Gauss theorem to show that the divergence of F cannot vanish at the origin. c. If f is a dierentiable function and A is a dierentiable vector eld, then show that ( f A ) = A f + f A . d. Calculate the divergence of a radial vector eld (i.e., everywhere parallel to r ) in three dimensions. Under what conditions does the divergence vanish at the origin? 4. (Chow 1.20) a. Find constants a , b and c such the the vector eld A := ( x + 2 y + az ) x + ( bx-3 y-z ) y + (4 x + cy + 2 z ) z is irrotational (i.e., curl-free). b. Show that the resulting vector eld can be expressed as the gradient of a scalar eld....
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This note was uploaded on 10/21/2011 for the course PHZ 3113 taught by Professor Staff during the Fall '10 term at FAU.
- Fall '10