A vector field is a point source at the origin in 3-spaceif its direction is away from
Chapter 19, Problem 64(choose chapter or problem)
A vector field is a point source at the origin in 3-spaceif its direction is away from the origin at every point, itsmagnitude depends only on the distance from the origin,and its divergence is zero except at the origin. (Such avector field might be used to model the photon flow outof a star or the neutrino flow out of a supernova.)(a) Show that v = K(x2+y2+z2)3/2(xi +yj +zk )is a point source at the origin if K > 0.(b) Determine the magnitude v of the source in part(a) as a function of the distance from its center.(c) Compute the flux of v through a sphere of radius rcentered at the origin.(d) Compute the flux of v through a closed surface thatdoes not contain the origin.
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