Reference no: EM131614944

Question: A vector field is a point source at the origin in 3-space if its direction is away from the origin at every point, its magnitude depends only on the distance from the origin, and its divergence is zero except at the origin. (Such a vector field might be used to model the photon flow out of a star or the neutrino flow out of a supernova.)

(a) Shoe 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 r centered at the origin.

(d) Compute the flux of v through a closed surface that does not contain the origin.