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Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S...

Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2)

(a) Find the divergence of F.

(b) Let S be any sphere not containing the origin. Find the outward flux of F across S.

(c) Let Sa be the sphere of radius a centered at the origin. Find the outward flux of F across Sa.

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+ 2 1 x2223/2 ) div(F) 2 (x y2+ 2 312 (22y2)3/2 2 2 x2 222)9/2 Cr2t222/2 322 (x22223/ 3(y2 222) - Cx?ty2+22)5/2 S: sphere con2 2 + 2 2 (cososin p, snO sin p, cos o) = (z A1x )=S Soa (-sino sind, cosOsind, (cosocos,sino cosd, - sinp) a2 sin, sin o,

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Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S...
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