Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.5 The Divergence Theorem, #23 · Multivariable Calculus · Green, Stokes & divergence

(c) Find a gradient field with … in the ball … and…

Inside a solid ball (radius $a$ , density 1, mass $M = 4 π a^{3} /3$ ) the gravity field is $F = - GM R / a^{3}$ .

(a) Check $\div F = - 4 π G$ in Gauss's Law.

(b) The force at the surface is the same as if the whole mass $M$ were ______.

(c) Find a gradient field with $\div F = 6$ in the ball $ρ \leq a$ and $\div F = 0$ outside.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.5 The Divergence Theorem, #23

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