Mathematical Methods in the Physical Sciences · Problem 8.1

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · poisson-equation-laplace-gravity

Problem

Show that the gravitational potential V=−Gm/rV = -Gm/r satisfies Laplace's equation, that is, show that ∇2(1/r)=0\nabla^2(1/r) = 0 where r2=x2+y2+z2r^2 = x^2 + y^2 + z^2, r≠0r \neq 0. (Also see Chapter 15, Section 8.)

Related theory

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