Assume that (r) and |G(r)| both go to zero faster than 1/r as r . (a) Let
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Assume that ϕ(r) and |G(r)| both go to zero faster than 1/r as r →∞.
(a) Let F = ∇ϕ and ∇ · G = 0. Show that ∫ d3r F · G = 0.
(b) Let F = ∇ϕ and∇ ×G = 0. Show that ∫ d3r F × G = 0.
(c) Begin with the vector with components ∂j (PjG) and prove that
Transcribed Image Text:
[d³r² = - [d³rrv. V V d³r r(V. P) +dS(-· P)r. S
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