Assume that (r) and |G(r)| both go to zero faster than 1/r as r . (a) Let

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 (P_jG) and prove that

Transcribed Image Text:

[d³r² = - [d³rrv. V V d³r r(V. P) +dS(-· P)r. S