Divergence theorem. (a) Use the divergence theorem to prove,v = -478 (7)(2.1)(b) [Problem 1.64, Griffiths] In case you're not persuaded with (a), try replacing r by (r² + e²)2and watch what happens when ɛ → 0. Specifically, let1-V².4л1D(r, ɛ)(2.2)p2 + g2By taking note of the defining conditions of 8°(7) [(1) at r = 0, its value goes to infinity, (2) forall r + 0, its value is 0, and (3) the integral over all space is 1], demonstrate that 2.2 goes to8*(F) as ɛ → 0.

b As given, Dr,ε=-14π∇21r2+ε2 By differentiating we get, Dr,ε=-14π ddrddr1r2+ε2=-14π…

Divergence theorem. (a) Use the divergence theorem to prove, - -478'(7) (2.1) (b) [Problem 1.64, Griffiths] In case you're not persuaded with (a), try replacing r by (r² + e²)2 and watch what happens when ɛ → 0. Specifically, let 1 V². Vr? + e D(r, ɛ) = - (2.2) By taking note of the defining conditions of 8°(7) [(1) at r = 0, its value goes to infinity, (2) for all r + 0, its value is 0, and (3) the integral over all space is 1], demonstrate that 2.2 goes to 8*(F) as ɛ → 0.

Divergence theorem. (a) Use the divergence theorem to prove, - -478'(7) (2.1) (b) [Problem 1.64, Griffiths] In case you're not persuaded with (a), try replacing r by (r² + e²)2 and watch what happens when ɛ → 0. Specifically, let 1 V². Vr? + e D(r, ɛ) = - (2.2) By taking note of the defining conditions of 8°(7) [(1) at r = 0, its value goes to infinity, (2) for all r + 0, its value is 0, and (3) the integral over all space is 1], demonstrate that 2.2 goes to 8*(F) as ɛ → 0.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.23P

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