(a) Let r = (x, Y, z) and r = ||r||. Assuming r cannot equal 0, is there a value of p for which the vector field f(r)=r/r^P is solenoidal? You must fully justify your answer. (b) Show that if f and g are twice differentiable scalar fields then V²(f g) = ƒ V^2g+ g V²f + 2Vƒ · Vg

(a) Let r = (x, Y, z) and r = ||r||. Assuming r cannot equal 0, is there a value of p for which the vector field f(r)=r/r^P is solenoidal? You must fully justify your answer. (b) Show that if f and g are twice differentiable scalar fields then V²(f g) = ƒ V^2g+ g V²f + 2Vƒ · Vg

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.24P

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(a) Let r = (x, Y, z) and r = ||r||. Assuming r cannot equal 0, is there a value of p for which the vector field f(r)=r/r^P is solenoidal? You must fully justify your answer.

(b) Show that if f and g are twice differentiable scalar fields then V²(f g) = ƒ V^2g+ g V²f + 2Vƒ · Vg

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