Inverse square fields are special Let F be a radial field F = r/ | r | p, where p is a real number and r = ⟨x, y, z⟩. With p = 3, F is an inverse square field.a. Show that the net flux across a sphere centered at the origin isindependent of the radius of the sphere only for p = 3.b. Explain the observation in part (a) by finding the fluxof F = r/ | r | p across the boundaries of a spherical box{(ρ, φ, θ): a ≤ ρ ≤ b, φ1 ≤ φ ≤ φ2, θ1 ≤ θ ≤ θ26 forvarious values of p.

Inverse square fields are special Let F be a radial field F = r/ | r | p, where p is a real number and r = ⟨x, y, z⟩. With p = 3, F is an inverse square field.a. Show that the net flux across a sphere centered at the origin isindependent of the radius of the sphere only for p = 3.b. Explain the observation in part (a) by finding the fluxof F = r/ | r | p across the boundaries of a spherical box{(ρ, φ, θ): a ≤ ρ ≤ b, φ1 ≤ φ ≤ φ2, θ1 ≤ θ ≤ θ26 forvarious values of p.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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