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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 is
independent of the radius of the sphere only for p = 3.
b. Explain the observation in part (a) by finding the flux
of F = r/ | r | p across the boundaries of a spherical box
{(ρ, φ, θ): a ≤ ρ ≤ b, φ1 ≤ φ ≤ φ2, θ1 ≤ θ ≤ θ26 for
various values of p.
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