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(a) In Example 3 of Section 15.1 we showed that ϕ(x, y)=−c(x2+y2)1/2 is a potential function for the two-dimensional inverse-square filed F(x, y)=c(x2+y2)3/2(xi+yj) but we did not explain how the potential function ϕ(x, y) was obtained. Use Theorem 15.3.3 to show that the two-dimensional inverse-square filed is conservative everywhere except at the origin, and then use the method of Example 4 to derive the formula for ϕ(x, y) .
(b) Use an appropriate generalization of the method of Example 4 to derive the potential function ϕ(x, y, z)=−c(x2+y2+z2)1/2 for the three-dimensional inverse-square filed given by Formula (5) of Section 15.1.
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Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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