Explanation Given: Flux F = e r r 2 through a sphere centered at the origin. Proof: We parametrize the sphere of radius R centered at the origin by, Φ : x = R cos θ sin ϕ , y = R sin θ sin ϕ , z = R cos ϕ , 0 ≤ θ ≤ 2 π , 0 ≤ ϕ ≤ π The outward pointing normal is n = R 2 sin ϕ e r We compute the product F ⋅ n on the sphere. On the sphere r = R , therefore we get: F ⋅ n = e r r 2 . R 2 sin ϕ e r = e r R 2 ...

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.5, Problem 20E

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To prove: The flux of $F = \frac{e_{r}}{r^{2}}$ through a sphere centered at the origin does not depend on the radius of the sphere.

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Chapter 17.5, Problem 19E

Chapter 17.5, Problem 21E

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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To prove: The flux of $F = \frac{e_{r}}{r^{2}}$ through a sphere centered at the origin does not depend on the radius of the sphere.