Explanation Given: Vector field F → = e r r 3 and G → = e r r 4 in R 3 . Formula used: If f is a potential function for the vector field F → then F → = ∇ → f In spherical coordinates ∇ → f = ∂ f ∂ r e ^ r + 1 r ∂ f ∂ θ e ^ θ + 1 r Sin θ ∂ f ∂ ϕ e ^ ϕ Calculation: The potential function of F → = e r r 3 is- F → = ∇ → f In spherical coordinates- ∇ → f = ∂ f ∂ r e ^ r + 1 r ∂ f ∂ θ e ^ θ + 1 r Sin θ ∂ f ∂ ϕ e ^ ϕ F → = ∇ → f = e ^ r r 3 ⇒ ∂ f ∂ r = 1 r 3 ⇒ f = ∫ d r r 3 = − 1 2 r 2 + c ∂ f ∂ θ = 0 ∂ f ∂ ϕ = 0 Where c is a constant...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.1, Problem 48E

To determine

the potential function for $\vec{F} = \frac{e_{r}}{r^{3}}$ and $\vec{G} = \frac{e_{r}}{r^{4}}$ in $R^{3}$ .

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Chapter 17.1, Problem 47E

Chapter 17.1, Problem 49E

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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the potential function for F → = e r r 3 and G → = e r r 4 in R 3 .

Solution Summary: The author explains how to determine the potential function of the vector field F.

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the potential function for $\vec{F} = \frac{e_{r}}{r^{3}}$ and $\vec{G} = \frac{e_{r}}{r^{4}}$ in $R^{3}$ .

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Chapter 17 Solutions

the potential function for F → = e r r 3 and G → = e r r 4 in R 3 .

Solution Summary: The author explains how to determine the potential function of the vector field F.

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the potential function for F→=err3 and G→=err4 in R3.

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Chapter 17 Solutions

the potential function for $\vec{F} = \frac{e_{r}}{r^{3}}$ and $\vec{G} = \frac{e_{r}}{r^{4}}$ in $R^{3}$ .