Explanation Substitute the value of r = x 2 + y 2 in φ = ln r and obtain the partial derivatives to obtain the gradient value in terms of the unit radial vector e r . Given: Let φ = ln r where r = x 2 + y 2 Calculation: Since r = x 2 + y 2 and φ = ln r , we have φ = ln x 2 + y 2 = 1 2 ln ( x 2 + y 2 ) We compute the partial derivatives as follows: ∂ ∂ x φ = 1 2 ( 2 x x 2 + y

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.1, Problem 50E

To determine

To express $\nabla φ$ in terms of the unit radial vector $e_{r}$ in $R^{2}$ .

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Chapter 17.1, Problem 49E

Chapter 17.1, Problem 51E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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To express ∇ φ in terms of the unit radial vector e r in R 2 .

Solution Summary: The author explains how to obtain the gradient value in terms of the unit radial vector e r.

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To express $\nabla φ$ in terms of the unit radial vector $e_{r}$ in $R^{2}$ .

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Chapter 17 Solutions

To express ∇ φ in terms of the unit radial vector e r in R 2 .

Solution Summary: The author explains how to obtain the gradient value in terms of the unit radial vector e r.

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To express ∇φ in terms of the unit radial vector er in R2.

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Chapter 17 Solutions

To express $\nabla φ$ in terms of the unit radial vector $e_{r}$ in $R^{2}$ .