Explanation The Laplace equation is used to find out the partial derivatives. The Laplace operator ∇ is defined by: ∇ φ = ∂ 2 φ ∂ x 2 + ∂ 2 φ ∂ y 2 For any vector field F = 〈 F 1 , F 2 〉 , define the conjugate vector field F ∗ = 〈 − F 2 , F 1 〉 . Given: It is given that F = ∇ φ . Formula Used: ∇ φ = ∂ 2 φ ∂ x 2 + ∂ 2 φ ∂ y 2 Proof: It is given that F = ∇ φ ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18.1, Problem 46E

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To prove:

If $F = \nabla φ$ ,then ${curl}_{z} (F^{*}) = \nabla φ$ .

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Chapter 18.1, Problem 45E

Chapter 18.1, Problem 47E

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Chapter 18 Solutions

CALCULUS (CLOTH)

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

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To prove: If F = ∇ φ ,then curl z ( F ∗ ) = ∇ φ .

Solution Summary: The author explains that the Laplace equation is used to find out the partial derivatives.

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To prove:

If $F = \nabla φ$ ,then ${curl}_{z} (F^{*}) = \nabla φ$ .

Want to see the full answer?

Chapter 18 Solutions

To prove: If F = ∇ φ ,then curl z ( F ∗ ) = ∇ φ .

Solution Summary: The author explains that the Laplace equation is used to find out the partial derivatives.

Concept explainers

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To prove: If F=∇φ,then curlz(F∗)=∇φ.

Want to see the full answer?

Chapter 18 Solutions

To prove:

If $F = \nabla φ$ ,then ${curl}_{z} (F^{*}) = \nabla φ$ .