Gradient fields Find the gradient field F = ?? for the

Chapter 14, Problem 25E

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QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the potential function \(\varphi\). Sketch a few level curves of \(\varphi\) and a few vectors of F.

\(\varphi(x, y)=x^{2}+y^{2}, \text { for } x^{2}+y^{2} \leq 16\)

Questions & Answers

QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the potential function \(\varphi\). Sketch a few level curves of \(\varphi\) and a few vectors of F.

\(\varphi(x, y)=x^{2}+y^{2}, \text { for } x^{2}+y^{2} \leq 16\)

ANSWER:

Step 1 of 2

 

The gradient field associated with T is

 

   

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