Gradient fields Find the gradient field F = ▿ϕ for the potential function ϕ. Sketch a few level curves of ϕ and a few vectors of F . 28. φ ( x , y ) = 2 x y , for | x | ≤ 2 , | y | ≤ 2
Gradient fields Find the gradient field F = ▿ϕ for the potential function ϕ. Sketch a few level curves of ϕ and a few vectors of F . 28. φ ( x , y ) = 2 x y , for | x | ≤ 2 , | y | ≤ 2
Solution Summary: The author explains how the gradient field for the potential function phi (x,y)=2xy is computed. The vector field is directed outward away from the origin in I and III quadrant.
Gradient fieldsFind the gradient fieldF = ▿ϕ for the potential function ϕ. Sketch a few level curves of ϕ and a few vectors ofF.
28.
φ
(
x
,
y
)
=
2
x
y
,
for
|
x
|
≤
2
,
|
y
|
≤
2
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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