(a) Find a potential field function for F(x, y) = (x + y)i + (x - y) or prove none exists. (b) Find a potential field function for Ģ(x, y) = xyi + (x+y)j), or prove none exists. (c) If H(x, y, z) = xyzi + sin(ry)] − cos(yz)k, compute ▼ × H(x, y, z).
(a) Find a potential field function for F(x, y) = (x + y)i + (x - y) or prove none exists. (b) Find a potential field function for Ģ(x, y) = xyi + (x+y)j), or prove none exists. (c) If H(x, y, z) = xyzi + sin(ry)] − cos(yz)k, compute ▼ × H(x, y, z).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Find a potential function for \(\vec{F}(x, y) = (x + y) \vec{i} + (x - y) \vec{j}\) or prove none exists.
(b) Find a potential function for \(\vec{G}(x, y) = xy \vec{i} + (x + y) \vec{j}\), or prove none exists.
(c) If \(H(x, y, z) = xyz \vec{i} + \sin(xy) \vec{j} - \cos(yz) \vec{k}\), compute \(\nabla \times H(x, y, z)\).
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