Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Choose K=2, please solve all the questions

Q1. What is vector field and potential function? Sketch the gradient field of
p(x, y) = x² + y? – k².
Q2. Find the Divergence and Curl of the vector field F = (2xy+ z')i +x²j+3xz*k.
Is F a conservative force field? If yes, Find the scalar potential q.
Q3. What is flux of a vector field? Find the flux of the vector field
F = xî + z*j + y°k
across the outward surface x + y + z = k lies in the first octant.
Also find the work done by the force field F on a particle that travels once around the boundary of
the above plane in the counterclockwise direction.
Transcribed Image Text:Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y? – k². Q2. Find the Divergence and Curl of the vector field F = (2xy+ z')i +x²j+3xz*k. Is F a conservative force field? If yes, Find the scalar potential q. Q3. What is flux of a vector field? Find the flux of the vector field F = xî + z*j + y°k across the outward surface x + y + z = k lies in the first octant. Also find the work done by the force field F on a particle that travels once around the boundary of the above plane in the counterclockwise direction.
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