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49-52. Equipotential curves Consider the following potential func- tions and the graphs of their equipotential curves. a. Find the associated gradient field F = V4. b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1). Illustrate this result on the figure. c. Show that the vector field is orthogonal to the equipotential curve at all points (x, y). d. Sketch two flow curves representing F that are everywhere orthogo- nal to the equipotential curves. 49. (x, y) = 2x + 3y 50. (x, y) = x + y² УА 51. (x, y)et-y УА -2 234 x 52. (x, y) = x² + 2y² y 2

49-52. Equipotential curves Consider the following potential func- tions and the graphs of their equipotential curves. a. Find the associated gradient field F = V4. b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1). Illustrate this result on the figure. c. Show that the vector field is orthogonal to the equipotential curve at all points (x, y). d. Sketch two flow curves representing F that are everywhere orthogo- nal to the equipotential curves. 49. (x, y) = 2x + 3y 50. (x, y) = x + y² УА 51. (x, y)et-y УА -2 234 x 52. (x, y) = x² + 2y² y 2

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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49-52. Equipotential curves Consider the following potential func- tions and the graphs of their equipotential curves. a. Find the associated gradient field F = V4. b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1). Illustrate this result on the figure. c. Show that the vector field is orthogonal to the equipotential curve at all points (x, y). d. Sketch two flow curves representing F that are everywhere orthogo- nal to the equipotential curves. 49. (x, y) = 2x + 3y 50. (x, y) = x + y² УА 51. (x, y)et-y УА -2 234 x 52. (x, y) = x² + 2y² y 2
Transcribed Image Text:49-52. Equipotential curves Consider the following potential func- tions and the graphs of their equipotential curves. a. Find the associated gradient field F = V4. b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1). Illustrate this result on the figure. c. Show that the vector field is orthogonal to the equipotential curve at all points (x, y). d. Sketch two flow curves representing F that are everywhere orthogo- nal to the equipotential curves. 49. (x, y) = 2x + 3y 50. (x, y) = x + y² УА 51. (x, y)et-y УА -2 234 x 52. (x, y) = x² + 2y² y 2
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