Consider the following potential functions and graphs of their equipotential curves. a. Find the associated gradient field

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Consider the following potential functions and graphs of their equipotential curves.image


a. Find the associated gradient field F = ∇φ.


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 orthogonal to the equipotential curves.

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Calculus For Scientists And Engineers Early Transcendentals

ISBN: 9780321849212

1st Edition

Authors: William L Briggs, Bernard Gillett, Bill L Briggs, Lyle Cochran

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