If the electric potential at a point (x, y) in the xy-plane is V(x, y), then the electric intensity vector at the point (x, y) is E = – vV(x, y). Suppose that V(x, y) = e¯2x cos 2y. (a) Find the electric intensity vector at (x/4, 0).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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If the electric potential at a point (x, y) in the xy-plane is
V(x, y), then the electric intensity vector at the point (x, y)
is E = – vV(x, y). Suppose that V(x, y) = e¯2x cos 2y.
(a) Find the electric intensity vector at (x/4, 0).
(b) Show that at each point in the plane, the electric po-
tential decreases most rapidly in the direction of the
vector E.
Transcribed Image Text:If the electric potential at a point (x, y) in the xy-plane is V(x, y), then the electric intensity vector at the point (x, y) is E = – vV(x, y). Suppose that V(x, y) = e¯2x cos 2y. (a) Find the electric intensity vector at (x/4, 0). (b) Show that at each point in the plane, the electric po- tential decreases most rapidly in the direction of the vector E.
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