Problem 2: The potential energy for a particular two-dimensional force field is given by V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency. (a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or the equivalent to plot contours of constant potential energy for various energy levels, over a region of the plane centered on the origin. (b) Show that an infinitesimal displacement along an equipotential line has the form dx dr = dz x + ŷ. kx (c) Find the expression for the force field, and plot this vector field over the same region of the plane (and with the same choice of constants) as in part (a).
Problem 2: The potential energy for a particular two-dimensional force field is given by V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency. (a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or the equivalent to plot contours of constant potential energy for various energy levels, over a region of the plane centered on the origin. (b) Show that an infinitesimal displacement along an equipotential line has the form dx dr = dz x + ŷ. kx (c) Find the expression for the force field, and plot this vector field over the same region of the plane (and with the same choice of constants) as in part (a).
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![Problem 2: The potential energy for a particular two-dimensional force field is given by
V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency.
(a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or
the equivalent to plot contours of constant potential energy for various energy levels,
over a region of the plane centered on the origin.
(b) Show that an infinitesimal displacement along an equipotential line has the form
dr
dr = dr x + ŷ.
kx
(c) Find the expression for the force field, and plot this vector field over the same region
of the plane (and with the same choice of constants) as in part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2F22c1d6b1-d24f-4168-b856-14aa3f84fddc%2F1poo4cf_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2: The potential energy for a particular two-dimensional force field is given by
V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency.
(a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or
the equivalent to plot contours of constant potential energy for various energy levels,
over a region of the plane centered on the origin.
(b) Show that an infinitesimal displacement along an equipotential line has the form
dr
dr = dr x + ŷ.
kx
(c) Find the expression for the force field, and plot this vector field over the same region
of the plane (and with the same choice of constants) as in part (a).
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