Solution Found!
Answer: Equipotential curves Consider the following
Chapter 14, Problem 35E(choose chapter or problem)
Equipotential curves Consider the following potential functions and graphs of their equipotential curves.
a. Find the associated gradientjield \(\mathbf{F}=\nabla \varphi\).
b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1), illustrate this result on thefigure.
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.
\(\varphi(x, y)=e^{x-y}\)
Questions & Answers
QUESTION:
Equipotential curves Consider the following potential functions and graphs of their equipotential curves.
a. Find the associated gradientjield \(\mathbf{F}=\nabla \varphi\).
b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1), illustrate this result on thefigure.
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.
\(\varphi(x, y)=e^{x-y}\)
ANSWER:
Solution 35E
Step 1
