Answered: (у, — 2х) F C: r(t) = (2 cos t, 4 sin…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Flux Consider the vector fields and curve.
a. Based on the picture, make a conjecture about whether the outward
flux of F across C is positive, negative, or zero.
b. Compute the flux for the vector fields and curves.

F and C given

(у, — 2х)
F
C: r(t) = (2 cos t, 4 sin t), for 0 <is 2m
V4r? + y
(y. –2x)
F =
yA
V4x2 +
y²
C: r(t) = (2 cos t, 4 sin t)

Expert Solution

Step 1

Given: $F = \frac{<y, - 2 x>}{\sqrt{4 x^{2} + y^{2}}}, C : <2 \cos t, 4 \sin t>, 0 \leq t \leq 2 π$

a. Whether flux is positive, negative, or zero.(Based on picture)

b. Calculate flux.

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