Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Flux across curves in a flow field Consider the flow field $\mathbf{F}=\langle y, x\rangle$ shown in the figure.a. Compute the outward flux across the quarter circle $C: \mathbf{r}(t)=\langle 2 \cos t, 2 \sin t\rangle,$ for $0 \leq t \leq \pi / 2$b. Compute the outward flux across the quarter circle $C: \mathbf{r}(t)=\langle 2 \cos t, 2 \sin t\rangle,$ for $\pi / 2 \leq t \leq \pi$c. Explain why the flux across the quarter circle in the third quadrant equals the flux computed in part (a).d. Explain why the flux across the quarter circle in the fourth quadrant equals the flux computed in part (b).e. What is the outward flux across the full circle?(FIGURE CAN'T COPY)

A. 4B. $$-4$$ C. identical D. identical E. 0

Calculus 3

Chapter 15

Vector Calculus

Section 2

Line Integrals

Vectors

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

05:48

Consider the vector field …

03:22

Flux across a circle Find …

03:28

Flux across a cylinder Let…

01:54

Circulation and flux For t…

02:16

Find the counterclockwise …

10:53

Find the flux of the field…

01:52

18:34

04:03

Our Prime 66 given F. Is why comma X. Compute outward flux for R. F. G. Equal to two. Co sign T. two sci fi. Mhm. From zero two Pi over two. So gradient is defined. Bye partial respect to X. Partial with respect to Y partial or the spec to see. So for a R. T. is to co sign TO two. Sine of T. Our prime FT. Good negative too Sine of T. To co sign T. The integral. EFTa. And yes Go to integral from zero. Hi over to of to scientific comma negative two eco sci fi ah two co scientific comma negative two Sine T. D. T. That equals in a girl from zero to pi over two for scientology. Cose I inti Plus four. Sine T. Cose I inti T. T. Or in a girlfriend pie overseas in trig identities of sign to T. T. T. Take the integral. Got four. It's negative. Co sign to T. Over two, Evaluated from Pi over 220. That gives us four. All right party new privatization of our to co sai inti to sign T. Our prime FT. To go negative too sci fi. Two eco sci fi integral would be integral From pi over two hi of to sign T comma negative to co sign T. Ah To co sai Inti Come on a -2. Sine of T G. T. Now again this is gonna equal to pi over 22 pi a sign T. Co. Sine T DT which is you go to four cents in the grove power teared up. I signed to T T. T. The integral simplifies two negative coastline to T. Over two evaluated however, to two pi Which is -4. So that's where fox is negative for parsi. Since the vector field F. In the normal vector and the first of the quadrants are negative. The flux is the same. So the flux is identical flux. Ah I tend to call and first and third quadrant party since F. And the normal vector and the second quadrant Um is negative as is in the 4th quadrant. Their product is the same. So flux is identical in second and four step E. Our flux is the combined flux across each quadrant. So net Does he go to 4 -4 plus 4 -4 Which is equal to zero.

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Consider the vector field $\mathbf{F}=\langle y, x\rangle$ shown in the figu…

Flux across a circle Find the flux of the fields$$\mathbf{F}_{1}=2 x \ma…

Flux across a cylinder Let $S$ be the cylinder $x^{2}+y^{2}=a^{2},$ for $-L …

Circulation and flux For the following vector fields, compute (a) the circul…

Find the counterclockwise circulation and the outward flux of the field $\ma…

Find the flux of the fields$$\mathbf{F}_{1}=2 x \mathbf{i}-3 y \math…

03:32

Flux across concentric spheres Consider the radial fields $\mathbf{F}=\frac{…

02:55

Jacobians in three variables Evaluate the Jacobians $J(u, v, w)$ for the fol…

02:46

$\mathbf{F}=\langle z-x, x-y, 2 y-z\rangle ; D$ is the region between the sp…

01:41

Miscellaneous surface integrals Evaluate the following integrals using the m…

02:41

Evaluate the line integral $\oint_{C} \mathbf{F} \cdot$ dr by evaluating the…

01:19

Compute the outward flux of the following vector fields across the given sur…

03:37

An identity Suppose the second partial derivatives of $f$ are continuous on …

04:09

Evaluate the line integral in Stokes" Theorem to evaluate the surface i…

03:05

singular radial field Consider the radial field $\mathbf{F}=\frac{\mathbf{r}…

03:58

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.