Apply Stokes' Theorem to evaluate (oint_{C} mathbf{F} cdot d mathbf{r}) by finding the flux of (operatorname{curl}(mathbf{F})) across
Question:
Apply Stokes' Theorem to evaluate \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) by finding the flux of \(\operatorname{curl}(\mathbf{F})\) across an appropriate surface.
\(\mathbf{F}=\langle 3 y,-2 x, 3 yangle, \quad C\) is the circle \(x^{2}+y^{2}=9, z=2\), oriented counterclockwise as viewed from above.
Transcribed Image Text:
THEOREM 1 Stokes' Theorem Let S be a surface as described earlier, and let F be a vector field whose components have continuous partial derivatives on an open region containing S. $. F.dr= - J1 The integral on the left is defined relative to the boundary orientation of aS. If S is a closed surface, then If cu curl(F). dS curl(F) dS=0 . 1
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Choose for the surface mathcalS the interior of the given circle and parametrize mathcalS by mathbfr...View the full answer
Answered By
Mehwish Aziz
What I have learnt in my 8 years experience of tutoring is that you really need to have a friendly relationship with your students so they can come to you with their queries without any hesitation. I am quite hardworking and I have strong work ethics. Since I had never been one of those who always top in the class and always get A* no matter what, I can understand the fear of failure and can relate with my students at so many levels. I had always been one of those who had to work really hard to get decent grades. I am forever grateful to some of the amazing teachers that I have had who made learning one, and owing to whom I was able to get some extraordinary grades and get into one of the most prestigious universities of the country. Inspired by those same teachers, I am to be like one of them - who never gives up on her students and always believe in them!
5.00+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
If you "load down" your car by placing passengers, cargo, etc into it, how does this affect the tires? Assume there are no leaks in the tires. Group of answer choices a. Tire pressure should increase...
-
The Lexus Company purchased a new machine on January 1, 2014. The supplier, Infinity, was paid $2,000 in cash. In addition, transportation and installation were $180 (paid in cash), legal costs...
-
BT is considering investing in government bonds. The current price of a P100 bond with 10 years to maturity is P88. The bonds have a coupon rate of 6% and repay face value of P100 at the end of the...
-
The temperature within the Earths crust increases about 1.0Co for 3each 30 m of depth. The thermal conductivity of the crust is 0.80 W/Co m. (a) Determine the heat transferred from the interior to...
-
Using the LIFO method, calculate the cost of ending inventory and cost of goods sold for Sandy Corporation. Use the following data of Sandy Corporation: A1 Total Unit Cost 4.00 $ 90 $ 180 $ 7.00 $...
-
Abbott Industries is a well-known supplier of pharmaceuticals worldwide. Founded by Dr. Wallace Abbott, the company was incorporated in 1900 after he had been developing and making pharmaceuticals...
-
Arrowbell Company is a growing company. Two years ago, it decided to expand in order to increase its production capacity. The company anticipates that the expansion program can be completed in...
-
Direct Materials Conversion Percent Percent Units Complete Beginning work in process inventory 2,800 100% Complete 25% Units started this period 6,800 Completed and transferred out 7,800 Ending work...
-
Apply Stokes' Theorem to evaluate \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) by finding the flux of \(\operatorname{curl}(\mathbf{F})\) across an appropriate surface. \(\mathbf{F}=\langle y z, x y,...
-
Calculate curl(F) and then apply Stokes' Theorem to compute the flux of \(\operatorname{curl}(\mathbf{F})\) through the given surface using a line integral. \(\mathbf{F}=\left\langle 2 y,...
-
To obtain the best separation of two weak acids in capillary electrophoresis, it makes sense to use the pH at which their charge difference is greatest. Prepare a spreadsheet to examine the charges...
-
(1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? 0 year =$0,1year =$100, 2year= $100, 3year = $100 (2) What is...
-
Evaluate the factorial. 15! 15! = (Use scientific notation. Use the multiplication symbo skaitsanna enmanent
-
Need recent 3 months news article which seems to connect with Micro Economics. What evidence is there in the article for the economic theory ? How does the theory apply to the article and what...
-
You are given the following information for Mobility Research, Inc. (MRI). Sales $200,000 Costs $105,000 SG&A $20,000 Interest $19,000 Dividend paid $7,000 Retained Earnings Added $19,000 Total...
-
Assume company XYZ (above) has been using FIFO accounting. For some reason, their sales increase drastically this year. Assuming the price that they sell the widgets does not change, and that they...
-
What were the main objectives of the Bretton Woods system?
-
Read Case Study Google: Dont Be Evil Unless and answer the following: Given its mission of providing information to the world, should Google censor searches in China?
-
Several terms of a sequence are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term...
-
Several terms of a sequence are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term...
-
Several terms of a sequence are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term...
-
Two resistors, 49.4 and 89.80, are connected in parallel. The current through the 89.8-Q resistor is 2.62A. (a) Determine the current in the other resistor. (b) What is the total power supplied to...
-
Use the Ohm's law equation to provide numerical answers to the following questions: A. An electrical device with a resistance of 3.0 will allow a current of 4.0 amps to flow through it. if a voltage...
-
A surface encloses the charges q = 3.3 C, 92 = 7.2 C, and q3 = -3.8 C Part A Find the electric flux through this surface. Express your answer using two significant figures.
Study smarter with the SolutionInn App