Use the surface integral in Stokes Theorem to calculate the circulation of the field F around the
Question:
Use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
F = x2i + 2xj + z2k
C: The ellipse 4x2 + y2 = 4 in the xy-plane, counterclockwise when viewed from above
Transcribed Image Text:
THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (3 reviews)
To apply Stokes Theorem we need to find the curl of F curl F Fy Fz i Fz Fx j Fx Fy k 2yi 0j 2zk Now ...View the full answer
Answered By
Deepak Sharma
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
Assume that Bill's marginal tax rate is 40%. If corporate bonds pay 10% interest, what interest rate would a municipal bond have to offer for Bill to be indifferent between the two bonds? A. 10% B....
-
Maria Young is the sole stockholder of Purl of Great Price Company (POGP Company), which produces high-end knitted sweaters and sweater vests for sale to retail outlets. The company started in...
-
In January, the Cabinet Company worked on six job orders for specialty kitchen cabinets. It began job A-62 are as follows: The Cabinet Company produced a total of 34 cabinets for job A-62. Its...
-
On February 1, 2017, Jura Corp. (Jura) issued an $8,000,000 bond with a 7 percent coupon rate and a maturity date of January 31, 2023. Interest is paid annually on January 31. The effective interest...
-
A circular aperture is lit up by a laser with wavelength 565 nm. The central maximum on the screen 50.0 cm away has the same diameter as the circular aperture. What is the diameter of the circular...
-
A survey of German adults found that 73% of customers who shop online pay through PayPal. You randomly select 150 German adults who shop online. Find the probability that the number who pay through...
-
Wallis Car Wash, Inc., expected to wash 2,000 cars during the month of August. Washing each car was expected to require 0.2 hours of labor. The company actually used 420 hours of labor to wash 1,880...
-
An air conditioner with cooling capacity of 7 . 3 5 kW consumes 1 . 4 7 kW of electricity during operation. The air conditioner is used to maintain the temperature of a room at 2 0 \ deg C during the...
-
"I was sure that when our battery hit the market it would be an instant success," said Roger Strong, founder and president of Solar Technology, Inc. "But just look at the gusher of red ink for the...
-
Approximate the double integral of (x, y) over the region R partitioned by the given vertical lines x = a and horizontal lines y = c. In each sub-rectangle, use (x k , y k ) as indicated for your...
-
The previous integrals suggest there are preferred orders of integration for spherical coordinates, but other orders give the same value and are occasionally easier to evaluate. Evaluate the...
-
Do you think that an ERP should be cost justified? Why?
-
Choose one of the following health crisis scenarios and write a two- minute press conference statement following the best practices in risk and crisis communication and present it to the class: a)...
-
Find the Pv work required to blow up a balloon to a diameter of 1 ft. Does the value you calculate account for all the work that is required? Explain.
-
A rigid container contains saturated water at a pressure of 2 bar and a quality of 0.42. The water undergoes a process in which it is heated to a fi nal temperature of 540C. Determine the fi nal...
-
Define the four categories of goods illustrated in the chapter. How would you distinguish one from another?
-
Visitors of the Carrs Park, a public park in Wilmslow, England, can use all available facilities, which include tennis courts and playgrounds, for free. In addition to this, there is no entry fee to...
-
Trans-Am Suppliers Ltd. is just completing negotiations to sell its manufacturing division to a competitor. The purchaser has agreed to purchase the inventory, manufacturing equipment, licence, and...
-
The graph of the sequence whose general term is an = n - 1 is which of the following? [8.1] A. B. TITTT 3-2-1 23.45 2.3.4
-
In Problems 39 52, find the real zeros, if any, of each quadratic function using the quadratic formula. What are the x-intercepts, if any, of the graph of the function? F (x) = 2x 2 5x + 3
-
In Problems 39 52, find the real zeros, if any, of each quadratic function using the quadratic formula. What are the x-intercepts, if any, of the graph of the function? g (x) = x 2 + 6x + 1
-
In Problems 39 52, find the real zeros, if any, of each quadratic function using the quadratic formula. What are the x-intercepts, if any, of the graph of the function? g (x) = x 2 4x 1
-
In what ways do team composition and diversity influence team dynamics, and how can teams leverage the strengths and mitigate the challenges associated with demographic, cognitive, and experiential...
-
A program consists of 1010 instructions where 70% of the instructions are ALU instructions, 20% are load instructions and 10% are jump instructions. The resulting values of the load instructions are...
-
Do you agree that in order for teams to be effective, there must be a climate of trust and mutual respect among the team members.. You are the leader of a team assigned to complete a project at work,...
Study smarter with the SolutionInn App