Question: Verify that Stokes Theorem is true for the vector field F = 7yzi-yj + 2xk and the surface S the part of the paraboloid

Verify that Stokes Theorem is true for the vector field F =

Verify that Stokes Theorem is true for the vector field F = 7yzi-yj + 2xk and the surface S the part of the paraboloid z = 7 - x - y that lies above the plane z = 3, oriented upwards. ute la To verify Stokes' Theorem we will compute the expression on each side. First compute curl F== where curl curl F. dS= n -[f curl F curl F. dS= Now compute of F C F. dr = F. dr. II. X1 x == M. M The boundary curve C of the surface S can be parametrized by: r(t) = ). 05152x E dr dydx y = 3/2 == =(2 cos(t). (Use the most natural parametrization) curl F. dS MM

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The detailed ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Verify that Stokes Theorem is true for the vector field F(x, y, z) = x 2 i + y 2 j + z 2 k, where S is the part of the paraboloid z = 1 - x 2 - y 2 that lies above the xy-plane and S has upward...

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = (x 2 , y, z), E is the solid cylinder y 2 + z 2 9, 0 x 2

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = y 2 z 3 i + 2yz j + 4z - k, E is the solid enclosed by the paraboloid z = x 2 + y 2 and the plane z = 9

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = (x 2 , 2y, z), E is the solid cylinder y 2 + z 2

(a) Let a and b be scalar fields with arbitrary but smooth dependence on location in curved spacetime, and let A(vector) and B(vector) be vector fields. Show that (b) Use Eq. (25.32) to show that (i)...

Use a computer algebra system to find the curl F for the vector field. F(x, y, z) = x + y + z (i + j + k)

Verify Stokes Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x 2 - y 2 , z 0, oriented with unit normal n pointing upward. THEOREM 6-Stokes' Theorem Let S be a piecewise...

Verify Stokess theorem for the vector field B = (rrcos sinby evaluating: (a) fC B.d1 over the semicircular contour shown in Fig. P3.46 (a), and...

Verify Stokess theorem for the vector field B = (r cosËsinby evaluating: (a) fC B. dl over the path comprising a quarter...

For the vector field E = xxz _ yyz2 _ zxy, verify the divergence theorem by computing: (a) The total outward flux flowing through the surface of a cube centered at the origin and with sides equal to...

In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends for the next two years. It will resume its annual cash dividend of $2.00 per share in 3 years. This level of...

What are the arguments for social responsibilities and the arguments against social responsibilities? Do you agree with these? Why?

Factorise each of the following expressions completely. (a) ax-5a+4x-20 (c)x+x+2y+2 (b) ax + bx+ay + by (d) -3x+2xy-6y

Consider a variant of the sealed-bid auctions with imperfect information considered in class in which the players are risk-averse. Specifically, assume that the payoff of a player with valuation v...

Company A is assessing the purchase of a machine. With the machine, the firm can generate a series of cash inflows as follows. Starting next year, there will be four cash flows, $200,000 each, once...

The economy of a certain country consists of just three sectors. In terms of market capitalization, Sector 1 makes up 20% of the entire economy, (that is, 20% of the market portfolio ), and the...

The Teenie Tiny Company is currently an un-levered firm with a beta of 1.3925. Since this is a start-up company with significant impact on the social well-being of the country, the firm was given a...

A ________ is the failure to raise an alarm when there is an issue. False positive True negative True positive False negative

( 1 point ) Verify that Stokes' Theorem is true for the vector field F = y i + z j + x k and the surface S the hemisphere x 2 + y 2 + z 2 = 4 , y 0 oriented in the direction of the positive y - axis....

(8 points EACH part) Verify the Divergence Theorem is true for the vector field F(x,y,z)=xi+y2j+zk and t surface S is the plane 2x+2y+z=6 bounded by the coordinate planes in octant 1.

1. [-/0.5 Points] DETAILS MY NOTES PRACTICE ANOTHER Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - V, Z= 1+ 2u + v, Osus 3, OS VS...

Divergence Theorem: If S is a closed surface in R' that bounds a solid region B and if the boundary S is oriented via an outward unit normal vector n, and if F = (P(x, y, z), O(x, y, Z), R(x, y, Z) )...

3. Verify that Stokes' Theorem is true for the vector eld F05: ya 2) = (37: Z2: '92) and the surface S that is the part of the paraboloid y = m2 + 22 that lies in the half-space { (3:, y, z) I y g...

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = x 2 i + xy j + zk, E is the solid bounded by the paraboloid z = 4 x 2 y 2 and the xy-plane Data from...