The base of the closed cubelike surface shown here is the unit square in the xy-plane....
The base of the closed cubelke surface shown here is the unit square in the planeThe four sides in the planes x, y, and y1. The top is an arbitrary smooth surface whose identity is unknown LetF- 23k and suppose the award of Frough Side Ais and through Side Bis-Can you conclude anything about the outward fough the top version for your answer Choose the correct answer below and recessary in the answer box to complete your choice O A...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Four closed surfaces are shown, each with circular top and bottom faces and curved sides. The areas top and Act of the top and bottom faces and the magnitudes B and Boot of the uniform magnetic fields through the top and bottom faces are given. The fields are perpendicular to the faces and are either inward or outward. Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, greatest first Surface Atop (m3 Btop (1)...
#4 please
3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
Four closed surfaces are shown, each with circular top and bottom faces and curved sides. The areas top and bot of the top and bottom faces and the magnitudes Brop and Boot of the uniform magnetic fields through the top and bottom faces are given. The fields are perpendicular to the faces and are either inward or outward. Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, greatest first Surface Atop (m? Biop (1)...
Four closed surfaces are shown, each with circular top and bottom faces and curved sides. The areas top and bot of the top and bottom faces and the magnitudes Bop and Bbet of the uniform magnetic fields through the top and bottom faces are given. The fields are perpendicular to the faces and are either inward or outward. Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, seatest first Surface Btop (T) Abott (m?...
4.8) a) Complete the statement of: The Divergence Theorem: Let D be a closed solid in space bounded by a closed surface s oriented by an outwardly directed unit normal vector n. If F(x, y, z)=(M(x,y,z), N(x, y, z), P(x, y, z)) where M, N, and P have continuous partial derivatives in D, then: D b) Use the Divergence Theorem to write as an iterated integral the flux of F=(x",x’y,x?:) over the closed cylindrical surface whose sides are defined by...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
(1 point) Compute the flux integral Ss F. dĀ in two ways, directly and using the Divergence Theorem. S is the surface of the box with faces x = 1, x = 2, y = 0, y = 3, z = 0, z = 3, closed and oriented outward, and Ě = 4x21 + 4y2] + 422K. Using the Divergence Theorem, SSF dĀ = So Sad Song dz dy dx = where a = b= d= p= and q =...