The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some...
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =
1. Supposed that the magnetic field in some region of space is of the form B(x, y, z) = Bo=2 (where a and B, are constants). Find the force on a square loop (side a) lying in the xy plane and centred on the origin if it carries a current I flowing anticlockwise when you look down the z axis toward the negative direction. [7 marks]
please help me solve the following question 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ F-n dS where F-: (x, y, z) and s is the cone z2 x2 + y2, 0 S 2 1; with the outward pointing normal. 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
Problem 2a (8 pts) Suppose that the magnetic field in some region is それ (where k > 0 is a constant). A quarter-circle wire loop of radius a is lying in the xy plane with the radius of the circle centered at the origin as shown in the diagram. A power course is applied to the loop with a constant voltage V Vo driving the current in a counter-clockwise direction as shown in the diagram. The loop has resistance R....
Question 9 Please! In a bathtub, the velocity of water near2 the drain is given by the vector field k: cm/sec (22 +1)2(22 +1)222 +1 where x, y, and z are measured in centimeters and (0, 0,0) is at the center of the drain 1. Rewriting F as follows, describe in words how the water is moving: (22 +1)2'(22 +1)2 2+1 Consider cach of the threc terms in cquation (4). (Look at some plots.) For fixed z, what is the...
Question 1 Please In a bathtub, the velocity of water near2 the drain is given by the vector field k: cm/sec (22 +1)2(22 +1)222 +1 where x, y, and z are measured in centimeters and (0, 0,0) is at the center of the drain 1. Rewriting F as follows, describe in words how the water is moving: (22 +1)2'(22 +1)2 2+1 Consider cach of the threc terms in cquation (4). (Look at some plots.) For fixed z, what is the...