across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
Let S be the sphere r2 + y2 + z2-k2 oriented outward and let F be the vector field (r, y, 2)/(a2 +y2 +2/2. Find (i) the normal vector field n on S (ii) the normal component of F on S and (ii) the flux of F across S Let S be the sphere r2 + y2 + z2-k2 oriented outward and let F be the vector field (r, y, 2)/(a2 +y2 +2/2. Find (i) the normal vector field n...
Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S be any sphere not containing the origin. Find the outward flux of F across S. (c) Let Sa be the sphere of radius a centered at the origin. Find the outward flux of F across Sa.
2. Find the flux of the vector field F = <xzyz,1> across the surface of the upper half of the sphere of radius 5, centered at the origin. Write a program that displays Welcome to Python
r 37. Singular radial field Consider the radial field (x, y, z) F (x2 + y2 + z2)1/2" a. Evaluate a surface integral to show that SsFonds = 4ta?, where S is the surface of a sphere of radius a centered at the origin. b. Note that the first partial derivatives of the components of F are undefined at the origin, so the Divergence Theorem does not apply directly. Nevertheless, the flux across the sphere as computed in part (a)...
Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x> 0, y> 0 and z> 0 )j+ (3z + 7)k be the velocity field of a fluid. Let B be the Determine the flux of F through B in the direction of the outward unit normal Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x>...
can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Use the Divergence Theorem to compute the net outward flux of the field F = (3x.y. -22) across the surface S, where is the sphere {x,y,z) x+yz? = 15) The net outward flux across the sphere is (Type an exact answer, using x as needed)
Let F(x, y, z) (xr,y, z). Compute the outward flux of F: 9y2622 on the bounded region inside of S. However, you may wish to consider the region bounded between S and the sphere of radius 100.) 7/Fthrough the ellipsoid 4c2 36. (Hint: Because F is not continuous at zero, you cannot use the divergence theorem Suppose that E is the unit cube in the first octant and F(z,y, z) = (-x,y, z). Let S be the surface obtained by...