Let S be the part of the plane 4r + 2 +z= 3 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F 4i + 3j + 1k across the surface S.
Let S be the part of the plane 4r + 2 +z= 3 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F 4i + 3j + 1k across the surface S.
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Solve 3
Transcribed Image Text:Let I be the flux of G = (5e", 7z°e" ,0) through the upper hemisphere S of the unit sphere.
G.
(a) Find a vector field A such that curl(A):
(b) Calculate the circulation of A around aS.
(c) Compute I, the flux of G through S.
(a) A
(b) , A- ds =
(c) I =
A uniform magnetic field B has constant strength b teslas in the z-direction (i.e., B = (0,0, 6) )
(a) Verify that A = B x ris a vector potential for B, where r = (r, y, 0)
(b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and Din Figure 17.
A
B
FIGURE 17
A = (9,0, 7), B= (9,5, 0), C = (0,5, 0),
D= (0,0, 7), F = (9,0,0)
Flux(B) =
Let S be the part of the plane 4r + 2 + z =3 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 4i + 3j + 1k across the surface S.
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