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A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1 (a) Verify that A = B x ris a vector potentlal 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 D in Figure 17. B FIGURE 17 А- (9,0, 7), В (9,5,0), С- (0,5, 0), D= (0,0,7), F = (9,0,0)

A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1 (a) Verify that A = B x ris a vector potentlal 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 D in Figure 17. B FIGURE 17 А- (9,0, 7), В (9,5,0), С- (0,5, 0), D= (0,0,7), F = (9,0,0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) 1 (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. 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.
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) 1 (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. 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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