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A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)] (a) Verify that A = Bxr is a vector potential for B, where r = (x, 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 A = (5,0,6), B = (5,4,0), C = (0,4,0), D= (0,0,6), F = (5,0,0) Flux(B) =

A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)] (a) Verify that A = Bxr is a vector potential for B, where r = (x, 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 A = (5,0,6), B = (5,4,0), C = (0,4,0), D= (0,0,6), F = (5,0,0) Flux(B) =

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 12P
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A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)] (a) Verify that A = B x r is a vector potential for B, where r = (x, 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. F A = (5,0,6), B=(5,4,0), C = (0,4,0), D = (0,0,6), F = (5,0,0) Flux (B) = B FIGURE 17
Transcribed Image Text:A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)] (a) Verify that A = B x r is a vector potential for B, where r = (x, 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. F A = (5,0,6), B=(5,4,0), C = (0,4,0), D = (0,0,6), F = (5,0,0) Flux (B) = B FIGURE 17
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