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Unformatted text preview: 6. (a) Direct method: 2 On the surface, has no-component, so the-component of does not contribute to the Fux. Thus Since is perpendicular to and on , we have Area of (b) Using Stokes theorem, we replace the Fux integral by two line integrals around the circular boundaries, and , of . See igure 1. On , the left boundary, , so , and therefore . On , the right boundary, , so . This vector eld has and is tangent to the boundary and pointing in the same direction as . Thus Length of Figure 1 7. (a) I Greens Theorem can be used. The curve is closed and the vector eld is smooth throughout the interior of the region enclosed II Greens Theorem cannot be used. The vector eld is not dened at the origin which is inside the curve. III Greens Theorem cannot be used. The curve is not closed. (b) or the integral in [I], let be the region enclosed by . See igure 2. Greens Theorem gives 3 Figure 2...
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- Spring '08