Trying to rewrite integrals using Green, Stokes or Divergence theorems. Don't have to evaluate.
Trying to rewrite integrals using Green, Stokes or Divergence theorems. Don't have to evaluate. (b) fe...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...