Integrate A=(sinx, yx, cosz) over the outer surface of a cube with side length 1. For simplicity, place one vertex of the cube at the origin and align its three neighboring edges along the positive x, y, z axis, respectively. For each face of the cube, calculate A•n before doing the integration, where n is the norm of that face (the unit vector perpendicular to the surface that points outward).
Integrate A=(sinx, yx, cosz) over the outer surface of a cube with side length 1. For...
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...