By Francis C. Moon
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Extra resources for Magneto-Solid Mechanics
Fig. 2-10 ' Paths of integration (Example 2-4). s are unity; rentid area, ld (2-33) - Solution: -First we must write the dot product F d t in Cartesian coordinates. Since this is a two-dimensional problem, we have, from Eq. - It is important to remember that dt' in Cartesian coordinates is always given by Eq. (2-44) irrespective of the path or the direction of integration. The direction of integration is taken care of by using the proper limits on the integral. Along direct path a-The equation of the path PIP2is This is easily obtained by noting from Fig.
If wc are to determine the electric field at a certain point in space, we gt least need to describe the posilion of the source and the locatlon of this point in p coordinate system. In a three-dimTnsiona1 space a point can be located as the intersection of three surfaceq. Assume that the three families of surfaces are described by u, = constant, u, = coqstant, and u, = constant, where the u's need not all be lengths. ) When these three surfaces are mutually perpendicular to one another, we have an orthogonal coorriinate system.
2-90); but a two-dimensional surface integral divided by a three-dimensional volume will lead to spatial derivatives as the volu~ne approaches zero. We shall now derive the expression for div A in Cartesian coordinates. Consider a differential volume of sides Ax, Ay, and Az centered about a point P(xo,yo, 2,) in the field of a vector A, as shown in Fig. 2-19. In Cartesian coordinates, a,A,. We wish to find div A at the point ( s o , yo, 2,). Since the A = a,A,-+a,& dikrentii~lvolumc has six fxcs, thc siirfucc intcgrnl in the nulncrator of Eq.
Magneto-Solid Mechanics by Francis C. Moon