Given the current density
a) Find the total current crossing the plane y= 1 in the aydirection in the region 0 < x <1, 0 < z<2: This is found through
b) Find the total current leaving the region 0 < x, x<1, 2 < z <3 by integrating J·dS over the surface of the cube: Note first that current through the top and bottom surfaces will not exist, since J has no z component. Also note that there will be no current through the x= 0 plane, since Jx= 0 there. Current will pass through the three remaining surfaces, and will be found through
c) Repeat part b, but use the divergence theorem: We find the net outward current through the surface of the cube by integrating the divergence of J over the cube volume. We have
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