Suppose the magnetic vector potential in a region of space is given by: a = a, exp/- (*+9° a (a) what are the units of the given constants a and ac? - determine the b-field from this vector potential, b = vxa (note: eq (1) is in cartesian coordinates - what coordinate system would make your calculations easier? use that! ) - determine the current density, j, from the b-field. (use an appropriate maxwell's eqn) (b) separately sketch the vector field a, the magnetic field b, and the current density j you found above, using any representation you feel conveys the most useful information. briefly, for each of the three plots, also use english words to describe what they look like. use mathematica (perhaps vectorplot3d might be handy) to plot at least one of these three fields - preferably the one(s) you feel is (are) the hardest to visualize. (c) integrate the current density to show that the total current flowing through any infinite plane parallel to the x-y plane is zero. then, give a simple argument (without doing any formal integral) why you might have known before calculating that this must be the case. (d) calculate the divergence of the current density j. what does the value of the divergence imply, in terms of griffiths: equation (5.29)? does this set of fields strike you as an unphysical math exercise, or can you imagine some physical system or device, which might be (approximately) represented by this problem?