2. Here is a problem that will let you both practice Ampere's Law and help you see how more complicated systems can be built from the simpler ones. The former cannot be solved by themselves using Ampere's Law applied to the whole system, but the simpler systems can, and then you can use the principle of superposition to put everything together. [Note: the geometry is identical to the analogous problem with Gauss's law; the prin- ciple of superposition, in fact, works in exactly the same way. Reviewing the solution to that problem before starting this one may help you.] (a) An infinite plate with thickness 2d is parallel with the z - y plane so that its mid-point (the point halfway through the plate) is at a = 0. (That way all the points on one surface have a = +d and on the other s = -d.) The plate carries a uniform current density in the +y direction: J = Jog Using the Biot-Savart law and symmetry, sketch the magnetic field lines in the 2 - x plane. Using a rectangular Amperian loop in the 2 - a plane of width 2x (along x) and & (along =), centered on the midplane, find the magnitude of the magnetic field for any value of r. Graph B,(x) (the projection of B onto the z axis), including for a