A thick-walled copper pipe (inner radius a and outer radius b) is centered on the z-axis and carries a current density of magnitude J(r)=B*r. (The parameter B has units A/m^3). A wire runs parallel to the pipe a distance R=2*b away from the z-axis. (a) What is B=B(vector), the magnetic field magnitude, inside the pipe (rb)? (b) Sketch a plot of the field magnitude B(r). Be sure to clearly label the axes of your plot, the value of the maximum B(max), the inner and outer radii a and b, and how B(r) depends on r in each region described in part (a). (c) Suppose that a current i(w) flows in the wire at R=2b. What force does the wire exert on the pipe if i(w) flows in the same direction as i(p), the total current in the pipe?