A long, thick, hollow cylindrical metal pipe has an inner radius of R and an outer radius of 2R. Its length is very long compared to its radius (you could treat it as being approximately infinitely long). The shaded area in this cross-sectional view represents the solid part of the pipe that carries a current in the direction that points out of the page. The total current carried by the pipe is I, and it is distributed uniformly through the shaded area. 2R (a) Given the direction of the current, what direction could the magnetic field of this object have? E.g., does it point upward everywhere? Radially inward? Looping clockwise? Something else? (b) Use Ampere's Law to find the magnitude of the magnetic field inside the hollow interior of the pipe at a distance r away from the center (where r 2R). Again, be clear about your made-up Amperian loop. (d) What is the current density, J, in the solid portion of this pipe? (Recall that current density is the current-per-cross-sectional-area, so it has units of amps-per-square-meter, and it's a quantity that we originally defined when we talked about resistors in Section 19.2.) Your answer should depend on I, R, and common constants. (e) Finally, use Ampere's Law to find the magnitude of the magnetic field at a distance r away from the center that lies within the solid shaded part of the pipe (where R