[This problem is optional extra credit, so the maximum score on this assignment is 40 out of 30.] An MRI machine works by using a high magnetic field to align the "spins" of the protons (these "spins" act kinda like tiny bar magnets. . . sorta) that are the nuclei of hydrogen atoms in a human body. Protons in this magnetically aligned state can absorb and re-emit radio waves. Once the spins are aligned, the machine sends a radio wave at the protons, which gives them enough energy to slightly alter their spin alignment to a different, excited state. When the radio waves are turned off, the protons lose and re-emit the energy they gained, realigning with the magnetic field. This re-emitted radio energy is detected, allowing the machine to map out the location of hydrogen atoms in the body. The stronger the magnetic field, the easier it is to detect this effect. Suppose you are designing an MRI machine. Because it must be designed to image human bodies, the tubular part of the machine in which patients lie must be about 1.5 meters long. The wiring of the machine can safely withstand electrical currents of up to 80 Amperes (which can be achieved by cooling the wires until they become superconducting). You require a magnetic field of about 1.5 T to obtain sufficiently useful images. How many times must a wire loop around the patient bed in order to generate the necessary magnetic field? (Hint: We've already derived a relevant formula for this problem (or we will if you're reading this over the weekend). You don't need calculus or anything for this problem, just one formula that we derived in class.)