# manufacturing planning and control

Problems:

Manufacturing Planning and Control

Problem 1

Magnetic fields and MRI. Magnetic resonance imaging (MRI) is a powerful imaging method that, unlike x-ray imaging, allows sharp images of soft tissue to be made without exposure to potentially damaging radiation. While a full explanation of MRI is beyond the scope of an introductory physics textbook, some understanding can be achieved by the relatively simple application of the classical (that is, non-quantum) physics of magnetism. The starting point for MRI is nuclear magnetic resonance (NMR), a phenomenon that depends on the fact that protons in the atomic nucleus have a magnetic field, . The origin of the proton’s magnetic field is the spin of the proton. Being charged, the spinning proton constitutes an electrical current analogous to a wire loop through which current flows. Like the wire loop, if the proton is subjected to an external magnetic field, , it experiences a torque and a magnetic moment, μp. The magnitude of the magnetic moment is about 1.4 × 10–26 J/T. The proton can be thought of as being in one of two states, with the magnetic moment oriented parallel or anti-parallel to the applied magnetic field, and work must be done to flip the proton from the low energy state to the high energy state.

An important consideration is that the net magnetic field of any given nucleus, except for hydrogen, consists of protons and neutrons. The hydrogen atom, of course, has only a proton. If a nucleus has an even number of protons and neutrons, they will pair in a way such that half of the protons have spins in one orientation and half have spins in the other orientation, so net magnetic moment for the nucleus is zero. Only nuclei with a net magnetic moment are candidates for MRI. Hydrogen is the atom most commonly imaged.

If a proton is exposed to an external magnetic field of 2T that has a direction perpendicular to the axis of the spin of the proton, what will be the torque on the proton?

A. 0

B. 1.4 × 10–26 N · m

C. 2.8 × 10–26 N · m

D. 0.7 × 10–26 N · m

Ans for problem 1:

Problem 2:

Ans:

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