Chapter 20, Problem 86PP

BIO Magnetic fields and MRI. Magnetic resonance imaging (MRI) is a powerful imaging method that, unlike x-ray imaging, can make sharp images of soft tissues without exposing the patient to potentially damaging radiation. A rudimentary understanding of this method 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 technique that depends on the fact that protons in the atomic nucleus have a magnetic field $\stackrel{\to }{B}$ The origin of the proton’s magnetic field is the spin of the proton. Being charged, the spinning proton constitutes an electric current analogous to a wire loop through which current flows. Like the wire loop, the proton has a magnetic moment $\stackrel{\to }{\mu }$ thus it will experience a torque when it is subjected to an external magnetic field ${\stackrel{\to }{B}}_0$ The magnitude of $\stackrel{\to }{\mu }$ is about 1.4 × 10⁻²⁶ J/T. The proton can be thought of as being in one of two states, with $\stackrel{\to }{\mu }$ oriented parallel or antiparallel to the applied magnetic field. Work must be clone to flip the proton from the low-energy state to the high-energy state, as Figure 20.76 shows.

Figure 20.76

Problems 86-88.

An important consideration is that the ret magnet field of any nucleus, except for that of hydrogen (which has only a proton), consists of contributions from both protons and neutrons. If a nucleus has an even number of protons and neutrons, they pair in such a way that half of the protons have spins in one orientation and half have spins in the other orientation. Thus the net magnetic moment of the nucleus is zero. Only nuclei with a net magnetic moment are candidates for MRI. Hydrogen is the atom that is most commonly imaged.

86. If a proton is exposed to an external magnetic field of 2 T that has a direction perpendicular to the axis of the proton’s spin, what is the torque on the proton?

1. A.    0
2. B.     1.4 × 10⁻²⁶ N · m
3. C.     2.8 × 10⁻²⁶ N · m
4. D.    0.7 × 10⁻²⁶ N · m