Chapter 27, Problem 27.76P

Quark Model of the Neutron. The neutron is a particle with zero charge. Nonetheless, it has a nonzero magnetic moment with z-component 9.66 × 10⁻²⁷A • m². This can be explained by the internal structure of the neutron. A substantial body of evidence indicates that a neutron is composed of three fundamental particles called quarks: an "up" (u) quark, of charge +2e/3, and two "down” (d) quarks, each of charge -e/3. The combination of the three quarks produces a net charge of $\frac{2}{3}\text{e - }\frac{1}{3}\text{e - }\frac{1}{3}\text{e }=0$. If the quarks are in motion, they can produce a nonzero magnetic moment. As a very simple model, suppose the u quark moves in a counterclockwise circular path and the d quarks move in a clockwise circular path, all of radius r and all with the same speed υ (Fig. P27.76). (a) Determine the current due to the circulation of the u quark, (b) Determine the magnitude of the magnetic moment due to the circulating u quark, (c) Determine the magnitude of the magnetic moment of the three-quark system. (Be careful to use the correct magnetic moment directions.) (d) With what speed ʋ must the quarks move if this model is to reproduce the magnetic moment of the neutron? Use r = 1.20 × 10⁻¹⁵ m (the radius of the neutron) for the radius of the orbits.

Figure P27.76