The exchange coupling mentioned in Module 32-8 as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of 10 nm away, along the dipole axis, from an atom with magnetic dipole moment 1.5 * 10-23 J/T (cobalt), and (b) the minimum energy required to turn a second identical dipole end for end in this field. (c) By comparing the latter with the mean translational kinetic energy of 0.040 eV, what can you conclude?

} M/Mmax 1.0 0.75 Curie's law 0.50 0.25 Approximately linear 1.0 2.0 Quantum theory 3.0 4.0 Bext/T (T/K) • 1.30 K • 2.00 K • 3.00 K • 4.21 K A magnetization curve for potassium chromium sulfate, a paramagnetic salt. The ratio of magnetization M of the salt to the maximum possible magnetization Mmax is plotted versus the ratio of the applied magnetic field magnitude Bext to the temperature T. Curie's law fits the data at the left; quantum theory fits all the data. Based on measurements by W. E. Henry. Consider a solid containing N atoms per unit volume, each atom having a magnetic dipole moment μ. Suppose the direction of μ can be only parallel or antiparallel to an externally applied magnetic field B (this will be the case if μ is due to the spin of a single electron). According to statistical mechanics, the probability of an atom being in a state with energy U is proportional to e-U/kT, where T is the temperature and k is Boltzmann's constant. Thus, because energy U is -μB, the…

Two magnetic systems in thermal contact Consider two isolated systems of noninteracting spins with NA = 4 and NB = 16. Their initial energies are EA = -2µB %3D %3D and Eb= -2µB. What is the most probable macrostate for the composite system?

A particle of mass "M" and charge "+Q" Travels at a velocity "V" in a plane perpendicular to a Magnetic Field of magnitude "B" as shown in the Picture. The particle will experience motion on a circular path. OB 20