物理代写|电磁学代写electromagnetism代考|ELEC3104

物理代写|电磁学代写electromagnetism代考|Paramagnetism

Paramagnetic materials are characterized by a small positive magnetic susceptibility $0<\chi \ll 1$ that is due to the existence of the permanent magnetic moments of atoms or ions. The dipole moments interact very weakly with one another, and hence they are randomly oriented when there is no external magnetic field. On the other hand, atomic magnetic moments of the paramagnetic line up with the field when an external magnetic field is present. The alignment process, however, is opposed by the thermal motion, which tends to randomize the magnetic moment orientations.

It was found experimentally by Pierre Curie and others that, under a wide range of conditions, the magnetization of a paramagnetic is proportional to the applied magnetic field $B_0$ and inversely proportional to the temperature $T$ (in Kelvin):
$$M=C \frac{B_0}{T}$$
Equation (8.51) is known as Curie’s law, and the constant $C$ is called Curie’s constant. The law implies that when $B_0=0$, the magnetization is zero, corresponding to a random orientation of magnetic moments. With increasing the ratio of the magnetic field to temperature, the magnetization approaches a maximum value, which corresponds to the complete alignment of its moments, and Eq. (8.51) becomes invalid.

When the temperature of a ferromagnetic substance is greater or equal to the critical Curie temperature, $T_C$, the substance loses its residual magnetization and becomes paramagnetic. Below $T_C$, the magnetic moments are aligned and the substance is ferromagnetic. For $T>T_C$, the thermal fluctuations are high such that they cause a random orientation of the magnetic moments, and the substance becomes paramagnetic, as shown in Fig. 8.6.

物理代写|电磁学代写electromagnetism代考|Diamagnetism

When an external magnetic field $\mathbf{B}_0$ is applied, a weak magnetic moment is induced opposite to the applied field direction, and a magnet only weakly repels the diamagnetic substances. Usually, the ferromagnetic and paramagnetic effects are much more significant than diamagnetic effects in all materials. Therefore, those effects are dominant only when the ferromagnetic and paramagnetic effects do not exist. To understand the diamagnetism, we may consider a classical model of two atomic electrons orbiting around the nucleus with the same speed in opposite directions. The electrons continue their circular orbits around the nucleus because of the attractive electrostatic force exerted by the positive charge of the nucleus. Since the magnetic moments of the two electrons are equal in magnitude but have opposite directions, their net magnetic moment in the atom is zero. However, when an external magnetic field is applied, it exerts an additional force on the electrons, $q \mathbf{v} \times \mathbf{B}$. That magnetic force combines with the electrostatic force increasing the orbital motion linear speed of the electron with a magnetic moment opposite to the field and in a decrease of that speed when the magnetic moment of the electron is parallel to the field. Therefore, the two magnetic moments of the electrons no longer cancel, and the substance gains a net magnetic moment opposite of the applied field.

As we mentioned, the superconductor is a material with zero electrical resistance below some critical temperature. There exist some types of superconductors that exhibit perfect diamagnetism in the superconducting state. Hence, the applied magnetic field is excluded by the superconductor such that the field is zero in its interior, known as the Meissner effect. When a permanent magnet is nearby a superconductor, they repel one another.

电磁学代考

物理代写|电磁学代写electromagnetism代考|Diamagnetism

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