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lec23 - Scott Hughes Massachusetts Institute of Technology...

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Scott Hughes 10 May 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 23: Magnetic materials 23.1 Magnetic fields and stuff At this stage of 8.022, we have essentially covered all of the material that is typically taught in this course. Congratulations — you now have a solid grounding in all the major concepts of electricity and magnetism! There remains one major, important subject which we have not discussed in depth: the interaction of magnetic fields and materials. At this point, we don’t even have a really good understanding of a bar magnet works — an unsatisfying state of affairs, given that this is the way in which we normally encounter magnetism in the real world! One reason we have avoided covering this subject is that it is not really possible to discuss it properly within getting into a detailed discussion of the quantum mechanical description of matter. The way in which matter responds to magnetic fields is totally determined by the quantum mechanical nature of their molecular structure, particularly their electrons. Nonetheless, we can make significant headway in understanding the interaction of mag- netic fields and materials by combining what we have learned so far with a somewhat ap- proximate, qualitative description of how materials respond to magnetic fields. The main concepts we will need are summarized in the following two subsections: 23.1.1 Electron orbitals The electrons in a molecule exist in orbits . Very roughly , we can picture an orbit as a simple loop of current: A loop of current like this of course tends to generate its own magnetic field. In most materials, there are an enormous number of orbits like this, randomly oriented so that they produce no net field. Suppose an external magnetic field is applied to some substance that contains many orbitals like this. The net tendency can be understood in terms of Lenz’s law: the orbits “rearrange” themselves in order to oppose the change in magnetic flux. This tendency for Lenz’s law to work on the microscopic scale ends up opposing the magnetic field from the material . 23.1.2 Intrinsic magnetic moment of the electron One other quantum mechanical property of electrons plays an extremely important role in this discussion: electrons have a built-in, intrinsic magnetic moment. Roughly speaking, 214
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this means that each electron all on its own acts as a source of magnetic field, producing a dipole-type field very similar to that of current loop. Because this field is associated with the electron itself, it does not exhibit the Lenz’s law type behavior of the field that we see from the orbits. Instead, the most important behavior in this context is the fact that a magnetic moment ~m placed in an external field ~ B feels a torque : ~ N = ~m × ~ B .
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