Phys2212_33.1+to+33.4

Phys2212_33.1+to+33.4 - Physics 2212 Electricity and...

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Unformatted text preview: Physics 2212 Electricity and Magnetism Lecture 21 (Knight:33.1-33.4) Electromagnetic Induction Induced Magnetic Dipoles When an unmagnetized ferromagnetic material is placed in an externally applied magnetic field, magnetic domains in the material that are aligned with the field are energetically favored. This causes such aligned domains to grow, and for domains that are nearly aligned to rotate their magnetic moments to match the field direction. The net result is that a magnetic dipole moment is induced in the material, with a new south pole close to the north pole of the external magnet. If, when the field is removed, some fraction of the magnetic dipole moment remains, the material has become a permanent magnet . Hysteresis* Some ferromagnetic materials can be permanently magnetized, and remember their history of magnetization. The hysteresis curve shows the response of a ferromagnetic material to an external applied field. As the external field is applied, the material at first has increased magnetization, but then reaches a limit at (a) and saturates . When the external field drops to zero at (b), the material retains about 60% of its maximum magnetization. Unmagnetized Partially magnetized Saturated Nuclear Magnetism A single proton (like the one in every hydrogen nucleus) has a charge (+ e ) and an intrinsic angular momentum (spin). If we (naively) imagine the protons charge circulating in a loop, it should have a magnetic dipole moment . And indeed it does. In an external B-field: Classically: There will be torques unless is aligned along B or against it. QM: The proton spin has only 2 projections onto B. Aligned: 1 U B = - Anti-aligned: 2 U B = Energy Difference: 2 1 2 U U U B - = In magnetic resonance imaging , this energy difference is used to determine the local ``environment of protons in, say, tissue using strong magnetic fields and high-frequency electromagnetic waves. Magnetic Resonance Imaging As mentioned previously, the behavior of the intrinsic spins and magnetic moments of nuclei in a magnetic field allows the spatial imaging of the positions of specific nuclei, which can produce a high-resolution image of the interior of the human body and other objects. This is called magnetic resonance imaging or MRI. The technique requires a very strong and homogeneous magnetic field. Large solenoids, often superconducting, are used for this purpose. The magnetic fields generated range up to a few tesla. The B-field is swept by auxiliary coils, so that the conditions for resonance are met at successive points in the volume of interest. Question Which magnet configurations will produce this induced magnetization?...
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This note was uploaded on 06/07/2009 for the course PHYSICS 2212 taught by Professor Geist during the Fall '09 term at Georgia Perimeter.

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Phys2212_33.1+to+33.4 - Physics 2212 Electricity and...

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