ece305_magnetic_mats

ece305_magnetic_mats - Magnetostatics of Materials ECE305:...

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Unformatted text preview: Magnetostatics of Materials ECE305: Week 10 Andrew Baczewski Michigan State University Department of Electrical and Computer Engineering November 14th, 2007 Andrew Baczewski Magnetostatics of Materials Last Lecture... Vector Magnetic Potential 1 The vector magnetic potential, ~ A ( ~ r ), is a potential function used to describe the magnetic field in a given region as an integral over sources (in this case, current densities). ~ A ( ~ r ) = 4 Z V ~ J ( ~ r ) ~ r- ~ r dV (1) 2 From this potential function, we can calculate the magnetic field through its curl: ~ B ( ~ r ) = ~ x ~ A ( ~ r ) (2) 3 Always remember to integrate over the primed/source coordinates. The unprimed coordinates represent the observation point, which will remain fixed as you integrate. Andrew Baczewski Magnetostatics of Materials Last Lecture... Magnetic Source Law 1 There are no point sources of magnetic charge (monopoles). The most elementary source of the magnetic field is a dipole. 2 We can state this as either an integral or differential equation: ~ ~ B = 0 (3) I S ~ B ndS = 0 (4) 3 In electrostatics, lines of electric flux terminate on point charges (singularities in the field). There are no such point charges for the magnetic field, so lines of magnetic flux terminate on themselves (i.e. magnetic flux flows in closed loops). 4 These equations set strong constraints on the behavior of the magnetic field, and you will see them later when deriving the wave equation....
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This note was uploaded on 01/17/2011 for the course ECE 305 taught by Professor Staff during the Summer '08 term at Michigan State University.

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ece305_magnetic_mats - Magnetostatics of Materials ECE305:...

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