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329lect01 - ECE 329 Lecture Notes Summer 09 Erhan Kudeki 1...

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ECE 329 Lecture Notes — Summer 09, Erhan Kudeki 1 Vector fields and Lorentz force Interactions between charged particles can be described and modeled 1 in terms of electric and magnetic fields just like gravity can be formulated in terms of gravitational fields of massive bodies. In general, charge carrier dynamics and electromagnetic field vari- ations 2 account for all electric and magnetic phenomena observed in nature and engineering applications. Electric and magnetic fields E and B generated by charge carriers — electrons and protons at microscopic scales — permeate all space with proper time delays, and combine additively. 2 1 1 2 x 2 1 1 2 y Consequently we associate with each location of space having Carte- sian coordinates ( x, y, z ) r a pair of time-dependent vectors E ( r , t ) = ( E x ( r , t ) , E y ( r , t ) , E z ( r , t )) 1 Interactions can also be formulated in terms of past locations (i.e., trajectories) of charge carriers. Unless the charge carriers are stationary — i.e., their past and present locations are the same — this formulation becomes impractically complicated compared to field based descriptions. 2 Time-varying fields can exist even in the absence of charge carriers as we will find out in this course — light propagation in vacuum is a familiar example of this. 1
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and B ( r , t ) = ( B x ( r , t ) , B y ( r , t ) , B z ( r , t )) that we refer to as E and B for brevity (dependence on position r and time t is implied ). Maxwell’s equations : · E = ρ o · B = 0 ∇ × E = - B t ∇ × B = μ o J + μ o o E t . such that F = q ( E + v × B ) , with μ o 4 π × 10 - 7 H m , and o = 1 μ o c 2 1 36 π × 10 9 F m , in mksA units, where c = 1 μ o o 3 × 10 8 m s is the speed of light in free space. (In Gaussian-cgs units B c is used in place of B above, while o = 1 4 π and μ o = 1 o c 2 = 4 π c 2 .) Field vectors E and B and electric charge and current densities ρ and J — describing the distribution and motions of charge carriers — are related by (i.e., satisfy) a coupled set of linear constraints known as Maxwell’s equations, shown in the margin. Maxwell’s equations are expressed in terms of divergence and curl of field vectors — recall MATH 241 — or, equivalently, in terms of closed surface and line integrals of the fields enclosing arbitrary volumes V and surfaces S in 3D space, as you have first seen in PHYS 212.
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