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Unformatted text preview: ECE 329 Lecture Notes — Summer 09, Erhan Kudeki Copyright c 2009 Reserved — no parts of this set of lecture notes (Lects. 139) may be re produced without permission from the author. 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 2 1 1 2 y – Consequently we associate with each location of space having Carte sian coordinates ( x, y, z ) ≡ r a pair of timedependent 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 Timevarying 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 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 = ∇× 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 Gaussiancgs 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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This note was uploaded on 09/22/2011 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Kim

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