329sp09notes - ECE 329 Lecture Notes Sp09, Erhan Kudeki 1...

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ECE 329 Lecture Notes — Sp09, Erhan Kudeki 1 Vector felds and Forces Fundamental building blocks of matter, electrons and protons , are electri- cally charged . Interactions between these “charge carriers” are described in terms of electric and magnetic felds , much as gravitational interactions are described in terms of gravitational felds produced by massive bodies. Maxwell’s equations : I S E · d S = Z V ρ ± o dV I S B · d S =0 I C E · d l = - Z S B ∂t · d S I C B · d l = μ o Z S ( J + ± o E ) · d S 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 , while ± o = 1 4 π and μ o = 1 ± o c 2 = 4 π c 2 .) In general, charge carrier interactions and electromagnetic ±eld vari- ations account for all electric and magnetic phenomena observed in nature. We think of electric and magnetic ±elds E and B produced by individual charge carriers permeating all space (with proper time delays). That is, we associate with each space location ( x,y,z ) r , a pair of time-dependent vectors E ( r ,t )=( E x ( r ) ,E y ( r ) z ( r )) and B ( r ) = ( B x ( r ) ,B y ( r ) z ( r )) that we refer to as E and B for brevity (dependence on position r and time t is implied ). Field vectors E and B and electric charge and current densities ρ and J (describing the distribution and motions of charge carriers) satisfy a set of coupled linear constraints known as Maxwell’s equations, shown in the margin. Maxwell’s equations are expressed in terms of closed surface and line integrals of the ±eld quantities enclosing arbitrary volumes V and surfaces S in 3D space — recall MATH 241 and PHYS 212 — or in equivalent di²erential forms (see the margin on the next page). Maxwell’s equations were “discovered” as a consequence of experi- mental and theoretical studies led by 19th century scientists includ- ing Gauss, Ampere, Faraday, and Maxwell. They remain intact as the valid description of electromagnetic ±elds despite the scienti±c upheavals (paradigm shifts) of 20th century: relativity and quan- tum mechanics 1 . Given the charge and current densities ρ and J , Maxwell’s equations can be solved for the ±elds E and B , which, in turn, specify the interaction force exerted on a “test particle” with a charge q , position r , and velocity v ˙ r = d r dt according to Lorentz Force formula Lorentz Force F = q ( E + v × B ) . As such, 1 Quantum mechanics — which you were exposed to in PHYS 214 — teaches us that electro- magnetic felds are quantized and interact with systems oF bound charge carriers (i.e., atoms and molecules) one quantum at a time, each quantum (photon) having a fnite amount oF energy proportional to the Frequency oF feld variations. In quantum electrodynamics, feld strength provides a measure oF likelihood For the detection (i.e., an atomic interaction) oF a feld quantum at a given time and locale — classical concepts oF position and trajectory are not used For feld quanta.

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329sp09notes - ECE 329 Lecture Notes Sp09, Erhan Kudeki 1...

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