329fa08notes - ECE 329 Lecture Notes Fall08 Erhan Kudeki 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 329 Lecture Notes — Fall08, Erhan Kudeki 1 Vector felds and Forces Fundamental building blocks of matter, electrons and protons , are elec- trically charged and exert attractive/repulsive forces upon one another (depending on algebraic signs of the charges involved) — in general, all electric and magnetic phenomena observed in nature can be attributed to the existence and motions of electric charge carriers . In classical descriptions, individual charge carriers (e.g., electrons and pro- tons) are modeled as point particles having: – mass m and charge q , conserved and quantized as integer multiples of proton charge e 1 . 6 × 10 - 19 C (coulombs) in all reference frames, well de±ned locations r =( x,y,z ) , and trajectories 1 r = r ( t ) obeying Newton’s 2nd Law of motion , m ¨ r = F , where ¨ r d 2 r dt 2 denotes a particle acceleration and F the force applied on the particle. Electric and magnetic components of force F on a point charge q are pro- portional to q and expressed in terms of an electric Feld E and magnetic Feld B produced by distant charge carriers — speci±cally Lorentz force F = q ( E + v × B ) , which is known as Lorentz force , where v ˙ r = d r dt is the velocity vector of charge q , – electric Feld E is by defnition the vector force per unit charge when q is stationary (i.e., v =0 ), Maxwell’s eqns in diferential Form (used starting in Chpt 3): ∇· E = ρ ± o B ∇× E = - B ∂t B = μ o J + μ o ± o E with, in MKSA units, μ o 4 π × 10 - 7 H m , and ± o 1 μ o c 2 , where c 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 .) – magnetic Feld B describes by defnition an additional force per unit charge which is experienced when q is in motion with a ±nite v within the frame of reference where E is measured (typically called the “lab frame”). E and B are related to and produced by distant charge carriers and their motions as described by Maxwell’s equations (see margin), which e²ectively reduce, in static cases (i.e., non-time varying cases), to Coulomb ’s and Biot-Savart laws (to be reviewed shortly). In the MKSA system where q is measured in coulombs (C) units, E is in Nt/C=V/m and B in V.s/m 2 =Wb/m 2 =T, where Nt, V, Wb, and T are abbreviations for newtons, volts, webers, and teslas, respectively. Particle positions r , velocities ˙ r , and accelerations ¨ r , as well as forces F and ±elds E and B are described in terms of 3D vectors . In Cartesian coordinates such vectors and vector functions are expressed in terms of mutually orthogonal unit vectors ˆ x , ˆ y , and ˆ z as in r = x ˆ x + y ˆ y + z ˆ z ( ) and E = E x ˆ x + E y ˆ y + E z ˆ z ( E x ,E y z ) etc., where 1 Quantum models (as opposed to classical) describe the likelihood of detection of charge carriers at locations r (as opposed to their speciFc trajectories), depending on applied force Felds F and related potentials — quantum approach remedies the shortcomings of classical models based on Newton’s dynamics at atomic and smaller scales.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 87

329fa08notes - ECE 329 Lecture Notes Fall08 Erhan Kudeki 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online