# Exam1Review - ECE 329 Exam 1 review TIME Sept 25 2008 7...

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ECE 329 Exam 1 review Fall 2008 TIME: Sept. 25, 2008, 7 - 8:15 pm LOCATION: Section X: CA 112 — Chemistry Annex (Other sections in SIEBEL 140) You will be allowed to bring one 8 1 2 × 11 inch sheet of notes (both sides) to the exam. Calculators are not allowed. Chapter 1 All electric and magnetic phenomena in nature can be attributed to the existence of electrical charge and charged particle motions. In classical descriptions, charge carriers having charge q and mass m are treated as “point particles" (or “test charges") which obey Newton’s 2nd law of motion ( F = m d v /dt ). In the presence of an electric ﬁeld E and magnetic ﬁeld B (which are related to distant charge carriers as described by Maxwell’s equations), such a point particle will not aFect the ﬁelds in its vicinity, yet it will experience a force F (and thus an acceleration) as it moves with a velocity v through the ﬁelds as described by the Lorentz force law : F = q ( E + v × B ) . Here, F , E , B and v are all vector ﬁelds which can be expressed in Cartesian coordinates in terms of mutually orthogonal unit vectors ˆ x , ˆ y and ˆ z . Principle of superposition. Dot product. Cross product. Right hand rule . Charge carriers generate E . The E generated by a stationary point charge having charge of Q [C] is radially symmetric around Q and decreases inversely as the square of the distance from the charge ( Coulomb’s Law: E = Q/ (4 π± 0 r 2 ) ˆ r [V/m]), where ± 0 is the permittivity of free space . The electric ﬁeld due to a positive charge Q is directed radially outward, while that of a negative charge is directed inward. The E ﬁeld arising from a distribution of multiple stationary point charges or extended line, surface, or volume charges can be found using Coulomb’s Law in superposition for each source (or diFerential charge element). ±or symmetric charge distributions, using Gauss’ Law for E is often a more e²cient approach for ﬁnding E (see Ch. 2 below). Either approach yields the following: An inﬁnite charge distribution of uniform density ρ L [C/m] along the ˆ z axis produces E at a distance r [m] given by E = ρ L / (2 π± 0 r ) ˆ r [V/m]. An inﬁnite surface charge distribution of uniform density ρ S [C/m 2 ] produces E given by E = ρ S / (2 ± 0 ) ˆn [V/m], in the direction normal to the sheet. A moving charge carrier (i.e., current ) generates B . The (inﬁnitesimal) magnetic ﬁeld generated at a radius r by an inﬁnitesimal current element I dl is along the direction I dl × ˆ r and is given by the Biot-Savart Law: dB = ( μ 0 / 4 πr 2 )( I dl × ˆ r ) [Wb/m 2 ], where μ 0 is the permeability of free space .

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## This note was uploaded on 08/25/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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Exam1Review - ECE 329 Exam 1 review TIME Sept 25 2008 7...

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