329examreview - ECE 329 Final Exam review Spring 2009 TIME...

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ECE 329 Final Exam review Spring 2009 TIME: Monday, May 11, 7-10 PM You will be allowed to bring one new 3 × 5 inch index card of notes (both sides) to the exam, along with the three cards from the previous midterms. Solutions to previous exams and homeworks may not be written on the card. Calculators are not allowed, but you should bring a compass and a straight ruler to use with Smith Charts. 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 affect 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 differential charge element). For symmetric charge distributions, using Gauss’ Law for E is often a more efficient approach for finding E . Gauss’s Law for E in integral form states that the flux of the electric displacement vector D 0 E [C/m 2 ] through a closed surface S equals the charge enclosed inside a volume V bounded by S . By considering a single point charge inside a spherical Gaussian surface, Coulomb’s Law can be derived from Gauss’s Law for E . When using Gauss’ Law to derive E generated by symmetric charge distributions, construct the Gaussian surface to exploit the symmetry and simplify the evaluation of the surface integration. 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].
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