Lecture_09_2097

# Lecture_09_2097 - Physics 0175 Lecture 9(July 6 2009...

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Physics 0175 Lecture 9 (July 6, 2009) Dielectrics and Capacitors Generalization of Gauss’s Law Electric Current Current Density Resistance and Resistivity Ohm’s Law 1

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Where to Go for Help 1. Your Recitation Section. 2. Office Hours: Lecturer: Prof. Brian R. D’Urso E-Mail: [email protected] Office Hours: Monday and Wednesday, 3:00 – 4:00 pm 315 Allen Hall TAs: Shonali Dhingra, [email protected] Office Hours: Tuesday and Thursday, 8:30 pm – 9:30 pm and Friday, 2:00 pm – 4:00 pm 514 Allen Hall (desk #16) Naufer Nusran, [email protected] Office Hours: Tuesday and Thursday, 3:00 pm – 5:00 pm 514 Allen Hall (desk #7) Sui Chi Woo, [email protected] Office Hours: Tuesday and Thursday, 1:00 pm – 3:00 pm 419 Allen Hall 3. Appointment with Lecturer or any TA. 2
Homework Assignment #3 Reading: Chapters: 25, 26 Problems: See WileyPLUS Homework due Thursday night / Friday morning! 3

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Exam 1 Tuesday, July 7 343 Alumni Hall Topics (Chapters 21-24) Coulomb’s Law Electric Field Gauss’ Law Electric Potential 4
Dielectric Constant and Permittivity Take account of the effects of polarization in a linear dielectric by introducing the dimensionless dielectric constant K: E E 0 = κ For a capacitor carrying charge q: •E 0 = Electric field in the absence of dielectric • E = Electric field with the dielectric present It is also useful to introduce the dielectric permittivity ε : ε 0 = Hence, ε 0 is the permittivity of free space (vacuum). To take the dielectric into account (for example, in the capacitance), replace ε 0 with ε . 1 5

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Halliday, Resnick and Walker: Problem 25-44 In the figure below, how much charge is stored on the parallel-plate capacitors by the 12.0 V battery? One is filled with air, and the other is filled with a dielectric for which κ = 3.00; both capacitors have a plate area of 5.00 × 10 -3 m 2 and a plate separation of 2.00 mm. 6
Polarization of a Dielectric q’ = polarization surface charge (bound charge) Polarization originates in electric dipole moments at the molecular level: • permanent dipoles partially oriented by the electric field opposed by random thermal motion • induced electric dipoles 7

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Gauss’s Law Reformulated for Dielectrics When treating dielectrics, it is convenient to write Gauss’s Law in a form that does not explicitly include the polarization charge q’. Apply Gauss’s Law to the “Gaussian pillbox” to obtain: = = = A q E q A E d 0 0 0 0 0 ε A E r r κ q q q = 0 E E = = q d 0 A E r r No dielectric: With dielectric: = = = A q q E q q EA d 0 0 0 A E r r Use to obtain 8
Parallel Plate Capacitor: Effect of a Dielectric κ q q q = Note that the result below, copied from the preceding slide, can be solved for the polarization charge. = 1 1 q q 9

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Consider an isolated capacitor, capacitance C 0 , carrying charge q. The stored energy is .
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