Lecture 15.2 :! Final Exam Review, Part 1

Transcription

1 Lecture 15.2 :! Final Exam Review, Part 1 April 23,

2 Announcements Online Evaluation s should have been sent to you.! Please fill out the evaluation form...it is completely confidential. May 6 is deadline.! Remember that PHY212 and PHY222 (lab) are separate courses!! Final Exam is May 4th (a Monday) from 3-5pm in Watson Theatre.! Watson Hall To ComArt, Lampe Athletics Complex, South Campus, Skytop Offices, Bernice Wright Nursery School See other side for South Campus M T. OL YM PU S D E O R ST OM R. A CO E LL GE PL. M S E DR I V E S TA A R SH A ST OU LL R C R W EE T A E EA ST AD AM S ST RE SO U OU SE A ET To Interstates 81, 690, and 90 (NYS Thruway). CR TH 2 ND AR T S TR EE T

3 Course Overview { Electric Charge and Forces (Ch. 25)! The Electric Field (Ch. 26)! Exam #1 Gauss s Law (Ch. 27)! The Electric Potential (Ch. 28)! { Potential and Field (Ch. 29)! Exam #2 Current and Resistance (Ch. 30)! Fundamentals of Circuits (Ch. 31)! Exam #3 { The Magnetic Field (Ch. 32)! Electromagnetic Induction (Ch. 33)! Electromagnetic Fields and Waves (Ch. 34) 3

4 Motivation What are the overall goals for this course? Maxwell s Equations Magnets? 1.To develop a basic understanding of the laws of electromagnetism.! 2.To develop the ability to apply these new concepts to physical situations.! 3.To develop an appreciation for the role that electromagnetism plays both in our modern society and in the universe.! 4

5 pacitance(of(the(field(cage( Motivation MicroBooNE Installation: June 2014 e field cage inside of the cryostat behaves like a network of capacitors. It can be arged up and hold an electric charge and hence store energy. The capacitance of an ect is only a function of the physical dimensions and geometry of the conductors and permittivity of the dielectric. can be seen in Figure!2 the cryostat-field cage geometry is rather complicated and nce it is difficult to easily calculate or measure the capacitance. In the course of 14 ure! 1! TPC resistive divider boards. The resistors are Slim-Mox (Ohmite) M FE ; Thick Film, 1G, 1%, 1.5W, 10kV, epoxy coated estigating a potential high voltage discharge condition, it was necessary to find a way determine the capacitance. The components that are easily identified are : 5

6 Motivation Dirty lightning in Chile s Calbuco volcano yesterday! 6

7 Model of Electric Charge Electric Charge is a property of matter. e = fundamental unit of electric charge (not defined yet).! Protons are TIGHTLY bound in nucleus they don t go anywhere.! Electrons are more loosely bound.! Object Charge (q) = N p e - N e e = (N p -N e )e 7

8 Coulomb s Law Magnitude of Electric Force K = electrostatic constant ( N m 2 /C 2 )! q 1 = charge on particle 1! q 2 = charge on particle 2! r = distance between particle 1 and 2 8

9 Electric Field source charge creates the electric field, E! probe charge q within this electric field experiences a force, F.! Electric field exists everywhere in space, regardless of whether there is a probe charge or not.! Units: N/C Electric Field of Point Charge 9

10 Electric Potential Energy We derived the potential energy shared by two point charges by calculating the Work done by one charge on the other. Looks like Coulomb s Law, but it s different! 10

11 Electric Potential We introduced Electric Field to indicate an electric charge s alteration of space. Now we need a concept of potential energy at all points in space due to a source charge. Electric Potential: V U q+sources q 1 volt = 1 V 1 J/C Alessandro Volta 1.5 V Battery 11

12 Example Problem 12

13 Symmetry and Electric Fields 13

14 Electric Flux and Gauss s Law Electric Flux = The amount of electric field passing through a surface. Gauss s Law 14

15 Gauss s Law This image shows a hollow cavity within a neutral conductor in equilibrium. A point charge Q is placed inside the cavity. What is the net electric flux through the closed surface that surrounds the conductor? 15

16 Gauss s Law Example: Inside/Outside a sphere of charge 16

17 Electric Potential and Field U = i f F ds V U q+sources q 17 V = E = f i V E ds

18 Capacitors V C = Ed Capacitance is a geometric property! C Q V C 1 farad = 1 F 1 C/V C Q V C = 0 A d For a parallelplate capacitor Energy Stored in a Capacitor. U C = Q2 2C = 1 2 C( V C) 2 18

19 Capacitors in Circuits 19

20 Current and Current Density Current was known long before electrons were discovered, so conventional definition of current is in terms of Charge: I dq dt 1 ampere = 1 A 1 coulomb per second = 1 C/s We define current density (J) to arrive at a property intrinsic to a material, and not specific to the cross-sectional Area of a conductor. J I A = n ee d 20

21 Resistance and Ohm s Law Resistance (R) characterizes ability of current to flow through specific piece of conductor with a specific geometry. R = L A 1 ohm = 1 # 1 Volt/Ampere = 1 V/A Ohm s Law: Establishing a potential difference ΔV across the ends of a conductor with resistance R causes a current I through the current. I = V R 21

22 Analyzing Circuits Kirchoff s Junction Law: V loop = ( V ) i =0 I in = I out Kirchoff s Loop Law: 22

23 Energy and Power in Circuits Power dissipated by a resistor Equivalent Resistance for Resistors in Series: R eq = R 1 + R R N Equivalent Resistance for Resistors in Parallel: 1 = R eq R 1 R 2 R N 23

24 Example Problem 24

25 Reminders! Last recitation of the semester tomorrow (Friday), will review selected problems from the textbook. Not an exhaustive selection, so please don t think these are the only topics for you to review.! Final Exam is May 4th from 3-5pm in Watson Theatre. 25