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# PHYSICS WITH CALC 2 PHY 2049

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This 41 page Class Notes was uploaded by Mrs. Linda Wiegand on Friday September 18, 2015. The Class Notes belongs to PHY 2049 at University of Florida taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/206781/phy-2049-university-of-florida in Physics 2 at University of Florida.

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Date Created: 09/18/15

Chapter 30 Electromagnetic Induction PHYZEIAB Chaptexl Subjects Induced emf oFaraday s law law 3 of electricity and magnetism oLenz s law oMotional emf Inductance RL circuits Magnetic energy Generators transformers PHY2049 Chapter 30 Magnetic Flux Magnetic ux Electric flux DB 2 d Tmz Paige2i N mZC Surface defined by a Closed surface conducheloop Gaussian surface Units 1 T m2 1 weber 1 Wb ltle B cose if Bis uniform and surface is flat PHY2049 Chapter 30 4 Faraday s Law Law 3 of EampM dgp K Flux through the loop 8 N B le emf of turns of the loop To avoid errors oUse Faraday s law to calculate only the magnitude of emf oUse Lenz s law to find the direction PHY2049 Chapter 30 5 Lenz s Law Same as the negative sign in Faraday s law 9 Lenz s law Direction of induced emf is such that resulting current opposes change in DB Let s examine three ways to change 05 through a coil 9 Change 5 9 Change area of the coil motional emf 9 Change angle 6 of the coil with respect to B motional emf principle of the generator PHY2049 Chapter 30 6 Changing B Q1 Is the induced emf and current clockwise or counterclockwise Clockwise Q2 What does the ammeter read when the magnet is held in place Zero Q3 What happens while the magnet is being pulled back Counterclockwise emf and current Q4 What happens ifthe S pole of the magnet is pushed toward the loop Counterclockwise emf and current PHY2049 Chapter30 B field points into screen Is induced emf clockwise or couterclockwise PHY2049 Chapter 30 Another Example What is the direction of induced emf RHR 3 and Lenz 0b Counterclockwise 0c No emf RHR 2 PHY2049 Chapter 30 9 Motional emf and Energy 398 392 LVB 1X Current i due to emf receives force from B l 42 FZ LB FQIZ39J Force required to pull the loop quot Freq iLB Power work per time required to pull the loop Freq distance 2 LVB2 req time req R Power dissipated in the wire as heat 2 2 3 i2RRM Agrees R R diss PHY2049 Chapter 30 10 Electric Power Generation when Faraday was endeavouring to explain to Gladstone Chancellor of the Exchequer and several others an important new discovery in science Gladstone39s only commentary was but after all what use is itquot Why sirquot replied Faraday there is every probability that you will soon be able to tax itquot W E H Lecky Democracy and Libe1yLongmans Green London 1899 Equot TV J rit PHY2049 Chapter 30 11 PHY2049 Chapter 23 1 Gauss Law Says iEdA2q 80 Total fluX depends only on the amount of enclosed charge not on shape and Size of the GauSSIan surface 9fCIZharges outside have no effecton the total uX aghis does not mean they do not contribute to Remember oOutward E field flux gt O oInward E field flux lt O PHY2049 Chapter 23 Conductors with No Current E is zero everywhere inside Wh Conductors are full of mobile charges Se conduction electrons in a bac ground formed by Immoblle posrtlve Ions fthere were E then the charges must be movrng because of the force FqE This would contradict no currentquot Note even if there is an externally imposed E it cannot go inside All excess charge and induced charge must be on surfaces Why Since E0 everywhere inside qencenclosed by any Gaussian surface is also zero everywhere Insude Nte distribution of surface charge must be such to make E0 everywhere msr e E is always normal to surface on conductor Why E component parallel to surface would cause surface charge to move This would contradict no current Note distribution of surface charge must be such to make E normal PHY2049 Chapter 23 Use Gauss Law to Calculate E Fields Spherica symmetry 9E field vs r inside uniformly charged sphere oCharges on concentric spherical conducting shells Cylindrical symmetry 9E field vs r for line charge 9E field vs r inside uniformly charged cylinder Rectangular symmetry 9E field for charged plane 9E field between conductors eg capacitors PHY2049 Chapter 23 Spherical Symmetry 1 Uniformly Charged Sphere Insulator or conductor oConducting sphere cannot be uniformly charged Inside oBy symmetry E must be radially symmetric o E field has constant mag L to Gaussian surface Gaussian sulface Gauss Law 4 3 i sphere iEdA E47tr2 37 QR3 Q 80 Qr3R3 1 E 4n80r2 4m90 R3 Solve forE Volume marge Outside E 1 Q Q density 47r80 PHY2049 Chapter 23 5 T Spherical Symmetry 2 Concentric Conducting Spherical Shell InSIde conductor 0E must be 0 Must be 0 ciEdA 0 2 80 Gauss Law oCharge can be only on surfaces Q uniformly distributed on inner wall Outside oBy symmetry E must be radially symmetric Gaussian surface sphere o E field has constant mag L to Gaussran surface if dA Emm k Q Points toward shell 80 Gauss Law Q uniformly distributed on outer surface E 294122 n80 r PHY2049 Chapter 23 6 Axial Symmetry 1 Line Charge Infinitey long line uniformly charged QBy symmetry E must be agtltiay symmetric QOn curved surface E eld has constant mag l to Gaussian su ace QThrough top and bottom surfaces no DE L 27 Gaussian surface since E IS Ah 1 55313511 Eh27rr 0 0 80 Gauss Law 1 A 2 linear may Solve for E E 2 80 FHanAu Chapta39ll Axial Symmetry 2 Uniformly Charged Cylinder Infinitely tall cylinder uniformly charged R o By symmetry E must be axially symmetric I 39 oOn curved surface E field has constant mag p i r L to Gaussian surface oThrough top and bottom surfaces no DE since E is 2 WW iE dA Eh27rr 0 0 8 0 1 E p Solve for E 280 3 ll7lllm Gapssian surface density cylindrical l l l i Gauss law l l l PHY2049 Chapter 23 8 Rectangular Symmetry 1 Uniformly Charged Sheet Infinitey wide and tall y oBy symmetry E must be L same on both a y 439 sides r t Gaussian a a r H 7 2 g 39 039 717quot V i de elay t r k V 55EdAEm2Em200 r n W s 80 Gauss law a E E Solve for E n t 0 Parae conducting plates read Section 238 PHY2049 Chapter 23 9 Some Comparisons Sphericay symmetric charge distribution EZLM 4mg r2 Uniformly charged infinitely long ie very long line E 1 A 27750 r Uniformy charged plane PHY2049 Chapter 23 10 Chapter 23 Gauss Law HALL DAY RESNICK WALKER PHY2049 Chapter 23 Conductors with No Current E is zero everywhere inside Why Conductors are full of mobile charges eg conduction electrons in a background formed by immobile positive ions If there were E then the charges must be moving around due to force FqE This would contradict no currentquot Note even if there is an externally imposed E it cannot go inside All excess charge must be on outer surface Why Since EO everywhere inside qenc enclosed by any Gaussian surface is also zero everywhere inside Note distribution of surface charge must be such to make EO everywhere inside E is always normal to surface on conductor Why E component parallel to surface would cause surface charge to move This would contradict no currentquot PHY2049 Chapter 23 2 Spherical Symmetry 1 Uniformly Charged Sphere Insulator or conductor oConducting sphere cannot be uniformly charged Inside oBy symmetry E must be radially symmetric o E field has constant mag L to Gaussian surface Gaussian sulface Gauss Law 4 3 r3 sphere plt w gt Q iE dA E47tr2 3 R3 Q 80 p 4 3 3 7rR3 E M 1 3 4n80r2 47 R3 Solve for E Outside E Z 1 2 Q 47r80 PHY2049 Chapter 23 3 T Spherical Symmetry 2 Concentric Conducting Spherical Shell InSIde conductor 0E must be 0 Must be 0 ciEdA 0 2 80 Gauss Law oCharge can be only on surfaces Q uniformly distributed on inner wall Outside oBy symmetry E must be radially symmetric Gaussian surface sphere o E field has constant mag L to Gaussran surface if dA Emm k Q Points toward shell 80 Gauss Law Q uniformly distributed on outer surface E 294122 n80 r PHY2049 Chapter 23 4 Spherical Symmetry 2 Concentric Conducting Spherical Shell Note Problem 234 on page 614 oIn this problem point charge Q in cavity is not at center This makes the problem harder In particular you do not need to understand explanation given in book for why charge on outer surface is uniform Rigorous explanation in fact requires a tool socalled uniqueness theorem which is beyond introductory physics PHY2049 Chapter 23 Axial Symmetry 1 Line Charge Infinitey long line uniformly charged QBy symmetry E must be agtltiay symmetric QOn curved surface E eld has constant mag l to Gaussian su ace QThrough top and bottom surfaces no DE L 2m Gaussian Since E IS Ah 7 55313511 Eh27rr 0 0 8 0 Gauss Law 1 A E Solve for E FHanAu Chapta39ll 6 Axial Symmetry 2 Uniformly Charged Cylinder Infinitely tall cylinder uniformly charged R o By symmetry E must be axially symmetric 39 39 oOn curved surface E field has constant mag p i r L to Gaussian surface H oThrough top and bottom surfaces no DE since E is 2 WW LE dA Eh27rr 0 0 8 0 1 E p Solve for E 280 l l l i Gauss law l l l Gapssian surface cylindrical PHY2049 Chapter 23 7 Rectangular Symmetry 1 Uniformly Charged Sheet Infinitey wide and tall 9 By symmetry E must be L same on both sides 07rr2 SESEaA E7tr2E7tr2 00 80 Gauss law E a a Solve for E Constant Parae conducting plates read Section 238 PHY2049 Chapter 23 8 Some Comparisons Sphericay symmetric charge distribution E 1 M 47th0 r2 Uniformly charged infinitely long ie very long line 1 A E 2 27750 r Uniformly charged plane 0 2 no distance dependence PHY2049 Chapter 23 How to calculate Efield if there is no symmetry Numericay integrate deroduced by all charge elements dq Usually easier to numerica ly compute electric potential lfirst and then E Electrical potential is subject of Chapter 24 PHY2049 Chapter 23 10 Chapter 30 Electromagnetic Induction FHYZEIAD Chapman Subjects Induced emf oFaraday s law law 3 of electricity and magnetism o Lenz s law 9 Motional emf Magnetic energy Inductance RL circuits Generators transformers PHY2049 Chapter 30 Faraday and Henry s Discovery z 2 Changing magnetic field produces current in a wire loop 0 Induced current depends on rate of change of B wire resistance 0 Induced emf that drives depends only on the rate of change of B o Direction of emf depends on direction of B whether Bincreases or decreases Magnetic Flux Magnetic UX Electric flux BJ dA Tmz 192412quot NmZC Surface defined by a cosec surface conduc veloop Gaussian surface 1Tm2 1weber 1Wb ltle B cose if Bis uniform and surface is flat Chapter 30 Faraday s Law Law 3 of EampM N d B Flux through the loop em i a of turns of the loop Use Faraday s law to calculate only the magnitude Use Lenz s law to find the direction PHY2049 Chapter 30 Lenz s Law About the negative sign in Faraday s law 9 Lenz s law Direction of induced emf is such that resulting current opposes change in 5 Let s examine three ways to change DB through a coil 0 Change 5 9 Change area of the coil motional emf 9 Change angle 9 of the coil with respect to B motional emf PHY2049 Chapter 30 6 Check Point Changing B Q1 Is the induced emf and current clockwise or counterclockwise Clockwise Q2 What does the ammeter read when the magnet is held in place Zero Q3 What happens while the magnet is being pulled back Counterclockwise emf and current Q4 What happens ifthe S pole of the magnet is pushed toward the loop Counterclockwise emf and current PHY2049 Chapter30 Check Point Changing Area 71M gtV L ezx W Is induced emf clockwise or couterclockwise PHY2049 Chapter 30 Motional emf and Energy 8 LvB Current i due to emf receives force from B 39 1 l2 F iLB Force required to pull the loop F iLB req Power work per time required to pull the loop P F v LVB2 Power dissipated in the wire as heat 2 2 P 12R R Checks R R diss PHY2049 Chapter 30 9 Electric Power Generation when Faraday was endeavouring to explain to Gladstone Chancellor of the Exchequer and several others an important new discovery in science Gladstone39s only commentary was but after all what use is itquot Why sirquot replied Faraday there is every probability that you will soon be able to tax itquot W E H Lecky Democracy and Liben yLondon 1899 5 PHY2049 Chapter 30 10

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