General Physics II
General Physics II PHY 114
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This 38 page Class Notes was uploaded by Miss Lucienne Hamill on Wednesday October 28, 2015. The Class Notes belongs to PHY 114 at Wake Forest University taught by Kamil Ucer in Fall. Since its upload, it has received 62 views. For similar materials see /class/230729/phy-114-wake-forest-university in Physics 2 at Wake Forest University.
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Date Created: 10/28/15
Inductance I SelfInductance I RL Circuits Energy in a Magnetic Field Mutual Inductance I Oscillations in an LC Circuit SelfInductance When the switch is closed the battery source emf starts pushing electrons around the circuit The current starts to rise creating an increasing magnetic flux through the circuit This increasing flux creates an induced emf in the circuit The induced emf will create a flux to oppose the increasing flux The direction of this induced emf will be opposite the source emf This results in a gradual increase in the current rather than an instantaneous one The induced emf is called the selfinduced emf or back emf Current in a Coil I l39fl39l z 395 l l 39 rm 139 llf39l39quot39 i law tilllr 5m 1 lib fil39it l39t uning if HIEr i39t usi Hg When changes an emf is induced in the coil lf is increasing and therefore increasing the flux through the coil then the induced emf will set up a magnetic field to oppose the increase in the magnetic flux in the direction shown lf is decreasing then the induced emf will set up a magnetic field to oppose the decrease in the magnetic flux SelfInductance Inductance of a Solenoid RL Circuits I Inductors are circuit elements with large self induc on A circuit with an inductor will generate some backemf in response to a changing current I This backemf will act to keep the current the way it used to be I Such a circuit will act sluggish in its response RL Circuit Analysis When 82 is at a When 82 is at b IRL O d t dt 5 R Concept Question When the switch is closed the current through the circuit exponentially approaches a value I 9 R If we repeat this experiment with an inductor having twice the number of turns per unit length the time it takes for the current to reach a value ofl2 1 increases 2 decreases 3 is the same Energy in a Magnetic Field d The ener stored in the inductor 6 IR L 0 9y I Battery Inductor Power Power Resistor Power 2 For energy density L 0quot A consider a solenoid Inductance of a Coaxial Cable 17 b q ZIBdAZJEWZMIi 011111 2 B a 2727 I 27r a 27r a Mutual Inductance A change in the current of one circuit can induce an emf in a nearby circuit Wireless Battery Charger Inil 1h15t A 301M l hmu39llczfl a LC Oscillators Provide a transfer of energy between the capacitor and the inductor Analogous to a springblock system The Oscillation Cycle Assume the capacitor is fully charged and thus has some stored energy When the switch is closed the charges on the capacitor leave the plates and move in the circuit setting up a current This current starts to discharge the capacitor and reduce its stored energy 0 392 lllll The Oscillation Cycle At the same time the current increases the stored energy in the magnetic field of the inductor When the capacitor is fully discharged it stores no energy but the current reaches a maximum and all the energy is stored in the inductor The Oscillation Cycle The current continues to flow and now starts to charge the capacitor again this time with the opposite polarity When the capacitor becomes fully charged with the opposite polarity the energy is completely stored in the capacitor again The efield sets up the current flow in the opposite direction The Oscillation Cycle Then the cycle completes itself in reverse Charge and Current in LC Circuits At some arbitrary time t Q 0 cos of 1n lX I 0 sin or Imax sin of ln x Natural frequency of oscillation Energy in LC Circuits 2 I max 2 sm 0t 0 v 7 U UC UL 2311 COS 0t 7 2 Qmax 2C 2 Oscillations in an LC Circuit a l l r 9 f 22l HZ 3 27 27rLC 27r281gtlt10 9x104 i 8 7 120 r39 b Qmaxz and maX I 00 1113K 1113K 275 me 679 gtlt 10 4A 9 PF 0 Qt and t Q 0 cow 2 108x10 10C r 1113K I 2 1 sinml 2 679gtlt10 4A sin 27rgtlt1061 1113K 5281 11111 0 v2 d U U648x10 J RLC Circuits Damped Oscillations RLC Circuit A more realistic circuit The resistor represents the losses in the system Can be oscillatory but the amplitude decreases For Next Class I Reading Assignment Chapter 33 Alternating Current Circuits WebAssign Assignment 1O Interference of Light Waves I Conditions for interference I Young s double slit experiment I Intensity distribution of the interference pattern I Phasor representation I Reflection and change of phase I Interference in thin films Conditions for Interference I If two waves have a definite phase relationship then they are coherent I OthenNise they are incoherent ex two light bulbs I For Interference I The sources must be coherent I The sources should be monochromatic Young s DoubleSlit Experiment 53 1 I39CC Lgtgtd 6 dsin 6 ml Constructive interference yb ght 7m 1L Concept Question An interference pattern is formed on a screen by shining a planar wave on a double slit arrangement left If we cover one slit with a glass plate right the phases of the two emerging waves will be different because the wavelength is shorter in glass than in air If the phase difference is 180 how is the interference pattern shown left altered 1 The pattern vanishes dome 51 mmm 2 The bright spots lie plsu mrvmve planm wave ll Closer together 3 The bright spots are farther apart 4 There are no changes 5 Bright and dark spots are interchanged Intensity Distribution of the Interference Pattern If 5 1 then zl zz z dsm6 i 27 A i EP E0 sin 01 sinat EP 2 2E0 cos sin 01 g 2 2 Intensity Distribution of the Interference Pattern Interference depends on the relative phase of the two waves It also depends on the path difference between them The resultant intensity at a point is proportional to the square of the resultant electric field at that point IoCE1E22 not gt 1 sin 0 Multiple Slit Patterns 1 l A I J39 I 39 u JLLKLVL3 quot 39 r39 3 xilix ryik r h 139 II ll 339 t u I V39VI HIM IJ u J LMJ Lj IV r quot 1 r m I II II 39 m quotI In a r I urr L39WJI IL39M39L 39 39 l I I l u wnnJ M ber Change of Phase in Reflection Vi C Wil 1g screen The positions of the fringes R6211 quot are reversed compared to source Young s experiment v I I 1 L S An EM wave undergoes a phase change of 180 upon reflection from a medium that has a higher index of refraction than the one in which it is traveling String Analogy 1806 Phase Change u plhusn rhzmgu lnr iulvm Wu ant39t lt39t l mm R1 39dsunorl 7 String analogy g1 H 1 1 1 mppmt Interference in Thin Films 180D phase N0 phase c hauge that 1946 1 o A wave traveling from a medium of index of refraction of n1 towards a medium with index of refraction of n2 undergoes a 180 phase change upon reflection if n2 gt n1 and no phase change if n2 lt n1 The wavelength of light 1 in a medium with index of refraction n is given by in Ln For constructive interference m O 1 2 For destructive interference Concept Question Two identical slides in air are illuminated with monochromatic light The slides are exactly parallel and the top slide is moving slowly upward What do you see in top view all black all bright fringes moving apart sequentially all black then all bright none of the above J lPOONA Newton s Rings centre is dark because efrt phase change during reflection at gins2 plate For destructive r z mlR n interference For constructive r z m12 ARn Interference Nonreflective Coatings SH phase tihnngr 2 1M 31 me Change Example 7 550 nm no reflection Since both paths have the same phase change at the interfaces take only the path differences into account For destructive interference i 550nm quot 4n 4145 94814111 Concept Question Monochromatic light shines on a pair of identical glass microscope slides that form a very narrow wedge The top surface of the upper slide and the bottom surface of the lower slide have special coatings on them so that they reflect no light The inner two surfaces A and B have nonzero reflectivities A top view of the slides looks like Jlllllllllllllllm1 I l l L l I Irl39azv 539 u I I l l N 393 edge edge
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