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### lecture25a

Course: PHYSICS 222, Spring 2011
School: Iowa Central Community...
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Word Count: 667

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22.2 ConcepTest The ConcepTest electric field in an EM wave traveling northeast oscillates up and down. In what plane does the magnetic field oscillate? Oscillations Oscillations 1) In the north-south plane. In 2) In the up-down plane. In 3) In the NE-SW plane. In 4) In the NW-SE plane. 5) In the east-west plane. ConcepTest 22.2 ConcepTest The electric field in an EM wave traveling northeast oscillates up and...

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Iowa Central Community College - PHYSICS - 222
7) Energy in electromagnetic wavesEnergy density:dU 1B22u== 0E +dV 22 0B = E/cfor e.m. wavefor any e.m. fieldU B2u= == 0E2V 0(U energy, V - volume)Poynting vector:Traveling EM waves transport energy. This energy transport can be describe
Iowa Central Community College - PHYSICS - 222
IV. OpticsNature of light. Spectrum of electromagnetic waves.Wavelength decreases Frequency increases Note: 1 nanometer = 10-9 meterA. Geometric optics1. Wave front and raysrayswave fronts2. Reflectioninnormal tosurfaceout1 21 = 2diffuse r
Iowa Central Community College - PHYSICS - 222
7. Spherical mirror1) Mirror equationCdohhhh &lt; &lt;1 ; ; d0diR = + = + + = 2 diif d i d o R 2 = fif d o d i R 2 = fExample:112+=d0 di R111+=d0 di fR = 1.0m121215. 0===d i R d 0 1.0m 3.0m 3.0md o = 3. 0 mdi =di ?3.0= 0.6m
Iowa Central Community College - PHYSICS - 222
8. Thin lensesThin lenses are those whose thickness is small compared to their radius ofcurvature. They may be either converging or diverging.1) Types of lensesExample: An air bubble in a piece of glasshas a double convex shape (see below).What type
Iowa Central Community College - PHYSICS - 222
e = 1.60 10 19 C ; me = 9.11 10 31 kgF =kk=V1 = V2 = . = VQ1Q2r21= 8.99 10 9 N m 2 / C 24 0 0 = 8.85 10 12 C 2 / N m 2Fnet = F1 + F2 + .F = qEE net = E1 + E 2 + ._ E = d E = E cosdA = EdA dEC eq = C1 + C 2 + .= 4kQencl = Qencl 0Q4 0 r
Iowa Central Community College - PHYSICS - 222
13. Comments about the induced electric field(nonelectrostatic field)For electrostatic field: Edl = 0When a charge goes arounda closed loop work is equalto zeroW =0Electrostatic field is conservativeElectric field lines donot form closed loopsF
Iowa Central Community College - PHYSICS - 222
Two questions:(1) How to find the force, F on the electric charge, q excreted by the field E and/or B?F = qE + qv B(2) How fields E and/or B can be created?Maxwells equationsGausss law for electric fieldElectric charges create electric field: E E
Iowa Central Community College - PHYSICS - 222
Lecture 15Review for Exam 1 (see lectures 1-14)No slide show - problems will be solved on the board
Iowa Central Community College - PHYSICS - 222
Lecture 14 will be presented by Professor Ruslan Prozorovlecture slides can be found athttp:/course.physastro.iastate.edu/phys222/Lectures%20(Prozorov)/Prozorov_14.pdf
Iowa Central Community College - PHYSICS - 222
ConcepTest 20.8a Magnetic Field of a Wire IMagnetic1) direction 1If the currents in these wires have2) direction 2the same magnitude, but opposite3) direction 3directions, what is the direction of4) direction 4the magnetic field at point P?5) th
Iowa Central Community College - PHYSICS - 222
8. Magnetic field of moving charge1) What is the problem with moving charge?2) For v=0 and a=0:(Coulombs law)3) ForqrE=k 2rr1k=4 0v=0 and a=0:()1 v2 c2 ( r r v c)E = kq( r r v c) 3Speed of light:4) ForB=0(c2 =v&lt;c and a=0: 0 qv rB=
Iowa Central Community College - PHYSICS - 222
vdAnNlA5. Magnetic forces on currentF = qv BlN nlAlv d = l v dF = Ftot = Nqvd B= nlAqvd B= nqAvd l B F = Il BnqAvd = I - angle between vd and BdF = Idl BF = IlB sin dF = IdlB sin Example: A straight wire carrying a current is placed i
Iowa Central Community College - PHYSICS - 222
III. Magnetism1. Electromagnetism in the laboratory and around us2. Electromagnetism is simple. (If you know what it is!)It is about:q - electric charges(magnetic charges do not exist)F - electromagnetic forcesE - electric fieldsB - magnetic field
Iowa Central Community College - PHYSICS - 222
Resistors in series and in parallel (review)IR1V1I = I1 = I 2I1R2IV2VII2V = V1 + V2I = I1 + I 2Req = R1 + R2ExampleR1 = 12VR1R2ER2 = 3012VI=== 0.26 AR1 + R1 + r 47V = V1 = V2111=+Req 15 30Req = 10rReq = 15 + 30R2111
Iowa Central Community College - PHYSICS - 222
12. RC circuitsi1) Charging capacitor = iR + vCdqq=R+dtCdqq+=dt RC R RCR(q = Q 1 e t / RCQ = CvC =C)(vC = 1 e t / RCV = i = I 0 e t / RCI0=R)qC2) Discharging capacitordqq+=dt RC Rq = q 0 e t / RC =0 RCvC = V0 e t
Iowa Central Community College - PHYSICS - 222
8. Power in electric circuitsIRVW QVP== IVttW = QVQ=ItV = IR2VP = IV = I R =R[ P] = 1W = 1V A = (1J / C ) (1C / s ) = 1J / s2Example: Two resistors, R1 = 5 , R2 = 10 , are connected in series.The battery has voltage of V = 12 V.a) F
Iowa Central Community College - PHYSICS - 222
6. Capacitance and capacitors6.1 Capacitors+Q+Q-Q+Q-QSymbol:6.2 CapacitanceDefinition:QC=VUnits:[C]= 1 F = 1 C / VV V V+ VC is independent from: Q and V (V is always proportional to Q)C depends on:the geometry of the systemthe dielectri
Iowa Central Community College - PHYSICS - 222
Two questions:(1) How to find the force, F on the electric charge, q excreted by the field E and/or B?F = qE + qv B(2) How fields E and/or B can be created?Maxwells equationsGausss law for electric fieldElectric charges create electric field: E E
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
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Berkeley - EE - 221A
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EE221A Linear System TheoryProblem Set 1Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/4; Due 9/13Problem 1: Fields.(a) Dene addition and multiplication on cfw_0, 1 to form a eld. Show th
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EE221A Linear System TheoryProblem Set 2Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/18; Due 9/27Problem 1: Useful properties of eigenvalues. Let A Rnm , B Rmn and let n m. Observe that
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EE221A Linear System TheoryProblem Set 3Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/27; Due 10/4Problem 1: Dynamical systems, time invariance.Suppose that the output of a system is rep
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EE221A Linear System TheoryProblem Set 4Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2006Issued 10/9; Due 10/18Dear 221A folks: Some problems like the ones below may be included on the midterm on Oct
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EE221A Linear System TheoryProblem Set 5Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 10/23; Due 11/1Problem 1.Suppose A Cnn is such that det(A) = 0. Is det(eA ) = 0? Explain why or why no
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EE221A Linear System TheoryProblem Set 6Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/6; Due 11/15Problem 1: Sti Dierential Equations.In the simulation of several engineering systems we
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EE221A Linear System TheoryProblem Set 7Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/15; Due 11/27Problem 1. Show thatA0c0,b0where A Rnn , b Rn , cT Rn is completely controllable
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EE221A Linear System TheoryProblem Set 8Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/27; Due 12/6Problem 1: State vs. Output Feedback.Consider the plant described by:XywhereA=07
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 9Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 12/4; Due 12/15221A folks: Homework 9 is due at the nal exam. However, if youd like to hand in your hom
Berkeley - EE - 221A
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Berkeley - EE - 221A
EE221A Linear System TheoryFinal ExamProfessor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 201012/14/10, 3-6pmYour answers must be supported by analysis, proof, or counterexample.There are 9 questions: Pleas
Berkeley - EE - 221A
Berkeley - EE - 221A
EE221A Linear System TheoryMidterm TestProfessor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 200710/16/07, 9.30-11.00amYour answers must be supported by analysis, proof, or counterexample.There are 6 questio
Berkeley - EE - 221A
EE221A Linear System Theoryhttp:/inst.eecs.berkeley.edu/ee221a/Course OutlineProfessor C. TomlinDepartment of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyFall 2011Lecture InformationLectures: TuTh 9.30-11, 521 C
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 1Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/1; Due 9/8Problem 1: Functions. Consider f : R3 R3 , dened1f (x) = Ax, A = 00as00110 , x R3
Berkeley - EE - 221A
EE221A Problem Set 1 Solutions - Fall 2011Note: these solutions are somewhat more terse than what we expect you to turn in, though the important thing isthat you communicate the main idea of the solution.Problem 1. Functions. It is a function; matrix m
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 2Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/8; Due 9/16All answers must be justied.Problem 1: Linearity. Are the following maps A linear?(a) A(
Berkeley - EE - 221A
EE221A Problem Set 2 Solutions - Fall 2011Problem 1. Linearity.a) Linear: A(u(t) + v (t) = u(t) + v (t) = A(u(t) + A(v (t)b) Linear:te (u(t ) + v (t )d =A(u(t) + v (t) =0te u(t )d +0te u(t )d0= A(u(t) + A(v (t)c) Linear:2s2A(a1 s + b1 s
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 3Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2010Issued 9/22; Due 9/30Problem 1. Let A : R3 R3 be a linear map. Consider two bases for R3 : E = cfw_e1 , e2 , e
Berkeley - EE - 221A
EE221A Problem Set 3 Solutions - Fall 2011Problem 1.a) A w.r.t. the standard basis is, by inspection,000 4 .022AE = 10b) Now consider the diagram from LN3, p.8. We are dealing with exactly this situation; we have one matrixrepresentation, and tw
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 4Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/30; Due 10/7Problem 1: Existence and uniqueness of solutions to dierential equations.Consider the fo
Berkeley - EE - 221A
EE221A Problem Set 4 Solutions - Fall 2011Problem 1. Existence and uniqueness of solutions to dierential equations.TTCall the rst system f (x, t) = x1 x2and the second one g (x) = x1 x2.a) Construct the Jacobians:D1 f (x, t) =1 et sin (x1 x2 )et
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 5Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 10/18; Due 10/27Problem 1: Dynamical systems, time invariance.Suppose that the output of a system is r
Berkeley - EE - 221A
EE221A Problem Set 5 Solutions - Fall 2011Problem 1. Dynamical systems, time invariance.i) To show that this is a dynamical system we have to identify all the ingredients:First we need a dierential equation of the form x = f (x, u, t): Let x(t) = y (t)