Lect22 - Physics 212 Lecture 22 Physics 212 Lecture 21,...

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Unformatted text preview: Physics 212 Lecture 22 Physics 212 Lecture 21, Slide 1 Music Who is the Artist? A) B) C) D) E) Billy Joel Boz Scaggs Mark Knopfler Mark Knopfler Donald Fagen Donald Fagen Michael McDonald 1976 Video 2004 Great band.. Good blues 1994 Theme of the week? Bay Area Memories.. Slim’s? Bay Slim p.s. I had another good idea, but I forgot to load it on my ipod last night!! p.s. ipod Physics 212 Lecture 21, Slide 2 Your Comments “You lied about electric potential being the hardest part of the You course! Please go through everything in detail because this is a course! confusing prelecture and I don't understand most of it at all. confusing prelecture “I feel like I don't understand this well enough to even feel ask questions about it. Little bit shell-shocked right now.” ask “THAT WAS AWESOME!! DISCUSS ALL PLEASE!!!! “ “wave equations, this is my first time seeing them wave (aside from oscillators)” (aside “more about the graphs of waves. they are confusing” “Do we have to know how to solve differential Do equations or will the problems be limited to these specific types of examples?” specific ALL TRUE We will try to We make clear, at least the BIG IDEAS BIG We will discuss waves We You will not have to solve new diff eqns eqns 40 30 20 “How can light act as both a wave and a particle?” PHYS 214 Ø PHYS 419 PHYS 10 0 05 Confused Confident Physics 212 Lecture 21, Slide 3 What We Knew Before Prelecture 22 06 Physics 212 Lecture 21, Slide 4 After Prelecture 21: Modify Ampere’s Law After Prelecture σ Q E= = ε0 ε0 A Φ = EA = Q ε0 Q = ε 0Φ dQ dΦ = ε0 ≡ ID dt dt 10 Physics 212 Lecture 21, Slide 5 Displacement Current Real Current: Charge Q passes through area A in time t: I= Displacement Current: Electric flux through area A changes in time ID = ε0 08 dQ dt dΦE dt Free space Physics 212 Lecture 21, Slide 6 Calculation Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. S C Ra At time t1, what is the magnetic field B1 at a radius r (point d) in between the plates of the capacitor? ●d I1 r R Q1 • Conceptual and Strategic Analysis • Charge Q1 creates electric field between the plates of C • Charge Q1 changing in time gives rise to a changing electric flux between the plates • Changing electric flux gives rise to a displacement current ID in between the plates • Apply (modified) Ampere’s law using ID to determine B 10 Physics 212 Lecture 21, Slide 7 Calculation S Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. c● ●d r I1 C Ra r R Q1 BB Compare the magnitudes of the B fields at points c and d. (A) Bc < Bd (B) Bc = Bd What is the difference? Apply (modified) Ampere’s Law point c: I(enclosed) = I1 11 r X (C) Bc > Bd r R point d: ID(enclosed) < I1 Physics 212 Lecture 21, Slide 8 Calculation Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. ●d I1 E S C Ra r σ R E=ε 0 Q1 BB What is the magnitude of the electric field between the plates? Q Q1 Q Q1π R 2 (A) E = (B) E = (C) E = 1 (D) E = 1 ε0 π R 2ε 0 r ε0 Q1 13 E= R σ ε0 σ= Q1 Q = 12 A πR E= Q1 ε 0π R 2 Physics 212 Lecture 21, Slide 9 Calculation S Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. ●d I1 E C Ra E= r Q1 π R 2ε 0 R Q1 BB What is the electric flux through a circle of radius r in between the plates? Q1 Q1 2 Q1π r 2 Q1r 2 2 (A) Φ E = π r (B) Φ E = π R (C) Φ E = (D) Φ E = 2 ε0 ε0 ε 0R2 ε0R r 15 R rr ΦE = E ⋅ A Q1 E = π r2 ε 0π R 2 Q1 r 2 ΦE = ε 0 R2 Physics 212 Lecture 21, Slide 10 10 Calculation S Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. ●d I1 E Q1 Ra Q1r 2 ΦE = ε 0R2 r R C dΦE ID = ε0 dt BB What is the displacement current enclosed by circle of radius r ? R2 (A) I D = I1 2 r r 17 r (B) I D = I1 R R r2 (C) I D = I1 2 R (D) I D = I1 R r d ΦE dQ1 r 2 r2 ID = ε0 = = I1 2 2 dt R dt R r2 I D = I1 2 R Physics 212 Lecture 21, Slide 11 11 Calculation S Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a V current I1 flows in the circuit and the capacitor carries charge Q1. ●d I1 E Ra r2 I D = I1 2 R r R C rr ∫ B ⋅ d l = µ o (I + I D ) Q1 BB What is the magnitude of the B field at radius r ? (A) B = µ0 I1 2π R r 19 µ0 I1 2π r µI R (C) B = 0 1 2 2π r rr Ampere’s Law: ∫ B ⋅ d l = µo (I + I D ) (B) B = R (D) B = r2 B ⋅ 2π r = µ0 0 + I1 2 R µ0 I1 r B= Physics 212 2π R 2 µ0 I1 r 2π R 2 Lecture 21, Slide 12 12 Preflight 4 Preflight BB A B C From the From calculation we just did: just µ0 I1 r B= 2π R 2 21 70 30 60 50 40 20 10 0 Physics 212 Lecture 21, Slide 13 13 Preflight 2 Preflight BB BB B= µ0 I1 r 2π R 2 B is proportional to I but At A, B = 0 !! 80 60 40 20 0 Physics 212 Lecture 21, Slide 14 14 Follow-Up Switch S has been open a long time when at t = 0, it is closed. Capacitor C has circular plates of radius R. At time t = t1, a current I1 flows in the circuit and the capacitor carries charge Q1. What is the time dependence of the magnetic field B at a radius r between the plates of the capacitor? (A) (B) S C BB V Ra B1 = µ0 I1 r 2π R 2 (C) B at fixed r is proportional to the current I Close switch: VC =0 fl I = V/Ra (maximum) I exponentially decays with time constant τ = RaC 25 Physics 212 Lecture 21, Slide 15 15 Follow-Up 2 Suppose you were able to charge a capacitor with constant current (does not change in time). Does a B field exist in between the plates of the capacitor? (A) YES (B) BB NO Constant current fl Q increases linearly with time Therefore E increases linearly with time ( E = Q/(Aε0) dE/dt is not zero fl Displacement current is not zero fl B is not zero ! Physics 212 Lecture 21, Slide 16 16 We learned about waves in Physics 211 30 Physics 212 Lecture 21, Slide 17 17 “How can light move at How the same velocity in any inertial frame of reference? That's really trippy. ” really see PHYS 225 see PHYS 33 Physics 212 Lecture 21, Slide 18 18 35 Physics 212 Lecture 21, Slide 19 19 37 Physics 212 Lecture 21, Slide 20 20 Preflight 6 Ex = E0sin(kz-ωt) BB 50 40 E = E0 sin (kz - ωt): t): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. coordinate 30 20 10 0 40 Physics 212 Lecture 21, Slide 21 21 Preflight 7 Ex = E0sin(kz-ωt) 60 50 E = E0 sin (kz - ωt): t): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. coordinate 40 30 20 10 0 45 Physics 212 Lecture 21, Slide 22 22 ACT Ex = E0sin(kz-ωt) Consider a point (x,y,z) at time t when Ex is negative and has its maximum value. At (x,y,z) at time t, what is By? A) B) C) D) 45 By is positive and has its maximum value By is negative and has its maximum value By is zero We do not have enough information We Physics 212 Lecture 21, Slide 23 23 ...
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