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Physics 212 Lecture 22

Physics 212 Lecture 22. Music. 1976. 1994. Who is the Artist? Billy Joel Boz Scaggs Mark Knopfler Donald Fagen Michael McDonald. Theme of the week? Tower of Power, Boz Scaggs – San Francisco sounds of the ’70s. Physics 212 Lecture 22.

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Physics 212 Lecture 22

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  1. Physics 212 Lecture 22

  2. Music 1976 1994 • Who is the Artist? • Billy Joel • Boz Scaggs • Mark Knopfler • Donald Fagen • Michael McDonald Theme of the week? Tower of Power, BozScaggs – San Francisco sounds of the ’70s Physics 212 Lecture 22

  3. ok. i gotta say Physics is awesome. the first time I say this word to a class ever since my college life “I got chills. This is incredible stuff!” Wide Range: We will try to make clear, at least the BIG IDEAS “Fun stuff! but kinda hard.” “The derivation of the wave equation lost me ” “This prelecture was so horrible. Maybe it was just me, but I’m not sure that was English being spoken. Please clarify these concepts that seemingly came out of nowhere.“ Your Comments Why we be stretching imaginary films? Why isn't it just what's in the loop. Do all electromagnetic waves travel at the speed of light? “I got the modified Ampere’s law, but you lost me at one-dimensional waves; I’ve never EVER seen that equation before. I don’t understand what we just derived; why did we differentiate one with respect to time and the other with respect to z?? This all went by so fast” I want us to consider more than one possible bounding surface that captures displacement current. It seems like some such surfaces could be punctured by more field lines than others, which I didn't think was what the prelecture said. The solutions of the wave equation are the important part “All of the derivations and second derivatives became a little jumbled. I feel like this isn’t a very hard topic, just the way it’s presented is a little overwhelming.” Checkpoint 1 was confusing. “If I were Gauss, Ampere or Faraday I’d be mad that Maxwell just came along and claimed all the formulas for himself.” “Woah, whoah! Lecture slide speed limit: 3.00x10^8 m/s!” 05 I've CURRENTLY been DISPLACED out of my natural state of mind. I'm so lost

  4. What We Knew Before Prelecture 22 06

  5. After Prelecture 22: Modify Ampere’s Law 10

  6. Displacement Current: Generalization Free space Real Current: Charge Q passes through area A in time t: Displacement Current: Electric flux through area A changes in time 08

  7. Calculation S C V Ra 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. At time t1, what is the magnetic field B1 at a radius r (point d) in between the plates of the capacitor? ● d r I1 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 (what does Amperian loop look like) to determine B 10

  8. Calculation S C V Ra Compare the magnitudes of the B fields at points c and d. (A) Bc < Bd (B) Bc = Bd (C) Bc > Bd R r r point c: I(enclosed) = I1 point d: ID(enclosed) < I1 X 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. c ● ● d r r I1 R Q1 What is the difference? Apply (modified) Ampere’s Law 11

  9. Calculation S C V Ra 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. ● d r I1 E R Q1 What is the magnitude of the electric field between the plates? (A) (B) (C) (D) Q1 R 13

  10. Calculation S C V Ra R r 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. ● d r I1 E R Q1 What is the electric flux through a circle of radius r in between the plates?(What does the Amperian loop look like?) (A) (B) (C) (D) 15

  11. Calculation S C V Ra R r 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. ● d r I1 E R Q1 What is the displacement current enclosed by circle of radius r ? (A) (B) (C) (D) 17

  12. Calculation S C V Ra Ampere’s Law: R r 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. ● d r I1 E R Q1 What is the magnitude of the B field at radius r ? (A) (B) (C) (D) 19

  13. Checkpoint 1b At time t=0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is toward the outer edge. A Compare the magnitudes of the magnetic fields at points A and B just after the switch is closed A. BA < BBB. BA = BBC. BA > BB “B has more flux enclosed, has a greater electric flux, and has greater B-field.” “the electric field is the same, so the magnetic field should also be the same.” “A is right in the center of the electric field, while B is further away, so A will be larger” 21

  14. Checkpoint 1b From the calculation we just did: At time t=0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is toward the outer edge. A Compare the magnitudes of the magnetic fields at points A and B just after the switch is closed A. BA < BBB. BA = BBC. BA > BB 21

  15. Checkpoint 1a At time t=0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is toward the outer edge. A After the switch is closed, there will be a magnetic field at point A which is proportional to the current in the circuit: A. True B. False “There is displacement current between the plates, this creates a magnetic field as well” “larger magnetic field will be produced by larger current.” “at A, the B field is zero”

  16. Checkpoint 1a B is proportional to I but At A, B = 0 !! At time t=0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is toward the outer edge. A After the switch is closed, there will be a magnetic field at point A which is proportional to the current in the circuit: A. True B. False

  17. Follow-Up S C V Ra (A) (B) (C) 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? B at fixed r is proportional to the current I Close switch: VC =0 I = V/Ra (maximum) I exponentially decays with time constant t = RaC 25

  18. Follow-Up 2 Constant current Q increases linearly with time 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) NO Therefore E increases linearly with time ( E = Q/(Ae0) dE/dt is not zero  Displacement current is not zero B is not zero !

  19. We learned about waves in Physics 211 30

  20. “How can light move at the same velocity in any inertial frame of reference? That's really trippy.” see PHYS 225 33

  21. 35

  22. 37

  23. Checkpoint 2a An electromagnetic plane-wave is traveling in the +z direction. The illustration below shows this wave at some instant in time. Points A, B and C have the same z coordinate. Ex = E0sin(kz-wt) Compare the magnitudes of the electric fields at points A and B A. EA < EBB. EA = EBC. EA > EB “A is always greater because it has 2 magnetic fields acting on it instead of just 1 like the other points. “ “points A and B are located in the electric field wave, so both would be influenced by the electric field. However, point C is located in the magnetic field and not the electric field and as such, has 0 electric field.“ “E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. “ 40

  24. Checkpoint 2a An electromagnetic plane-wave is traveling in the +z direction. The illustration below shows this wave at some instant in time. Points A, B and C have the same z coordinate. Ex = E0sin(kz-wt) Compare the magnitudes of the electric fields at points A and B A. EA < EBB. EA = EBC. EA > EB E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. 40

  25. Checkpoint 2b An electromagnetic plane-wave is traveling in the +z direction. The illustration below shows this wave at some instant in time. Points A, B and C have the same z coordinate. Ex = E0sin(kz-wt) Compare the magnitudes of the electric fields at points A and C A. EA < ECB. EA = ECC. EA > EC “A is always greater because it has 2 magnetic fields acting on it instead of just 1 like the other points. “ “points A and B are located in the electric field wave, so both would be influenced by the electric field. However, point C is located in the magnetic field and not the electric field and as such, has 0 electric field.“ “E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. “ 45

  26. Checkpoint 2b An electromagnetic plane-wave is traveling in the +z direction. The illustration below shows this wave at some instant in time. Points A, B and C have the same z coordinate. Ex = E0sin(kz-wt) Compare the magnitudes of the electric fields at points A and C A. EA < ECB. EA = ECC. EA > EC E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C. 45

  27. Follow-up Ex = E0sin(kz-wt) 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? • 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 45

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