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Physics 212 Lecture 22

Physics 212 Lecture 22. Main Point 1.

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Physics 212 Lecture 22

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  1. Physics 212 Lecture 22

  2. Main Point 1 First, we described Maxwell’s modification to Ampere’s law that would allow a changing electric flux to produce a magnetic field in much the same manner that a changing magnetic flux produces an electric field in Faraday’s law. In particular, Maxwell defined the displacement current as e0 times the time rate of change of the electric flux and added it to the real current in the right hand side of Ampere’s law.

  3. Main Point 2 Second, we used this modified version of Ampere’s law in conjunction with Faraday’s law to demonstrate that components of the electric and magnetic fields satisfied a wave equation in which the velocity of the wave was identified as 1/sqrt(m0e0). The numerical value of this velocity was found to be identical to the speed of light and thereby supports the identification of light as an electromagnetic wave.

  4. Main Point 3 Finally we determined that for an electromagnetic wave traveling in the z-direction the Ex and By waves were in phase and that the ratio of the amplitudes, E0/B0 is equal to c, the speed of light.

  5. After Prelecture 21: Modify Ampere’s Law 10

  6. Displacement Current 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. c ● ● d r r I1 R Q1 Conceptual and Strategic Analysis

  8. 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. 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

  9. 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. 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

  10. 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

  11. We learned about waves in Physics 211

  12. 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 40

  13. 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 45

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