Physics 2112 Unit 22

1. Physics 2112Unit 22 Outline Displacement Current Maxwell’s Equations (Final Form) E&M Waves

2. Where we are now Faraday’s Law Gauss’ Law Ampere’s Law Gauss’ Law for B field Our equations so far…..

3. Displacement Current 3 Points, all a distance r from axis of a current c carrying wire connected to capacitor 1 3 2 ● ● ● r I1 Define “displacement current” such that:

4. Modify Ampere’s Law

5. Displacement Current Real Current: Charge Q passes through area A in time t: Displacement Current: Electric flux through area A changes in time

6. Example 22.1 A parrallel plate capacitor has plates that are 2cm in diameter and 1mm apart. If the current into the capacitor is 0.5A, what is the magnetic field between the plates 0.5cm from the axis of the center of the plates? What is the magnetic field 3cm from the axis of the center of the plates? ● d r 1cm I1 0.5cm R Q1 Conceptual Plan Use modified Ampere’s Law Strategic Plan Find electric flux contained within circle with radius of 0.5cm Find time rate of change of that flux

7. CheckPoint1(A) 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 at 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. • True • False A

8. CheckPoint1(B) 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 at the outer edge.. • Compare the magnitudes of the magnetic fields at points A and B just after the switch is closed: • BA< BB • BA= BB • BA> BB A

9. 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? A B C

10. 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) NO

11. Final form Faraday’s Law Gauss’ Law Ampere’s Law Gauss’ Law for B field Tada!..... Maxwell’s Equations

12. Wave Equation Remember from 2111?? Remember this guy? Not the spring constant!

13. Some Calculations + + - -

14. Some Calculations A wave equation???? With a velocity of …? see PHYS 2115

15. Only true for E&M wave traveling in space

16. Keep us warm Keep us safe The Sun

17. Example 22.2 • An electromagnetic plane wave has a wavelength of 0.100nm. • What is its wave number, k? • What is its frequency? • What portion of the electro-magnetic spectrum does it fall in?

18. Past Confusion Nothing is moving here. Arrows only represent strength of field. Actually a plane wave.

19. CheckPoint2(A) Ex=E0sin(kz- wt) An electromagnetic plane wave is traveling in the +z direction. The illustration below shows this wave an some instant in time. Points A, B, and C have the same z coordinate. • Compare the magnitudes of the electric field at points A and B. • Ea < Eb • Ea = Eb • Ea > Eb E=E0 sin (kz-wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C.

20. CheckPoint2(B) Ex=E0sin(kz- wt) An electromagnetic plane wave is traveling in the +z direction. The illustration below shows this wave an some instant in time. Points A, B, and C have the same z coordinate. • Compare the magnitudes of the electric field at points A and C. • Ea < Ec • Ea = Ec • Ea > Ec E=E0 sin (kz-wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C.