1. MIDTERM 3 UTC 4.132 Thu-Nov 15, 7:00PM - 9:00PM Course Summaries Unit 1, 2, 3 Provided TA session Monday Homework Review (attendance optional) Bring pencils, calculators (memory cleared)

2. Chapter 24 Classical Theory of Electromagnetic Radiation

3. Maxwell’s Equations Gauss’s law for electricity Gauss’s law for magnetism Complete Faraday’s law Ampere’s law (Incomplete Ampere-Maxwell law)

4. No current inside Current pierces surface Ampere’s Law

5. Time varying magnetic field leads to curly electric field. Time varying electric field leads to curly magnetic field? I ‘equivalent’ current combine with current in Ampere’s law Maxwell’s Approach

6. Works! The Ampere-Maxwell Law

7. Four equations (integral form) : Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere-Maxwell law + Lorentz force Maxwell’s Equations

8. Time varying magnetic field makes electric field Time varying electric field makes magnetic field Do we need any charges around to sustain the fields? Is it possible to create such a time varying field configuration which is consistent with Maxwell’s equation? Solution plan: Propose particular configuration Check if it is consistent with Maxwell’s eqs Show the way to produce such field Identify the effects such field will have on matter Analyze phenomena involving such fields Fields Without Charges

9. Key idea: Fields travel in space at certain speed Disturbance moving in space – a wave? 1. Simplest case: a pulse (moving slab) A Simple Configuration of Traveling Fields

10. Pulse is consistent with Gauss’s law for magnetism A Pulse and Gauss’s Laws

11. Since pulse is ‘moving’, B depends on time and thus causes E Area does not move emf E=Bv Is direction right? A Pulse and Faraday’s Law

12. =0 A Pulse and Ampere-Maxwell Law

13. E=Bv Based on Maxwell’s equations, pulse must propagate at speed of light E=cB A Pulse: Speed of Propagation

14. Question At this instant, the magnetic flux  mag through the entire rectangle is: A)B; B) Bx; C) Bwh; D) Bxh; E) Bvh

15. Question In a time  t, what is  mag ? A) 0; B) Bv  t; C) Bhv  t; D) Bxh; E) B(x+v  t)h

16. Question emf =  mag /  t = ? A) 0; B) Bvh; C) Bv; D) Bxh; E) B(x+v)h

17. Question A)Eh; B) Ew+Eh; C) 2Ew+2Eh; D) Eh+2Ex+2Ev  t; E)2Ev  t

18. Question What is E? A) Bvh; B) Bv; C) Bvh/(2h+2x); D) B; E) Bvh/x

19. Exercise If the magnetic field in a particular pulse has a magnitude of 1x10 -5 tesla (comparable to the Earth’s magnetic field), what is the magnitude of the associated electric field? Force on charge q moving with velocity v perpendicular to B:

20. Direction of speed is given by vector product Direction of Propagation

21. Electromagnetic pulse can propagate in space How can we initiate such a pulse? Short pulse of transverse electric field Accelerated Charges

22. 1.Transverse pulse propagates at speed of light 2.Since E(t) there must be B 3.Direction of v is given by: E B v Accelerated Charges

23. We can qualitatively predict the direction. What is the magnitude? Magnitude can be derived from Gauss’s law Field ~ -qa  1. The direction of the field is opposite to qa  2. The electric field falls off at a rate 1/r Magnitude of the Transverse Electric Field

24. Field of an accelerated charge 1 2 3 4 vT A B Accelerates for t, then coasts for T at v=at to reach B. cT ct No charge

25. Field of an accelerated charge 1 2 3 4 vT A B cT ct