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Chapter 7 Electrodynamics

Chapter 7 Electrodynamics. 7.0 Introduction 7.1 Electromotive Force 7.2 Electromagnetic Induction 7.3 Maxwell’s Equations. 0. 0. 7.0 Introduction. electrostatic. static. magnetostatic. =. conservation of charge. 7.0 (2). Maxwell’s equations:. 7.0 (3). =. Magnetic flux.

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Chapter 7 Electrodynamics

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  1. Chapter 7 Electrodynamics 7.0 Introduction 7.1 Electromotive Force 7.2 Electromagnetic Induction 7.3 Maxwell’s Equations

  2. 0 0 7.0 Introduction electrostatic static magnetostatic = conservation of charge

  3. 7.0 (2) Maxwell’s equations:

  4. 7.0 (3) = Magnetic flux Induced electric field (force) induce

  5. e.g. , ~ 7.0 (4) E,B fields propagate in vacuum wave

  6. 7.0 (5) A.C. current can generate electromagnetic wave antenna cyclotron mass free electron laser …..

  7. 7.1 Electromotive Force 7.1.1 Ohm’s Law 7.1.2 Electromotive Force 7.1.3 Motional emf

  8. for perfect conductors 7.1.1 Ohm’s Law Current density conductivity force per unit charge of the medium resistivity ( a formula based on experience) usually true but not in plasma; especially, hot. Ohm’s Law

  9. Ohm’s Law (based on experience) Potential current resistance [ in ohm (Ω) ] V=I R 7.1.1 (2) Total current flowing from one electrode to the other Note : for steady current and uniform conductivity

  10. uniform I=? R=? uniform V 7.1.1 (3) Ex. 7.1 sol:

  11. A=const Ex. 7.3 Prove the field is uniform V=V0 V=0 =const 7.1.1 (4) i.e.,

  12. V 7.1.1 (5) Ex. 7.2

  13. The physics of Ohm’s Law and estimation of microscopic s the charge will be accelerated by before a collision time interval of the acceleration is 7.1.1 (6) mean free path typical case for very strong field and long mean free path

  14. 7.1.1 (7) The net drift velocity caused by the directional acceleration is = mass of the molecule e charge molecule density free electrons per molecule Joule heating law Power is dissipated by collision

  15. The current is the same all the way around the loop. 7.1.2 Electromotive Force Produced by the charge accumulation due to Iin > Iout electrostatic force electromotive force outside the source

  16. 7.1.3 motional emf

  17. = Work is done by the pull force, not . 7.1.3 (2)

  18. for the loop 7.1.3 (3) magnetic flux flux rule for motional emf

  19. 7.1.3 (4) a general proof

  20. =? 7.1.3 (5) Ex. 7.4

  21. 7.2 Electromagnetic Induction 7.2.1 Faraday’s Law 7.2.2 The Induced Electric Field 7.2.3 Inductance 7.2.4 Energy in Magnetic Fields

  22. 7.2.1 Faraday’s Law M. Faraday’s experiments loop moves B moves induce induce Induce Faraday’s Law (integral form) Faraday’s Law (differential form)

  23. 7.2.1 (2) A changing magnetic field induces an electric field. (b) & (c) induce that causes (a) drive Lenz’s law : Nature abhors a change in flux ( the induced current will flow in such a direction that the flux it produces tends to cancel the change. )

  24. Induced ? 7.2.1 (3) Ex. 7.5 sol: at center , spread out near the ends

  25. ring jump. 7.2.1 (4) Ex. 7.6 Plug in, induces Plug in, why ring jump?

  26. 7.2.2 The Induced Electric Field

  27. = 7.2.2 (2) Ex. 7.7 induced = ? sol:

  28. The charge ring is at rest torque on 7.2.2 (3) Ex. 7.8. sol: What happens? the angular momentum on the wheel

  29. Induced 7.2.2 (4) sol: quasistatic

  30. Constant K( s , t ) 7.2.2 (5) = s << c t t = I / (dI/dt)

  31. 7.2.3 Inductance mutual inductance

  32. 7.2.3 (2) Neumann formula The mutual inductance is a purely geometrical quantity M21 = M12 = M F1 = M12 I2 F1 = F2 if I1 = I2

  33. 7.2.3 (3) n2 turns per unit length Ex. 7.10 n1 turns per unit length 1 I given 2 sol: assume I too. B1 is too complicated… 2 = ? Instead, assume I running through solenoid 2

  34. 7.2.3 (4) changing current in loop1, induces current in loop2 • self inductance self-inductance (or inductance ) [ unit: henries (H) ] • back emf

  35. N turns b a L(self-inductance)=? 7.2.3 (5) Ex. 7.11 sol:

  36. 7.2.3 (6) Ex. 7.12 sol: general solution particular solution

  37. 7.2.4 Energy in Magnetic Fields In E.S. From the work done, we find the energy in , test charge But, does no work. WB = ? In back emf

  38. 7.2.4 (2) In volume

  39. ＜ ＜ 7.2.4 (3) Ex. 7.13 sol:

  40. 7.3 Maxwell’s Equations 7.3.1 Electrodynamics before Maxwell 7.3.2 How to fix Ampere’s Law 7.3.3 Maxwell’s Equations 7.3.4 Magnetic Charge 7.3.5 Maxwell’s Equation in Matter 7.3.6 Boundary Conditions

  41. 7.3.1 Electrodynamics before Maxwell (Gauss Law) (no name) (Faraday’s Law) (Ampere’s Law) but =0 Ampere’s Law fails because

  42. 7.3.1 an other way to see that Ampere’s Law fails for nonsteady current loop 1 2 For loop 1, Ienc = 0 For loop 2, Ienc = I they are not the same.

  43. A changing electric field induces a magnetic field. 7.3.2 How to fix Ampere’s Law continuity equations, charge conservation such that, Ampere’s law shall be changed to Jd displacement current

  44. 7.3.2 = loop 1 2 for the problem in 7.3.1 between capacitors

  45. 7.3.3 Maxwell’s equations Gauss’s law Faraday’s law Ampere’s law with Maxwell’s correction Force law continuity equation ( the continuity equation can be obtained from Maxwell’s equation )

  46. Since , produce , 7.3.3

  47. 7.3.4 Magnetic Charge Maxwell equations in free space ( i.e., , ) symmetric With and , the symmetry is broken. If there were ,and . symmetric and So far, there is no experimental evidence of magnetic monopole.

  48. 7.3.5 Maxwell’s Equation in Matter bound charge bound current Q surface charge

  49. 7.3.5 (2) Ampere’s law ( with Maxwell’s term )

  50. 7.3.5 (3) In terms of free charges and currents, Maxwell’s equations become displacement current one needs constitutive relations:

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