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time-varying magnetic fields equation of continuity

time-varying magnetic fields equation of continuity. Faraday 1791-1867. An induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804-65). either B or

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time-varying magnetic fields equation of continuity

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  1. time-varying magnetic fields equation of continuity

  2. Faraday 1791-1867

  3. An induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804-65).

  4. either B or change in time or both change in time Faraday’s law

  5. z B ds y x a a magnetic field changes in time

  6. z B ds y x size of loop changes in time

  7. z B y x L R w j size of loop changes in time

  8. Faraday’s law apply Stoke’s theorem

  9. This is a big one!

  10. I eat all magnetic monopoles! This is a big one!

  11. 2w L u I x DV wire carrying current I nonuniform B field

  12. Bewley’s book • trick questions • not every motion generates a voltage • uniform B & v • substitution of circuit • Vgen = 0!

  13. X B u c 1 2

  14. u c 1 2 X B V12= 0

  15. X B u c 1 2 V12= Bcu

  16. X B u c 1 2 V12= Bcu

  17. u c 1 2 X B V12= Bcu

  18. X B u c 1 2 V12= Bcu V12= -Bcu

  19. X B u c 1 2 V12= Bcu V12= -Bcu

  20. I1 dl1 I2 dl2 1 B2 B1

  21. I induced

  22. electromagnetic launcher

  23. J. Phys. D 33, 120 (2000)

  24. before after

  25. Iowa State gun

  26. Equation of continuity • economics • If more comes out than you put in, the bag will decrease! • There will be a flux of $. • Flux is related to what is or was inside the bag.

  27. note that there is a flux out through a surface Dz • Dy @ a time t > 0 • [flux density] • Ds = - [ ($ density)/t] • Dv • evaluate @ xo

  28. Gauss's theorem

  29. equation of continuity

  30. example: place some charges on a conductor. How long does it take for the charges to spread out?

  31. metal has a conductivity Ohm's law

  32. Poisson's equation

  33. Poisson's equation solution time constant

  34. U. S. Congress has a source. Gutenberg What Congress brings home?

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