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+ Q free on inner surface. + + + + + + + + + + + +. - - - - - - -. - q bound. Symmetry – fields must be uniform – field lines perpendicular to plates. + q bound. + + + + + +.

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  1. +Qfreeon inner surface + + + + + + + + + + + + - - - - - - - -qbound Symmetry – fields must be uniform – field lines perpendicular to plates +qbound + + + + + + - - - - - - - - - - - - -Qfreeon inner surface Interior points electric field must be zero

  2. area of plates A + + + + + + + + + + + + +Qfreeon inner surface plate separationd -Qfreeon inner surface - - - - - - - - - - - -

  3. + + + + + conductor - - - dielectric Gauss’s Law

  4. dielectric Constant (polar molecules) frequency

  5. Fme dy + + + + + + + + + + + + + + + + + + F - - - - - - - - -

  6. + + + + + + + + + + + + - - - - - - - - + + + + + + + + - - - - - - - - - - - - Electric field Electric displacement Polarization

  7. only some of the windings are shown A Integration paths B C

  8. L Bz Bz dA1 dA2 Br dA3

  9. Z Y X

  10. Bz1 Br = 0 Ienclosed = 0 I A Bz2 s x

  11. Bz1= 0 C Br = 0 Ienclosed = nsI I Bz2 s Ienclosed = 0 I Bz1= 0 Bz2 x x x x x x

  12. single turn of wire with current I B around integration loop B dr = 0 and Br = 0 outside loop Bz = 0

  13. iron core BFe HFe gap region Bgap Hgap i coil windings Bair Hair

  14. . . . . . . . . 3 X X X X X X 2 Current i out of page Circulation loop: square of length L 1 4 Current i into page Cross-section through electromagnet

  15. thickness t width L q = - e area A electrons are the charge carriers in copper

  16. + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

  17. + + + + + + + + + dy + + + + + + + + + F - - - - - - - - - -q +q

  18. C + + + + + + + + + V r CA CB - - - - - - - - - L-x C = CA + CB x

  19. Induced dipole moment – helium atom +2e +2e -e -e -e -e Zero electric field – helium atom symmetric  zero dipole moment A B effectively charge +2e at A and -2e at B dipole moment p = 2ed

  20. Induced dipole moment – sulfur atom +16e +16e -8e -8e -8e -8e Zero electric field – helium atom symmetric  zero dipole moment A B effectively charge +16e at A and -16e at B dipole moment p = 16ed

  21. Er E P r2  r + (d/2)cos r1  r – (d/2)cos r (d/2)cos  +q -q

  22. dA +f + + + + + + + + +  -b   +b  - - - - - - - - - -f

  23. -q +q

  24. S +f -b O r +b -f

  25. Width of ring r d Radius of ring r sin + + + Area of the shaded ring between  and  + d surface S d  r - Pcos - - 

  26. + + + electric field at O due to charge dqe E0 cos  E0 element of charge dqe - - -

  27. +Ze +Ze d a a d << a

  28. F F +Q  d F - Q

  29. + p E U 0 - p E π π/2 0 

  30. U = - p E Lowest energy state U = 0 U = + p E highest energy state - - -  = 90o + + +  = 0  = 180o

  31. r - 1 1/T

  32. Po T

  33. 1 slope = 1/3 0 10 pE/kT

  34. Gaussian surface S conducting sphere q air a r non-conducting liquid Symmetry  field lines must be radial

  35. conducting sphere q Eairt air Eliquidt non-conducting liquid Symmetry  Eairt = Eliquidt Eair = Eliquid = E

  36. field lines of E field lines of D +

  37. field lines of D + + + + + + + + + + greater concentration of charge on surface bounded by liquid field lines of E +

  38. - + + - - + + shift in atoms due to ionic nature of bond induced dipoles due to shift in electron cloud rotation orientation of polar molecules

  39. 6 5 4 S N HFe Hair Circulation loop: square side L 2 1 3

  40. Cylindrical Gaussian surface Gauss’s Law for magnetism B-field lines – form continuous loops

  41. N pole im Bound surface currents im (right hand screw rule)  

  42. un-magnetized piece of iron Bar magnet bought near un-magnetized piece of iron N N N  Bar magnet will attract the iron that was initially un-magnetized north pole attracts south pole

  43. Cu ramp Fe ramp plastic ramp N N N

  44. Circulation loop for circulation integration used in applying Ampere’s Law N N Hair Hiron

  45. B I I (0,0) d H B d

  46. Miron PERMANENT MAGNET Hiron B B, Hgap Mgap = 0 B = Bgap = Biron ELECTROMAGNET Miron Hiron B Mgap = 0 B, Hgap B = Bgap = Biron

  47. Y thickness t area A = wt width w X current in X direction Z magnetic field in Z direction Schematic diagram of a Hall Probe

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