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

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

  3. dielectric constant frequency

  4. + + + + + + + + + + + + - - - - - - - - - - - - V = 0

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

  6. . . . . . . . . 3 4 X X X X X X Current i out of page Circulation loop: square of length L 1 2 Current i into page Cross-section through electromagnet

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

  8. + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

  9. + + + + + + + + + dy + + + + + + + + + F - - - - - - - - - -q +q

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

  11. 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

  12. 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

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

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

  15. -q +q

  16. S +f -b O r +b -f

  17. - - - S d  r + Pcos + +  The area of the shaded ring between  and  + d is equal to

  18. +Ze +Ze d a a d << a

  19. F F +Q  d F - Q

  20. + p E U 0 - p E π π/2 0 

  21. Po T

  22. 1 slope = 1/3 0 10 pE/kT

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

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

  25. field lines of E field lines of D

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

  27. 6 5 4 S N HFe Hair Circulation loop: square side L 2 1 3

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

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

  30. 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

  31. Cu ramp Fe ramp plastic ramp N N N

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

  33. if if d

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