+ + + + + + + + + + + +

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

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

9. L Bz Bz dA1 dA2 Br dA3

10. Z Y X

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

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

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

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

16. . . . . . . . . 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

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

18. + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

19. + + + + + + + + + dy + + + + + + + + + F - - - - - - - - - -q +q

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

21. 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

22. 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

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

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

25. -q +q

26. S +f -b O r +b -f

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

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

29. +Ze +Ze d a a d << a

30. F F +Q  d F - Q

31. + p E U 0 - p E π π/2 0 

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

33. r - 1 1/T

34. Po T

35. 1 slope = 1/3 0 10 pE/kT

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

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

38. field lines of E field lines of D +

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

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

41. 6 5 4 S N HFe Hair Circulation loop: square side L 2 1 3

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

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

45. 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

46. Cu ramp Fe ramp plastic ramp N N N

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

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

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

50. 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