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

2. + + + + + + - - - - - - + Q free on inner surface - Q free on inner surface plate separation d area of plates A

3. conductordielectric ++++ +++++ + ------ Gauss’s Law

4. frequency dielectric Constant (polar molecules)

5. + + + + + + + + + --------- dy F F me

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

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

9. L dA 3 BzBz dA 1 BzBz dA 2 BrBr

10. Z Y X

12. Bz1Bz1 s Bz2Bz2 x I B r = 0 A I enclosed = 0

13. s Bz2Bz2 x I B r = 0 C I enclosed = n s I B z1 = 0 I enclosed = 0 x I Bz2Bz2 B z1 = 0 x x xx

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

15. B Fe H Fe B gap H gap B air H air i coil windings gap region iron core

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

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

18. + -

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

20. + + + + + + + + + - - - - - - - - - x L-x V rr C = C A + C B C CACA CBCB

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

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

23. -q-q +q+q r 1  r – (d/2)cos  r 2  r + (d/2)cos  r  P ErEr EE (d/2)cos 

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

25. +q+q -q-q

26. +f+f -b-b +b+b -  f O r S

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

28. +  + + - - - element of charge dq e electric field at O due to charge dq e E0E0 E 0 cos 

29. a +Ze a d d << a

30. F F F d +Q+Q - Q 

31. 0 π/2 π 0 + p E - p E  U

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

33. 1/T  r - 1

34. T PoPo

35. p E / k Tp E / k T 1 0 10 slope = 1/3

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

37. non-conducting liquid air conducting sphere q Symmetry  E airt = E liquidt  E air = E liquid = E E airt E liquidt

38. field lines of E field lines of D +

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

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

41. NS 1 2 3 4 H Fe H air Circulation loop: square side L 5 6

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

44. Bound surface currents i m (right hand screw rule)  N pole imim

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

46. Fe ramp Cu ramp plastic ramp N N N

47. Circulation loop for circulation integration used in applying Ampere’s Law N N H iron H air

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

49. B, H gap M gap = 0 B = B gap = B iron H iron M iron B B, H gap M gap = 0 B = B gap = B iron H iron M iron B PERMANENT MAGNET ELECTROMAGNET

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

51. + + + + + - - - - - + + + + + - - - - - I X Y. Z direction out of page charge carriers electrons (-) eg wire, N-type semiconductor charge carriers positive (+) eg holes in P-type semiconductor + _ VHVH VHVH width w

52. I area A length L + _ V resistance R resistivity  conductivity  number density n _ v electron

54. X Y Z object image electron beam A

55. +Y +X +Z BzBz ByBy vyvy FxFx Electron at A moving parallel to +Y-axis Electron acted upon by the radial component of the magnetic field  force on electron in +X direction  +X- component to the velocity axis for the motion of the electron beam radial component of magnetic field due to B z

56. +Y +X +Z BzBz ByBy vxvx FyFy Electron at B has a velocity component in the +X direction Electron acted upon by the axial component of the magnetic field B y  force on electron in -Z direction i.e. towards to axis  focusing action axis for the motion of the electron beam radial component of magnetic field FzFz due to B y due to B z

57. ........ i free

59. external magnetic field

63. Electrostatic capacitor Electrolytic capacitor

64. Electrostatic capacitor Electrolytic capacitor

65. Electrochemical double layer capacitor conductive electrode conductive electrode separator activated carbon d

66. ++++++++++++++++++ ------------------ ++++++++++++++++++ ------------------ ++++++++++++++++++ ------------------

68. + - + - - Electric Field

69. Zero applied stress Compressive stress Induces a voltage Applied voltage produces An expansion + -

72. + - + - + - + - + - + - + - + - + - Ferroelectric material + - + - + - + - + - + - + - + - + - Antiferroelectric material + - + - + - + - + - + -

73. + + + + + - - - - - + Q on inner surface - Q on inner surface Interior points electric field must be zero Symmetry – electric field must be uniform – electric field lines perpendicular to conductive plates ++ +0.2 Q on outer surface Interior points electric field must be zero

74. + + + + + - - - - - + Q on inner surface - Q on outer surface Interior points electric field must be zero Symmetry – fields must be uniform – field lines perpendicular to plates Interior points electric field must be zero + + + + + - - - - - - Q on inner surface + Q on outer surface

75. +V+V +q+q +q+q +q+q -q-q -q-q -q-q Electric field between Adjacent plates

76. ... Series branch V Capacitors in series (charge on each plate) Capacitors in parallel (voltage across each capacitor is the same)

77. V Capacitors in parallel V  +Q 1 +Q 2 -Q 2 -Q 1 Q =Q 1 +Q 2 Capacitors in series C1C1 C2C2 C eq = C 1 +C 2 V C1C1 C2C2 +Q -Q V Q 1/C eq = 1/C 1 +1/C 2

78. fuel air w h l fuel

79. - + +Q+Q r Induced dipole

80. 5a5a Slab 1 Slab 2 a a a a a

81. S1S1 S2S2 S3S3 S4S4

82. + Q - Q + Q b1 - Q b1 + Q b2 - Q b2 C1C1 C2C2 + Q - Q Capacitors in series

83. E = 0

84. + + + + + + + + + + + + + + + ++ + + + + + + + - - - - - - - -

85. V1V1 +Q/2 - Q/2 C 1 = Q / 2V 1 Q = 2 C 1 V 1 V2V2 +q A +q B - q B - q A C1C1 C1C1 C1C1 q A = C 2 V 2 =  r C 1 V 2 q B = C 1 V 2 Q = q A + q B = C 1 V 2 (  r + 1) = 2 C 1 V 1 V 2 = 2 V 1 / (  r + 1) q A = 2 C 1 V 1  r / (  r + 1) q B = 2 C 1 V 1 / (  r + 1) C2C2

86. +Qf+Qf -Qf-Qf

87. +q - q rr d t

89. + + + + + + + - - - - - - - Dielectric is neutral Homogenous dielectric – uniformly polarized The electrical field is reduced in the dielectric material

90. + - + + - - + - + + + + + + + - - - - - - - Flat plate L = 1 Max polarization Thin long rod L = 0 Zero polarization Sphere L = 1/3 Concentration of charges At surface given by

91. - Q + Q

92. +Q -Q +Q b1 -Q b1 +Q b2 -Q b2 E1E1 E2E2

93. R1R1 R2R2