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

5. + + + + + + - - - - - - V = 0

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

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

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

9. + -

10. + + + + + + + + + - - - - - - - - - dy F +q+q -q-q

11. + + + + + + + + + - - - - - - - - - x L-x V rr C = C A + C B

12. 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

13. 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

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

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

16. +q+q -q-q

17. +f+f -b-b +b+b -  f O r S

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

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

20. a +Ze a d d << a

21. F F F d +Q+Q - Q 

22. 0 π/2 π 0 + p E - p E  U

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

24. 1/T  r - 1

25. T PoPo

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

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

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

29. field lines of E field lines of D +

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

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

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

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

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

36. 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

37. Fe ramp Cu ramp plastic ramp N N N

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

39. d ifif ifif

40. 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

41. + + + + + - - - - - + + + + + - - - - - 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

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

44. X Y Z object image electron beam A

45. +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

46. +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

47. ........ i free

49. external magnetic field