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

3. frequency dielectric constant

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

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

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

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

8. + -

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

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

11. 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

12. 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

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

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

15. +q+q -q-q

16. +f+f -b-b +b+b -  f O r S

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

18. a +Ze a d d << a

19. F F F d +Q+Q - Q 

20. 0 π/2 π 0 + p E - p E  U

21. T PoPo

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

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

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

25. field lines of E field lines of D

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

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

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

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

31. 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

32. Fe ramp Cu ramp plastic ramp N N N

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

34. d ifif ifif