1. Agenda This Week –Ch. 27-29 –Skip Lab, No Quiz Next Week –Finish 29, No Quiz –Review Following –Exam II on Monday (2 weeks) –April 6 th [Or previous Friday if prefer] Sections –27.1-27.8 –28.1-28.5, skim28.8: No worry about “how” Mag fields arise –29.1-29.5

2. Chapter 28 Origin of Mag fields See end of chapter for B fields from various distributions Today cover simple distributions, point charge, relationship to permanent magnets.

3. Symmetry & Fields Symmetry in magnetism: –B fields act on moving charges –moving charges create B fields Symmetry in electrostatics: –E fields act on charges –charges create E fields Symmetry in gravity: –G fields act on massive objects –Massive objects create G fields

4. Fields From Charges Implications? B & E Related B Perpendicular Reference Frame?

5. Unit Analysis Why do it? Forget equation?: can make it up Can solve things never seen before Can discover fundamental relationships

6. Examine Units of Tesla F = qvBsin(  ) Newtons = Coulombs (meters/second) Tesla T = (N / C) (s / m) = (N s) / ( C m) Units of  0 ?

7. Examine Units of  0 B =  0 Qvr/r 3 [just looking for units]  0 = Br 2 /Qv  0  ( T m 2 s) / (C m)  (T s m)/(C ) T = (N s) / ( C m)  0  [s m / C] [N s / C m]  0  [ N s 2 / C 2 ] Fun yet?

8. Examine Units of  0  0  [ N s 2 / C 2 ]  0 = Q / (4  E r 2 )  0  C / (N m 2 /C) = C 2 / (N m 2 ) Know E & B related, why not constants? Good way to combine constants? Multiply or divide What units do you get?

9. Combine Constants  0  [ N s 2 / C 2 ]  0  C 2 / (N m 2 )  0 = 4  x10 -7 [ N s 2 / C 2 ]  0 = 8.85x10 -12 [C 2 / (N m 2 )] Multiply  0  0 = 1.112x10 -17 (?)  0  0 = 1.112x10-17 s 2 /m 2 Any ideas?

10. Combine Constants  0  0 = 1.112x10-17 s 2 /m 2 Looks like inverse velocity squared Take inverse: (  0  0 ) -1 = 9x10 16 m 2 /s 2 Hope you see it now Take Square Root

11. Combine Constants Implications? E & B & c related B related to reference frame? What involves c & reference Frames? Relativity, E, B, c intimately involved?

12. Back to Reality(?)

13. B Field from Wire Right Hand Rule.. Wire, Current goes Up Thumb points in current direction Field follows fingers I B B =  0 I/(2  r)  0 = magnetic constant = 4  x10 -7 r

14. B Field from Loop (at Center) Right Hand Rule.. Wire, Current Goes Around Thumb points in current direction of Field Current follows fingers B I B =  0 I/(2R)  0 = magnetic constant = 4  x10 -7 R

15. B Field from N Loops (at Center) Right Hand Rule.. Wire, Current Goes Around Thumb points in current direction of Field Current follows fingers B I B =  0 NI/(2R)  0 = magnetic constant = 4  x10 -7 R

16. B Field from Lots of Loops B field constant inside, ~ zero Outside Soleniod Wire, Current Goes Around Thumb points in current direction of Field Current follows fingers B B =  0 IN/L

17. What Happens Inside? N S Magnets are Metals Electrons Inside Move about in circles A lot like a solenoid

18. Polarization & Magnetism Permanent Magnets –Ferromagnets [Iron, rare earths….] –“Magnetized” Magnetic Materials –Can be magnetized, but aren’t –Ferromagnetics [Iron, rare earths…] Interaction between magnets? Interaction between magnets & metals? Relationship to electrostatics?

19. Agenda This Week –Ch. 27-29 –Skip Lab, No Quiz Next Week –Finish 29, No Quiz –Review Following –Exam II on Monday (2 weeks) –April 6 th [Or previous Friday if prefer] Sections –27.1-27.8 –28.1-28.5, skim28.8: No worry about “how” Mag fields arise –29.1-29.5