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. Today Work done by B fields Induction Bad News –No Sub for Sub Good News Quizzes –Will curve so that Average is > or = Exam Avg –Exam Avg between C+ & B- –Essentially, add ~ 5 pts to quiz average

3. What Happens Here? B Field Points Into Screen What is the trajectory for this particle? Positive Charge, Constant Velocity Right? Initial: Force points ? … Down XX X X X X X X X XX X X XX X X X XX X X X XX X X X XX X X X X -

4. All Perpendicular: Circular Motion XX X X X X X X X XX X X XX X X X XX X X X XX X X X XX X X X X - Velocity, Force & Field Always Perpendicular When Force always points inwards… Circular Motion FBFB

5. Circular Motion Force points inwards Perpendicular to velocity Force & speed constant F C = mv 2 /r Here: F B = F C Right Hand Rule says Force points inwards What says force is constant?

6. Examine Energy Does energy of particle change because of B field? Does B field do work on particle? E F = E I + W B PE F + KE F = PE I + KE I + W B PE Same (why not?)  KE = W B So for speed to be constant, W B = zero

7. What is W B ? So for speed to be constant, W B = zero What is angle between magnetic force & motion?

8. All Perpendicular: Circular Motion XX X X X X X X X XX X X XX X X X XX X X X XX X X X XX X X X X - Velocity, Force & Field Always Perpendicular When Force always points inwards… Circular Motion FBFB

9. What is W B ? So for speed to be constant, W B = zero What is angle between magnetic force & motion? 90 o  cos(90 o ) = 0 Dot product is zero  W B = 0 Always?

10. Chapter 29: Induction What do these things have in common? –Credit Cards –Electric Guitars –Electric Motors –Electric Generators See Title of Page…

11. Chapter 29: Induction Charges make E fields –E fields from V? Moving charges make B fields –Can B fields make E fields? –Dr. Seuss? What do “moving” B fields make? –Voltage –Voltage makes charges move –Moving Charges make B fields….

12. “Induction” Changing B fields “induce” a voltage Voltage creates moving charges Which have B fields of their own These B fields attempt to cancel out the change Simple: Things don’t like change Laziness is the rule – even if it takes work

13. Changing Fields? Actually “Effect of Field” Important thing is actually Magnetic Flux Flux? [See Gauss’s Law…] Total field passing thru some Area How much B field affects something

14. Changing Fields? Actually “Effect of Field” Important thing is actually Magnetic Flux Flux? [See Gauss’s Law…] If B constant

15. Principle Magnetic systems are Luddites Do NOT like change If possible, will act to oppose a change in magnetic flux Math: V IND = - d   /dt A change in magnetic flux will induce a voltage that will attempt to create moving charges to oppose this change.

16. Example Less words Area of uniform magnetic field (pointing into screen) A closed loop of wire is hanging out inside this field The field begins to increase in magnitude. What happens? XX X X X X X X X X X X X XX X X X X X X XX XX X X X X

17. Example Less words Area of uniform magnetic field (pointing into screen) A closed loop of wire is hanging out inside this field The field begins to increase in magnitude. What happens? XX X X X X X X X X X X X XX X X X X X X X XX X X X X Voltage induced in loop Creates current Current opposed flux change

18. Example Less words Area of uniform magnetic field (pointing into screen) A closed loop of wire is hanging out inside this field The field begins to decreases in magnitude. What happens? XX X X X X X X X X X X X XX X X X X X X XX XX X X X X

19. Example Less words Area of uniform magnetic field (pointing into screen) A closed loop of wire is hanging out inside this field The field begins to increase in magnitude. What happens? XX X X X X X X X X X X X XX X X X X X X X XX X X X X Voltage induced in loop Creates current Current opposed flux change

20. Example Less words Area of uniform magnetic field (pointing into screen) An open loop of wire is hanging out inside this field The field begins to increase in magnitude. What happens? XX X X X X X X X X X X X XX X X X X X X XX X X X X Voltage induced in loop Would creates current Current would opposed flux change + -

21. Induction rarely wins Attempting to keep flux constant Nearly all materials have some resistance Induced motion electrons lose energy Eventually Induced current reduces to zero Unless superconductor –Magnetic Fields cannot penetrate superconductor –Levitation…

22. Next Week Monday –More interesting bits of induction –Complex Examples Tuesday –Maybe short lab –No quiz –Problem solving? W&F –Wrap up induction, review for exam

23. 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