W13D3 More Patterns

1. Easy! W13D3 More Patterns Fields, Patterns, Maxwell’s Equations and Begin Induction/Faraday’s Law 2049 SCALE-UP

2. Calender

3. THE EVAN SHOW

4. Field Patterns From Last Time “Curly Field” No diverging source Diverging Field Point Sources Electrostatic Fields Magnetic Fields

5. Maxwell’s Equations

6. A puzzlement .. Let’s apply this to the gap of a capacitor.

7. Consider the poor little capacitor… i i ? CHARGING OR DISCHARGING …. HOW CAN CURRENT FLOW THROUGH THE GAP In a FIELD description??

8. Through Which Surface Do we measure the current for Ampere’s Law? I=0 Huh??

9. In the gap… DISPLACEMENT CURRENT Fixes the Problem!

11. NEXT Fix the Last Maxwell Equation

12. First, Let's DO the Demo !

13. The Coil and the Magnet Galvanometer Coil

14. Magnetic Flux FM Integral over a SURFACE

15. What’s Happening Here?? A

16. Observation Variables Direction Polarity Pitch Velocity Meter Deflects There must be an emfaround the loops!

17. Down the Hatch Aluminum Pipe

18. Down the Hatch S B There mustbe an Electric Field in the metal that is pushing the current!! N REPEL!! N Induced Current Aluminum Pipe

19. HEY BINDELL – WAIT A SECOND ……. • You said that there is a conducting loop. • You said that there is therefore a current induced around the loop if the flux through the loop changes. • But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop? • Or a current??? • ‘tis a puzzlement!

21. REMEMBER when I said E Fields start and end on CHARGES??? DID I LIE??

22. The truth • Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously. • Electric Fields created by changing magnetic fields (NON-Coulombic) can actually be shaped in loops. BUT WAIT, YOU STILL LIE!

23. Why do you STILL think I am a liar? Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO volts, won’t I? How can there be a current??

24. Yes … but this doesn’t make me a liar! Let Me Explain.

25. The POTENTIAL between two points • Is the WORK that an external agent has to do to move a unit charge from one point to another. • But we also have (neglecting the sign): Ds

26. So, consider the following: x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x E Conductor

27. THEREFORE WHAT WILL A VOLTMETER READ FROM A to A? x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x A The emf B Zero C Can’t tell E  A Conductor

28. How Big is the emf? Faraday’s Law MINUS????

29. Q: Which way does E point? A: The way that you don’t want it to point! (Lenz’s Law). Lenz’s Law Explains the (-) sign!

30. Push a magnet into a coil of two wires and a current is produced via an emf. In this case, 2 coils, each have the SAME emf so we add.. Ohm’s Law still works, so

31. Faraday’s Experiments ? ?

32. Insert Magnet into Coil

33. Remove Coil from Field Region

34. That’s Strange ….. These two coils are perpendicular to each other

35. All Involve Changing The MagneticFlux through the Loops

36. Remember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface:

37. Magnetic Flux • Applies to an OPEN SURFACE only. • “Quantity” of magnetism that goes through a surface. surface

38. In the figure below a 120-turn coil of radius 1.8 cm and resistance 6.8 Wis coaxial with a solenoid with 209 turns/cm and diameter 3.2 cm. The solenoid current drops from 1.5 A to zero in time interval Δt = 25 ms. What current is induced in the coil during Δt? 0.0224 A

39. DONE