1. Apr 5 2002web.mit.edu/8.02x/www Electricity and Magnetism Announcements Review for Quiz #3 –Exp EB –Force in B-Field on free charge on current –Sources of B-Field Biot-Savart Ampere’s Law –Exp MF –Magnetic Induction Faradays Law Lenz’ Rule

2. Apr 5 2002web.mit.edu/8.02x/www Announcements Review tonight –7:30 – 9:30 PM –Room 1-190 Quiz #3 –Friday, 4-19, Walker Gym –10AM-11AM –Closed book, no calculators

3. Apr 5 2002web.mit.edu/8.02x/www Announcements Reading suggestions: 27-1,2,3,4 27-7,9 28-1,2,3,4,5,6,8 29-1,2,3,5 (eddy currents)

4. Apr 5 2002web.mit.edu/8.02x/www Electrical Breakdown Need lot’s of free charges But electrons stuck in potential well of nucleus Need energy  U to jump out of well How to provide this energy? U e-e- UU

5. Apr 5 2002web.mit.edu/8.02x/www Impact Ionization e-e- U kin  U E Define V ion =  U/q Ionization potential One e - in, two e - out Avalanche? E

6. Apr 5 2002web.mit.edu/8.02x/www Impact Ionization e-e- E To get avalanche we need:  U kin between collisions (1) and (2) > V ion * e Acceleration in uniform Field  U kin = V 2 – V 1 = e E d 12 Avalanche condition then E > V ion / mfp (1) (2) mfp mfp : Mean Free Path

7. Apr 5 2002web.mit.edu/8.02x/www Impact Ionization (i) If Density n is big ->  mfp small How big is Mean Free Path? (ii) If size  of molecules is big ->  mfp small  mfp = 1/(n  ) Avalanche if E > V ion / mfp = V ion n 

8. Apr 5 2002web.mit.edu/8.02x/www Magnetism Observed New Force between –two Magnets –Magnet and Iron –Magnet and wire carrying current –Wire carrying current and Magnet –Two wires carrying currents Currents (moving charges) can be subject to and source of Magnetic Force

9. Apr 5 2002web.mit.edu/8.02x/www Magnetic Force Force between Magnets Unlike Poles attract S N Like Poles repel S N FF S NSN FF

10. Apr 5 2002web.mit.edu/8.02x/www Magnetic Force Magnets also attract non-magnets! F Iron nail

11. Apr 5 2002web.mit.edu/8.02x/www Current and Magnet Wire, I = 0 S N Wire, I > 0 S N X

12. Apr 5 2002web.mit.edu/8.02x/www Magnet and Current F I Force on wire if I != 0 Direction of Force depends on Sign of I Force perpendicular to I Wire F

13. Apr 5 2002web.mit.edu/8.02x/www Current and Current II FF II FF AttractionRepulsion Experiment MF

14. Apr 5 2002web.mit.edu/8.02x/www Force on moving charge -q E v FEFE F L = q E + q v x B B x FBFB R = m v/(q B) Cyclotron Radius Lorentz-Force R

15. Apr 5 2002web.mit.edu/8.02x/www dW = F B dL = (q v x B) dL = (q dL/dt x B) dL = 0 Work done on moving charge -q E v FEFE W = F E L = q E L B x FBFB L Magnetic Field does no Work!

16. Apr 5 2002web.mit.edu/8.02x/www Force on Wire carrying current I dF B = dq v x B = dq dL/dt x B = I dL x B B x Wire I dL

17. Apr 5 2002web.mit.edu/8.02x/www Sources of the Magnetic Field

18. Apr 5 2002web.mit.edu/8.02x/www Currents and B-Field Current as Source of B Magnetic Field lines are always closed –no Magnetic Charge (Monopole) Right Hand Rule I

19. Apr 5 2002web.mit.edu/8.02x/www Currents and B-Field Superposition Principle! II

20. Apr 5 2002web.mit.edu/8.02x/www Currents and B-Field Solenoid: Large, uniform B inside Superposition Principle! I xxxx

21. Apr 5 2002web.mit.edu/8.02x/www Magnetic Field vs Electric Field +Q v B E r E = 1/(4   0 ) Q/r 2 r B =  0 /(4  ) Q/r 2 v x r  0 = 8.85 10 -12 C 2 /(Nm 2 )  0 = 4  10 -7 T m /A 1/(  0  0 ) = (3 10 8 m/s) 2 = c 2 Speed of Light Deep connection between B and E Field

22. Apr 5 2002web.mit.edu/8.02x/www Magnetic Field for Current I dB =  0 /(4  ) dQ/r 2 v x r for charge dQ I = dQ/dt -> dQ v = dQ dl/dt = I dl dB =  0 /(4  ) I dl x r/r 2 Magnetic Field dB for current through segment dl Law of Biot-Savart For total B-Field: Integrate over all segments dl

23. Apr 5 2002web.mit.edu/8.02x/www Magnetic Field for Current I z x y dl I r  +L -L dl r

24. Apr 5 2002web.mit.edu/8.02x/www Magnetic Field for Current I For quiz: –No long calculations –But need to understand how to use Biot- Savart to find direction of B

25. Apr 5 2002web.mit.edu/8.02x/www Remember: Gauss’ Law Electric Flux  E Integral over any closed surface Electric Charge is the Source of Electric Field

26. Apr 5 2002web.mit.edu/8.02x/www Gauss’ Law for Magnetic Fields Magnetic Flux through closed surface is 0 This says: There are no magnetic monopoles Important Law – one of Maxwell’s equations Unfortunately of limited practical use

27. Apr 5 2002web.mit.edu/8.02x/www Ampere’s Law I B Ampere’s idea: Relate Field B to its Source: I Closed Line instead of closed surface !

28. Apr 5 2002web.mit.edu/8.02x/www Ampere’s Law I B Ampere’s Law helps because we can choose integration path! Right-Hand rule for relating sign of dl and I

29. Apr 5 2002web.mit.edu/8.02x/www Ampere’s Law I B Ampere’s Law helps because we can choose integration path!

30. Apr 5 2002web.mit.edu/8.02x/www Field of a Solenoid xxxxxxxx a c d Loop C L h b B Current I n turns per unit length (infinite length) B =  0 I n

31. Apr 5 2002web.mit.edu/8.02x/www Coaxial Cable Outside field vanishes for I 2 = I 1 I2I2 Insulator Conductor I1I1

32. Apr 5 2002web.mit.edu/8.02x/www Cylindrical Conductor Uniform Current-Density J Radius R r R Uniform Current-Density J Radius R J = I/(  R 2 ) I

33. Apr 5 2002web.mit.edu/8.02x/www Magnetic Induction Currents give rise to B-Field Q: Can B-Field give rise to current? A: Only if Magnetic Flux changes with time! Took a very long time to realize...

34. Apr 5 2002web.mit.edu/8.02x/www Faradays Law Magnetic Flux (usually, A not closed surface)

35. Apr 5 2002web.mit.edu/8.02x/www Faradays Law  B can change because –|B| changes –Angle between B and A changes –|A| (size of circuit in B) changes

36. Apr 5 2002web.mit.edu/8.02x/www Faradays Law B x F v +q Moving circuit: Induced EMF is consequence of force on moving charges

37. Apr 5 2002web.mit.edu/8.02x/www Lenz’ Rule Lenz’ Rule: Sign of I ind such that it opposes the flux change that generated it

38. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v To find I ind : Calculate  B Find, what makes  B change Find sign of I ind using Lenz’ rule

39. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v To find I ind : Calculate  B Find, what makes  B change Find sign of I ind using Lenz’ rule

40. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v To find I ind : Calculate  B Find, what makes  B change Find sign of I ind using Lenz’ rule

41. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v Sign of current: Opposing change of  B -> Reducing B

42. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v Sign of current: Opposing change of  B -> Reducing B I ind

43. Apr 5 2002web.mit.edu/8.02x/www Use of Faradays Law B x v Sign of current: Opposing change of  B -> Reducing B I ind Lenz’ Rule: Effect of I ind current opposing d  B /dt is like ‘drag’ or ‘inertia’

44. Apr 5 2002web.mit.edu/8.02x/www My favorite Demo B Falling Al disk Falling Al ring is slowed down in B-Field Induced Eddy-currents Energy converted to heat

45. Apr 5 2002web.mit.edu/8.02x/www Faradays Law B x F v +q Moving circuit: Induced EMF is consequence of force on moving charges What about changing B?