1. v B EE ???? + -  V>0 Hall Effect h

2. v B EE >0 + -  V>0 v B EE ???? + -  V<0 Hall Effect for Opposite Charges

3. By measuring the Hall effect for a particular material, we can determine the sign of the moving particles that make up the current Hall Effect Edwin Herbert Hall (1855 - 1938)

4. What is the magnitude of the Hall effect in a metal? Knowing the charge (e) we can measure n Monovalent metals: n is the same as # of atoms per m 3 Some metals: n is larger than # of atoms per m 3 Hall Effect in a Metal

5. B=1T 5mm 0.1mm I=20A What is  V Hall for the shown copper ribbon? n Cu =8.4. 10 28 m 3 What is potential difference along 5 mm of copper ribbon to sustain current 20 A?  Cu = 6. 10 7 (A/m 2 )/(V/m 2 ) Exercise

6. Voltmeter 1 reading is POSITIVE Voltmeter 2 reading is POSITIVE Mobile charges are: A) Positive (holes) B) Negative (electrons) C) Not enough information Clicker Question

7. Current: many charges are moving Superposition: add up forces on individual charges Number of moving charges in short wire: Total force: I Force of a short wire: In metals: charges q are negative. Will this equation still work? Magnetic Force on a Current-carrying Wire

8. Short circuit the battery for maximum current. Will the wire move? Where? B FmFm What if we connect 2 batteries in series? What if we connects 2 batteries in parallel? Experiment

9. What is the total force on this wire? What is the magnitude of the force on part L if: I = 10 A B = 1 T L = 10 cm Exercise

10. I B F What will happen if current is reversed? What will happen if magnet is reversed? Experiment

11. F I B What is the force if loop is in the middle? I Experiment

12. I F Torque! Experiment

13. Ampere is defined as a current at which two very long parallel wires 1 m apart create a force on each other of 2. 10 -7 N per meter length. From this also follows that  0 /(4  ) = 10 -7 T. m/A Forces Between Parallel Wires Definition of 1 Ampere:

14. For long wire: Magnetic force on lower wire: Magnetic force on upper wire: What if current runs in opposite directions? Forces Between Parallel Wires Electric forces: “likes repel, unlikes attract” Magnetic forces: “likes attract, unlikes repel”

15. Magnetic force acts only on moving charges Mobile electrons experience magnetic force The motion of the wire is an electric side-effect of the magnetic force on the moving electrons. Why does the Wire Move? Atomic cores are not moving – no magnetic force! Atomic cores feel an unbalanced force. Wire moves down!

16. I 1 = I 2 = 10 A d = 1 cm L = 1 m F = ??? Exercise

17. X Y Z Clicker Question

18. Metal bar FmFm polarization Static equilibrium: Metal is in static equilibrium: but E  0 inside! What is  V ? Currents Due to Magnetic Forces

19. Metal bar FmFm Static equilibrium: How much force do we need to apply to keep the bar moving at constant speed? Does this polarized bar remind you anything we’ve already studied? Currents Due to Magnetic Forces

20. FmFm Non-Coulomb force drives e against F E Non-Coulomb work: What is emf of this ‘battery’? Non-Coulomb work per unit charge: Bar may have some resistance r int : ‘motional emf’ Non-Coulomb Work

21. Is round trip  V zero? E E Round-trip Potential Yes! Looks like any other emf.

22. B = 0.1 T v = 10 m/s ? ? ? I L=1cm Will it light up? To get a sizable emf – need larger B, longer wires and higher speeds If move fast past the magnet – emf will not last long! Exercise

23. P=I  V=I(emf) Are we getting something for nothing? FmFm Bar – current I: FIFI F Work: Power: Main principle of electric generators: Mechanical power is converted to electric power Moving Bar and Energy Conservation x

24. Clicker Question

25. A current carrying loop has a tendency to twist in magnetic field Compass needle: collection of atomic current loops Magnetic Torque on a Magnetic Dipole Moment

26. Torque (  ) = distance from the axle (lever arm) times perpendicular component of the force. Works with loops of any shape! Magnetic Torque: Quantitative Analysis

27. Calculate amount of work needed to rotate from angle  I to  f : Potential energy for a magnetic dipole moment Magnetic Dipole Moment: Potential Energy

28. Clicker Question Y Z X Direction of B I A)+Z B)-Z C)+Y D)-Y E)None of above

29. Potential energy for a magnetic dipole moment U= min -µB 0max µB 0 What is the energy difference between the highest and the lowest state? Picture of the U and µ in magnetic field – important in atomic and nuclear physics. Magnetic Dipole Moment: Potential Energy

30. charged tape Any magnetic field? Reference Frame

31. Two protons +e r 1 2 v v Electric force: E1E1 F 21,e Magnetic field: B1B1 Magnetic force: F 21,m Magnetic Forces in Moving Reference Frames

32. Electric force: Magnetic force: +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Ratio: (m/s) 2 =c 2 it is not accidental! Magnetic Forces in Moving Reference Frames

33. +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m For v<<c the magnetic force is much smaller than electric force How can we detect the magnetic force on a current carrying wire? Full Lorentz force: Magnetic Forces in Moving Reference Frames downward

34. +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Who will see protons hit floor and ceiling first? 20 ns 15 ns Time must run slower in moving frame. Einstein 1905: “On the electrodynamics of moving bodies” Magnetic Forces in Moving Reference Frames

35. Our detailed derivations are not correct for relativistic speeds, but the ratio F m /F e is the same for any speed: According to the theory of relativity: Relativistic Field Transformations

36. Still: Moving: Slow case: v<<c  Field transformation is consistent with Biot-Savart law Electric and magnetic fields are interrelated Magnetic fields are relativistic consequence of electric fields Magnetic Field of a Moving Particle

37. Electric Field of a Rapidly Moving Particle

38. v E Moving Through a Uniform Magnetic Field

39. There may be different mechanisms for different observers in different reference frames, but all observers can correctly predict what will happen in their own frames, using the same relativistically correct physical laws. The Principle of Relativity