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Hall Effect for Opposite Charges

Hall Effect for Opposite Charges. E . E . v. v. B. B. >0. ????.  V >0. -. -. +. +.  V <0. Magnetic Force on a Current-carrying Wire. Current: many charges are moving Superposition: add up forces on individual charges. Number of moving charges in short wire:. I.

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Hall Effect for Opposite Charges

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

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

  3. Exercise 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

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

  5. Forces Between Parallel Wires Definition of 1 Ampere: 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

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

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

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

  9. Currents Due to Magnetic Forces Metal bar Fm 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?

  10. Non-Coulomb Work Fm Non-Coulomb force drives e against FE Non-Coulomb work: What is emf of this ‘battery’? Non-Coulomb work per unit charge: ‘motional emf’ Bar may have some resistance rint:

  11. Round-trip Potential E E What electric fields are produced by the surface charges? Is round trip V zero? Round trip due to these Coulomb electric fields has to be zero.

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

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

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

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

  16. Magnetic Dipole Moment: Potential Energy Potential energy for a magnetic dipole moment min -µB U= 0 max 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.

  17. Reference Frame Any magnetic field? charged tape

  18. Magnetic Forces in Moving Reference Frames +e v 1 r F21,m B1 2 +e v E1 F21,e Electric force: Two protons Magnetic field: Magnetic force:

  19. Magnetic Forces in Moving Reference Frames +e v 1 r F21,m B1 2 +e v E1 F21,e =c2 Electric force: Magnetic force: Ratio: (m/s)2 it is not accidental!

  20. Magnetic Forces in Moving Reference Frames +e v 1 r F21,m B1 2 +e v E1 F21,e 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: downward

  21. Magnetic Forces in Moving Reference Frames +e v 1 r F21,m B1 2 +e v E1 F21,e 20 ns 15 ns Who will see protons hit floor and ceiling first? Time must run slower in moving frame. Einstein 1905: “On the electrodynamics of moving bodies”

  22. Moving Through a Uniform Magnetic Field E v

  23. The Principle of Relativity 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.

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