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Chapter 25 Magnetism

Chapter 25 Magnetism. Magnets. Magnets : interact on iron objects / other magnets. 1) North pole ( N-pole ) & south pole ( S-pole ). 2) Opposite poles attract, like poles repel. 3) Magnetic monopoles have not been found. 2. create. interact on. Magnetic field.

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Chapter 25 Magnetism

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  1. Chapter 25 Magnetism

  2. Magnets Magnets: interact on iron objects / other magnets 1) North pole (N-pole) & south pole (S-pole) 2) Opposite poles attract, like poles repel 3) Magnetic monopoles have not been found 2

  3. create interact on Magnetic field Magnets interact each other by magnetic field Magnets magnetic field magnetic field lines 3

  4. I Currents produce magnetism H. C. Oersted found in 1820: An electric current produces a magnetic field. magnet ←→ magnet magnet ←→ current current ←→ current (molecular currents) A. M. Ampère: Magnetism is produced by electric currents. 4

  5. Nature of magnetism Magnetism is the interaction of electric currents or moving charges. A. Einstein: electromagnetic field in relativity Magnetic field: 1) Created by / interacts oncurrents or moving charges 2) Closed field lines without beginning or end 5

  6. I, l Force on a current Magnetic field exerts a force on a current (wire) It’s called Ampère force 1) Uniform field: 6

  7. Define magnetic field by using: where is a differential length of the wire Definition of B SI unit for B : Tesla (T), 1T =1N/A·m =104 G 2) General case: nonuniform B & curved wire integral over the current-carrying wire 7

  8. Example1: Uniform magnetic field . Show that any curved wire connecting points A and B is exerted by the same magnetic force. F on curved wire Solution: Total magnetic force: It is equivalent to a straight wire from A to B 8

  9. a I R b o B . Discussion: 1) It is valid only if B is uniform 2) Total force exertedon a current loop (coil)? 3) 9

  10. Example2:I1 and I2 are on the same plane. What is the force on I2, if the magnetic field created by I1 is I1 a b I2 dl r dr Nonuniform field Solution: Total force on I2 direction? 10

  11. I1 I2dl R I2 Interaction of currents Question: Infinitely long current I1 and circular current I2 are insulated and on the same plane. What is the force between them? 11

  12. *Railgun Weapon for space war in future → railgun High power ~ 107 J High velocity ~ 10Mach Battery & rail 12

  13. Torque on a current loop (1) Rectangular current loop in a uniform field 13

  14. Torque on a current loop (2) Torque on the loop: Magnetic dipole moment: where the direction is defined by right-hand rule compare with 14

  15. Magnetic dipoles These are valid for any plane current loop A small circular current → a magnetic dipole 1) =/2: maximum torque 2) =0 or : stable / unstable equilibrium 3) N loops coil / solenoid: 15

  16. Magnetic moment of atom Example3: Show that μ of an electron inside a hydrogen atom is related to the orbital momentum L of the electron by μ=eL/(2m). Solution: Orbital (angular) momentum: Classic / quantum model 16

  17. . μ of rotating charge Example4: A uniformly charged disk is rotating about the center axis (σ, R, ω). Determine the magnetic moment. Solution: Magnetic moment Rotating charge: Total magnetic moment: direction? 17

  18. If q < 0, has an opposite direction to Force on moving charges Magnetic field exerts a force on a moving charge: → Lorentz force 1) Magnitude: 2) Direction: right-hand rule, sign of q 3) Lorentz force doesn’t do work on the charge! 18

  19. 1) : 2) : Motion in a uniform field (1) Point charge moves in a uniform magnetic field Free motion Uniform circular motion 19

  20. Motion in a uniform field (2) 3) General case: Free motion + uniform circular motion Combination: the charge moves in a helix 20

  21. plasma coil coil Aurora & magnetic confinement Aurora: Caused by high-energy charges Magnetic confinement: “magnetic mirror” 21

  22. Lorentz equation Example5:A proton moves under both magnetic and electric field. Determine the components of the total force on the proton. (All in SI units) Solution: Total force 22

  23. Different regions Example6:A proton moving in a field-free region abruptly enters an uniform magnetic field as the figure.(a) At what angle does it leave ? (b) At what distance x does it exit from the field? Solution: Circular motion (a) (b) 23

  24. - Challenging question Question:A electron is released from rest. If the field is shown as the figure, how does the electron move under the field? What is the path? The path is a cycloid 24

  25. The Hall effect Current-carrying conductor / semiconductor placed in a magnetic field → Hall voltage Lorentz force→Hall field→equilibrium IH→ Hall current 25

  26. Applications of Hall effect 1) Distinguish the semiconductors 2) Measure magnetic field Hall sensor / switch 3) Measure the carrier concentration 26

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