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Magnetism: Magnets, Currents, and Forces - A Comprehensive Guide

Explore the fascinating world of magnetism through this guide, covering topics such as magnets, magnetic fields, Ampère's force, current interactions, torque, magnetic dipoles, Lorentz force, and more. Learn about the applications of the Hall effect and delve into theoretical examples and challenging questions on magnetic phenomena.

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Magnetism: Magnets, Currents, and Forces - A Comprehensive Guide

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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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