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Magnet Forces and Magnetic Fields

Magnet Forces and Magnetic Fields. 1) Magnets and Magnetic Fields. a) Natural permanent magnets Like poles repel, unlike attract come in pairs (no monopoles) Interact with earth; define N (or north-seeking) pole as pole attracted to North pole of earth. b) Magnetic field direction:

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Magnet Forces and Magnetic Fields

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  1. Magnet Forces and Magnetic Fields

  2. 1) Magnets and Magnetic Fields a) Natural permanent magnets • Like poles repel, unlike attract • come in pairs (no monopoles) • Interact with earth; define N (or north-seeking) pole as pole attracted to North pole of earth

  3. b) Magnetic field direction: - direction of force on N pole B

  4. c) Field of dipole

  5. d) Magnetostatics for poles (identical to electrostatics for charges) • 2 types: N, S vs +,- • Unlike attract, like repel • Inverse square law • Force along joining line • Magnetic Field:

  6. e) Why study magnetism? • No monopoles (yet) • Poles (dipoles) produced by moving charges (no direct control of pole distribution) • Charges affected by magnetic field i.e. fundamental unit is still charge; want magnetic field due to charge, and force on charge due to magnetic field

  7. 2) Magnetic field due to current(direction) • Oersted (1820)

  8. Forceper unit length 3) Magnetic force on current a) Orthogonal case Direction from RHR1: B fingers, I thumb, F palm defines B

  9. Units:

  10. Force per unit length b) General case

  11. 4) Force between parallel wires

  12. FE v FB FB v FE + + Attraction or repulsion? Does it depend on reference frame?

  13. - - - - - - + + + + + + v v

  14. • Then • Define Ampere as the quantity of current that produces a force per unit length of 2 x 10-7 N/m for separation of 1 m • This defines C and gives

  15. Then • Permeability of free space

  16. 5) Field due to long straight wire(magnitude)

  17. 6) Force on a moving charge • Zero at rest • Zero parallel to B • Max perpendicular to B

  18. • Proportional to component of v perp to B (Alternative definition of B) • Perpendicular to B • Perpendicular to v

  19. 7) Motion of a charge in a magnetic field a) Constant force motion is parabolic electric or gravitational field not everywhere perp to velocity not magnetic field

  20. radial field (circular motion) mass on a string b) Constant magnitude perpendicular to motion motion is circular magnetic field produces circular motion (initial vel. perp. to B)

  21. Force due to the field: For circular motion: So, r depends on v, B angular freq. independent of speed, radius

  22. Tracks in a bubble chamber • electron-positron creation • 1, 3 positive • 2 negative • energy: 3 > 2 > 1 • energy decreases by collisions

  23. Example: Find speed and radius for proton B = 0.10 T V = 2100 V

  24. F displacement, x Work by a force F c) Work done by magnetic field For a magnetic field, Work = 0

  25. Force due to E (down): d) Velocity selector Force due to B (up): For zero deflection, FE = FB :

  26. Ion energy: e) Mass Spectrometer Radius of motion:

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