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Magnetic field II

Magnetic field II. Plan. Motion of charge particle in electric and magnetic fields Some applications of magnetic fields. Recap………. Force due to magnetic field. Work done by F B. Recap………. Magnetic forces can only alter the direction. Recap………. Lorentz force. Combined E and B fields.

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Magnetic field II

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  1. Magnetic field II

  2. Plan • Motion of charge particle in electric and magnetic fields • Some applications of magnetic fields

  3. Recap……… Force due to magnetic field

  4. Work done by FB Recap……… Magnetic forces can only alter the direction

  5. Recap……… Lorentz force

  6. Combined E and B fields Acts on any particle, whether moving or in rest Acts on moving particle only

  7. Motion of charge particle in the crossed B and E fields

  8. If Particle for which v = E/B, passes un deflected. Particles with other fields are deflected.

  9. Calculation of e/m for electron

  10. Motion of charged particle in constant uniform Electric field Neglecting gravity A Parabolic path

  11. Substituting

  12. Constant uniform Magnetic field • B does not change the speed • It changes direction of motion • Thus particle should move in a circle, if moves in a plane perpendicular to B.

  13. x x x x x x x x x x x x x x x x x x x x x x x x FB x x x x x x x x x x x x

  14. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x FB FB x x x x x x x x x x x x x x x x x x x x x x x x Angular frequency

  15. Applications of magnetic fields

  16. Application I- Mass spectrometer R  m To separate the ionized atoms

  17. Application II - Cyclotron E. O. Lawerence (1930)

  18. World’s largest cyclotron

  19. This is at TRIUMF (CANARA) • Accelerates protons to energies up to 520 MeV • Diameter of machine = 18 m • During the course of acceleration proton travels 45 km

  20. Magnetic Mirror • Non uniform magnetic field Strong B Strong B Weak B

  21. The Hall effect • Provides a way to determine sign and density of charge carriers. w conductor

  22. + + + + + + + + + + + + - - - - - - - - - - - - - - - - If electrons are majority charge carriers E E conductor EH B

  23. + + + + + + + + + + + + - - - - - - - - - - - - - - - - If the electrons are majority charge carriers - conductor VH +

  24. Density of charge carriers

  25. Convention • If the voltage of lower terminal is negative, electrons are the majority charge carriers. • If the voltage of lower terminal is positive, holes are the majority charge carriers.

  26. Show that , in terms of hall electric field EH, and the current density j, the number of charge carriers per unit volume is given by

  27. Show that the ratio of hall electric field to the electric field is given by

  28. A metal strip 10 cm long, 1 cm wide and 1mm thick moves with constant speed v through a magnetic field of 1mT perpendicular to the strip. A potential difference of 4 V is measured between the points x and y across the strip. Calculate the speed v Vd is the velocity of strip now Vd = 0.4 m/s

  29. A strip of copper 150 m thick is placed in a magnetic field B = 0.65 T perpendicular to the plane of the strip. A current 23 A is setup in the strip. What hall potential difference will appear across the width of the strip if there were 8.5 x 1028 electrons/m3 ?

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