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Magnetic field

Magnetic field. Chapter 28. Magnetism. Refrigerators are attracted to magnets!. Where is Magnetism Used??. Motors Navigation – Compass Magnetic Tapes Music, Data Television Beam deflection Coil Magnetic Resonance Imaging (MRI) High Energy Physics Research. Cathode. Anode. (28 – 8).

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Magnetic field

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  1. Magnetic field Chapter 28

  2. Magnetism • Refrigerators are attracted to magnets!

  3. Where is Magnetism Used?? • Motors • Navigation – Compass • Magnetic Tapes • Music, Data • Television • Beam deflection Coil • Magnetic Resonance Imaging (MRI) • High Energy Physics Research

  4. Cathode Anode (28 – 8)

  5. N S Consider a Permanent Magnet The magnetic Field B goes from North to South.

  6. Units

  7. Typical Representation

  8. q • If the charge is moving, there • is a force on the charge, • perpendicularto both v and B. • F = q vxB q A Look at the Physics There is NO force on a charge placed into a magnetic field if the charge is NOT moving. There is no force if the charge moves parallel to the field.

  9. The Lorentz Force This can be summarized as: F or: v q m B q is the angle between B and V

  10. Nicer Picture

  11. The Wire in More Detail Assume all electrons are moving with the same velocity vd. L B out of plane of the paper

  12. i . (28 – 12)

  13. Current Loop What is force on the ends?? Loop will tend to rotate due to the torque the field applies to the loop.

  14. F=BIL F q L S N B I F F=BIL Magnetic Force on a Current Loop

  15. Magnetic Force on a Current Loop Simplified view: F=BIL q L d I F=BIL

  16. Magnetic Force on a Current Loop Torque & Electric Motor Simplified view: F=BIL q L d I F=BIL

  17. F=BIL for a current loop q L d I F=BIL Magnetic Force on a Current LoopTorque & Electric Motor

  18. Side view Top view C C (28 – 13)

  19. Magnetic Force on a Current Loop Torque & Magnetic Dipole By analogy with electric dipoles, for which: The expression, implies that a current loop acts as a magnetic dipole! Here is the magnetic dipole moment, and (Torque on a current loop)

  20. Dipole Moment Definition • Define the magnetic • dipole moment of • the coil m as: • =NiA t=m x B We can convert this to a vector with A as defined as being normal to the area as in the previous slide.

  21. (28 – 14)

  22. R L L R L R (28 – 15)

  23. Motion of a chargedparticle in a magneticField

  24. v B + + + + + + + + + + + + + + + + + + + + F Trajectory of Charged Particlesin a Magnetic Field (B field points into plane of paper.) B + + + + + + + + + + + + + + + + + + + + v F

  25. Trajectory of Charged Particlesin a Magnetic Field (B field pointsinto plane of paper.) v B B + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + v F F Magnetic Force is a centripetal force

  26.  = s / r  s =  r  ds/dt = d/dt r  v =  r s  = angle,  = angular speed,  = angular acceleration  r at = r  tangential acceleration ar = v2 / rradial acceleration  The radial acceleration changes the direction of motion, while the tangential acceleration changes the speed. at ar Uniform Circular Motion  = constant  v and ar constant but direction changes ar  KE = ½ mv2 = ½ mw2r2 ar = v2/r = 2 r v F = mar = mv2/r = m2r Review of Rotational Motion

  27. Radius of a Charged ParticleOrbit in a Magnetic Field Centripetal Magnetic Force Force = v B + + + + + + + + + + + + + + + + + + + + F r

  28. v B + + + + + + + + + + + + + + + + + + + + F r Cyclotron Frequency The time taken to complete one orbit is: V cancels !

  29. Smaller Mass Mass Spectrometer

  30. An Example A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B  such that

  31. r Problem Continued

  32. #14 Chapter 28 A metal strip 6.50 cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B= 1.20mTdirected perpendicular to the strip, as shown in the Figure. A potential difference of 3.90 ηV is measured between points x and y across the strip. Calculate the speed v.

  33. 21.  (a) Find the frequency of revolution of an electron with an energy of 100 eV in a uniform magnetic field of magnitude 35.0 µT . (b) Calculate the radius of the path of this electron if its velocity is perpendicular to the magnetic field.

  34. 39.  A 13.0 g wire of length L = 62.0 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.440 T. What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads?

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