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Exploring Magnetism: Applications and Physics

Discover the versatile applications of magnetism in refrigerators, motors, navigation, magnetic tapes, music, TV, MRI, high-energy physics research, and more. Learn about the physics behind magnetic forces and magnetic dipoles. Understand the motion of charged particles in a magnetic field and delve into concepts like centripetal force and rotational motion. Solve problems related to magnetic fields, current loops, and electron orbits. Enhance your knowledge of magnetism and its practical implications.

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Exploring Magnetism: Applications and Physics

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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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