Chapter 29 Magnetic Fields

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Chapter 29 Magnetic Fields

• PHYS 2326-16

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Concepts to Know

• Permanent Magnets
• Magnetic Poles
• N-Pole (north seeking)
• S-Pole (south seeking)
• Magnetic Field

3
Concepts to Know

• Magnetic field lines
• Magnetic Monopole (never found)
• Magnetic force on moving charge
• Cyclotron frequency
• Velocity selector
• Mass spectrometer

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Magnetic Field

• Vector B represents the magnetic field with a
  direction from N-pole to S-pole
• Unit is Tesla
• alternate unit is Gauss 10-4 typical earth
  field 0.5 Gauss
• North pole of magnets attracted earths north
  pole which is opposite polarity

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Units

• 1 Tesla 1 N/(Coulomb meter/s)
• a Coulomb/second is an ampere so
• 1 T 1 N/(A m)
• 104 Gauss (G) 1 Tesla (T)

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Magnetic Force on Moving Charge
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Electromagnetic Force

• on a moving charge

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Electric Magnetic Force Differences

• Force for electric field is along the direction
  of the field line, force for magnetic field is
  perpendicular to the field
• Electric field force operates on any charge,
  Magnetic field force acts only on moving charge
• Electric field performs work when displacing
  charged particle, Magnetic field moves charges
  perpendicular to displacement performing no work.

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Right Hand Rule
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Right Hand Rule

• Cross product reverses sign when reverse vectors
  v x B -B x v
• Result is perpendicular to the plane that
  contains v and B.
• Direction for result F is the same as a screw
  moves when rotated in the direction from v to B
  (clockwise moves screw in and CCW moves screw out

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Charged Particle in Uniform Field

• Magnetic force F is perpendicular to v and B
• Has constant magnitude qvB.
• Motion is in a circle for uniform B and no other
  forces acting on the moving charged particle
• centripetal acceleration mv2/r
• r mv/qB (top is momentum) eqn 29.3
• ? v/r qB/m angular speed
• T2pr/v 2 p/ ? 2 pm/ qB period

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Cyclotron Frequency

• Cyclotron frequency is ? the angular speed
• A cyclotron is an essentially obsolete particle
  accelerator mostly now used in nuclear
  medicine.
• If there is a velocity component parallel to B
  there is no effect on the particle due to this
  component and the path becomes a helix

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Cyclotron

• Atom smasher
• Hollow cylinder in 2 insulated halves with a
  uniform magnetic field along the cylinder axis.
• Particles released near the center
• The two halves flip flop an E field drawing
  particles from one side to the other and back
  imparting kinetic energy each time qV
• Particle spirals out with increased speed
• Exits when fast enough to reach exit point

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Velocity Selector

• An apparatus where there is an electric field
  perpendicular to a magnetic field and both
  perpendicular to the initial motion of a stream
  of charged particles one can create a velocity
  selector.
• FB qvB (direction right hand rule)
• FE qE (direction E)
• FB - FE (- is opposite directions)
• qE qvB so that v E/B (magnitude)
• Particles with velocity v go through undeflected,
  others are diverted

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Mass Spectrometer

• Separates ions according to mass / charge ratio
• Bainbridge mass spec. beam enters a velocity
  separator then through a perpendicular magnetic
  field B
• Ions move in semicircle striking the detector at
  a point P. Negative ions are deflected one way,
  positive the other.

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Mass Spectrometer Equations

• Starting with 29.3 the radius eqn rmv/qBo for
  uniform and perpendicular motion and Bo field.
• m/q Bo r/v by rearranging
• substituting 29.7 the velocity selector equation,
  vE/B
• m/q r Bo B/E