Chapter 29 Magnetic Fields continued

1
Chapter 29 Magnetic Fieldscontinued

• PHYS 2326-16

2
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.

4
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 force 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

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Chapter 29 Magnetic Forces on Currents

• PHYS 2326-17

13
Concepts to Know

• Magnetic Force on a Current Element
• Magnetic Dipole
• Magnetic Dipole Moment
• Magnetic Torque on a current loop
• Solenoid

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Why Magnetics Might be Important during Your
Careers

• Control and automation of ????
• Rail guns magnetic propulsion of material
• Magnetic levitation trains, transport
• Electric/hybrid vehicle design
• Fusion power generation containment
• EMP protection
• Your latest electric kitchen gizmo invention to
  be peddled by Ronco

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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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Solenoid

• A solenoid is a coil of wire wrapped as a helix
• It also refers to a device that uses an
  electromagnet to switch something on or off
• A relay is a solenoid device for switching an
  electric circuit on/off.
• A solenoid may actuate a valve for liquids or
  gases to permit or block flow

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Magnetic Force on a Current Element

• Current is free charges moving with the drift
  velocity vd.
• I n q vd A

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Magnetic Force on a Current Loop

• See Example 29.4
• Conclusions for uniform field are
• Force on conductor depends only on end points
• Net magnetic force on closed current loop is zero

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Magnetic Torque

• Given a current carrying loop of 4 sides
• Sides 13 are parallel to field no effect
• Sides 24 are perpendicular to field

Side View
Top View
1
F
A
a
I
x
2
.
4
F
b
B
B
3
20
Magnetic Torque
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For a Solenoid

• A solenoid is a coil of wire with more than 1
  turn
• µ N I A magnetic dipole moment for a coil of
  N turns, I amperes and area A

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Potential Energy of Magnetic Dipole