Magnetism: Force and Field

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Magnetism Force and Field
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General Characteristics

• Like poles repel
• Unlike poles attract
• You can never isolate a north pole from a south
  pole.

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Earths Magnetic Field

• North pole of compass is attracted to the north.
  Therefore, the north pole is a magnetic south
  pole.
• Measurements have indicated that the earths
  magnetic field is decreasing.
• There is evidence of pole reversal at the
  mid-Atlantic ridge.

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Earths Magnetic Field

• Barnes noticed a 5 reduction in the earths
  magnetic field in 130 yrs.
• Reversing Magnetic Field recorded in the earths
  crust.
• Humphreys proposes rapid reversals due to the
  flood.

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Unique Earth

• Stable sun
• Nearly circular orbit
• Water present in 3 phases
• Magnetic field
• Ozone
• Nitrogen atmosphere
• Probability
• 1069 to 1

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Magnetic Force

• Magnetic fields exert forces on moving charges.
• Magnitude of the force is given by
• Direction of the force is determined by the
  right-hand rule.
• Units - Wb/m2 or T (1T 104G)

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Force on a proton

• Ex. What is the force on a proton traveling 60
  with respect to a uniform magnetic field of 2.5
  tesla at half the speed of light?

Only the perpendicular component of the
velocity produces a magnetic force.
Will move in a helix.
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Velocity Selector

• Lorentz Force
• When F 0 and
• then

E
p
B
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Mass Spectrometer

• When the velocity is known, then the mass is
  known by the charge and radius of curvature in a
  B field.

B
E
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Motion in a Magnetic Field

• component of velocity will cause circular
  motion.

r
B
Cyclotron Frequency
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Cyclotron

• 2 sets of D magnets are set up to bend charged
  particles into a circular path.
• An alternating electric field between the D
  magnets causes the particles to speed up.
• The particles spiral outward with increasing
  speed.

E
B
p
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Force on a Wire

• In a uniform magnetic field a straight wire
  experiences a force.
• In general for all wires in magnetic fields
• For a uniform magnetic field only the
  displacement from the starting point to the
  ending point affects the magnetic force.

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Force on a Loop

• Ex. What is the force on a semicircle shaped
  loop, if the straight portion has a force of 8 N
  on it?
• What is the current in the loop if the radius of
  curvature is 0.75m and the magnetic field is 2 T?

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Torque on a Loop

• Remember
• For a uniform field to the current
• then for a force arm
• to the magnetic force

B
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Torque on a Dipole

• Remember
• then

F
F
E
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Moments

• Magnetic Moment
• Electric Dipole Moment

is a unit vector going from the negative
to the positive charge
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Electric Energy

• Ex. What is the torque on a circular loop with
  radius of 5 cm rotating at 0.25 Hz if it has a
  current of 1A and is in a uniform magnetic field
  of 0.2 T?

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Biot-Savart Law

• Magnetic fields are generated by moving charge.

I
ds
r
m0 - permeability of free space
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B Field for a Wire

• For a thin straight conductor carrying current
  the magnetic field is
• Use the right hand rule to determine the
  direction. (Place thumb in direction of current
  and B Field is in direction of fingers grabbing
  the wire.)
• Effect of moving charges is transmitted at the
  speed of light. Magnetism is the result of moving
  charges.

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Attraction of Wires

• Magnetic Force of one wire interacts with the
  current in the other wire.
• This concept is used to define the Ampere and the
  Coulomb.
• Find the attraction between two wires carrying 10
  A each that are 1 mm apart?

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Amperes Law

• The line integral of Bds around any closed path
  equals m0I, where I is the total steady current
  flowing through the surface bounded by the closed
  path.

I
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B field for a Wire

• Chose a closed loop which follows the magnetic
  field, which is constant in value.
• Therefore,
• This matches our result from using Biot-Savart
  Law.

r
I
ds
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B field for a Toroid

• A toroid is a donut shape with a coil wrapped
  around it.
• Therefore,
• Get a concentrated field inside the toroid.

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B field in a Solenoid

• A long wire is wound in the form of a helix.
• Let a solenoid consist of N turns over a distance
  of l.

l
ds
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Gauss Law

• Magnetic Flux - Amount of magnetic field leaving
  a surface.
• Since magnetic field lines form loops you can
  never find an isolated magnetic pole.

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Magnetism

• Sources
• Orbital magnetic moment of an electron.
• Spin magnetic moment of an electron.
• Types of Magnetism
• Ferromagnetic
• Paramagnetic
• Diamagnetic

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Ferromagnetism

• Consists of small regions (called domains) where
  the magnetic moments are aligned.
• Using an external magnetic field you can align
  the domains.

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Hysteresis

• A remnant magnetic field remains when an external
  field is removed.
• To remove a magnetic field a oscillating magnetic
  field with decreasing amplitude needs to be used.

Binternal
Bapplied
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Magnetic Recording

• Iron embedded on a surface can store direction of
  a magnetic field.

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Paramagnetism

• Weak interaction between magnetic moments within
  the material.
• Magnetic moments will align in the presence of an
  external magnetic field.
• If the material is lowered below the Curie
  temperature, it will maintain its magnetic
  alignment.

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Diamagnetism

• Has no permanent magnetic moment.
• The presence of an external magnetic field causes
  a weak opposing magnetic moment in the material.

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