Magnetic Moments

1
Magnetic Moments

• When you place a loop of wire carrying a current
  in a magnetic field, the sections of the wire
  that arent parallel to the magnetic field will
  experience a force
• Remember,
• Since there will be two sides of the loop that
  experience opposite forces, a torque is exerted
  on the loop!

2
Magnetic Moments
The current flows upward in the left arm of the
loop. The force exerted by the magnetic field is
into the page. The current flows downward in
the right side of the loop. The force is out of
the page. The combination is a torque which will
rotate the loop.
3
Magnetic Moments
The same situation looking from above the loop.
The current is upward in the left wire and
downward in the right wire. The resulting forces
are shown. Clearly, the loop experiences a
torque which will make the loop rotate.
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Magnetic Moments
As the coil rotates, notice that the effective
moment arm is decreased. This lowers the torque,
although the forces are unchanged.
5
Magnetic Moments
6
Magnetic Moments

• If we have N turns of wire in the loop
• If the coil makes an angle other than 90o with
  the magnetic field, we just throw in a sine term

7
Magnetic Moments

• The term NIA is called the magnetic dipole moment
  of the coil and is actually a vector
• The direction of the area is perpendicular to the
  plane of the coil
• These ideas are independent of the shape of the
  coil and depend only on the area!

8
Galvanometers

• We can use the applied torque to measure the
  current!!!
• The torque is proportional to the current
• Recall Hookes Law for springs

9
Galvanometers
The higher the current, the more we twist the
spring and the stronger the resistive torque
becomes. The rotation stops when the two torques
are equal. We can calibrate the pointer position
with the current in the coil, and thus have an
instrument to measure current.
10
Galvanometers

• You may have figured out that as the coil turns,
  the angle changes and the sine term comes into
  play.
• To fix this we change the coil in a shrewd way
  to take angle out of the picture!!!

11
Galvanometers
We curve the poles of the magnet and wrap the
coil around an iron core. The iron concentrates
the field lines and the curve keeps the lines
parallel to the face of the coil!! This takes
angle out of the game.
12
DC Motors
Again, we need to be sneaky. When the coil
rotates to the point where the sine is zero, we
need to reverse current direction in the coil,
so we can continue to exert a torque in the same
direction as the rotational inertia keeps the
coil going past that point. See the brushes
which make the connection to the coil!
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The Hall Effect

• The Hall Effect results from the force exerted by
  a magnetic field on a moving charge.
• We will lock a conductor so it cant move in a
  magnetic field. When electrons move through the
  conductor, they are forced to one side. This
  creates a charge separation and a resulting
  electric field.

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The Hall Effect
Electrons move from left to right. The magnetic
field is into the page. The force on the
electron is downward. See the charge separation
in the conductor as positive ions are left behind
on top.
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The Hall Effect
The electrons stop moving when the force of the
electric field is equal to the magnetic force.
This creates a stable configuration with balanced
forces.
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The Hall Effect

• Suppose we have a material in which the charge
  carriers are not electrons, but are positively
  charged.
• We have always said that there is no difference
  between negative charges going left to right and
  positive charges going right to left when we
  deal with currents
• NOT TRUE for the Hall Effect

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The Hall Effect
Notice that the Hall EMF is now reversed for
positive charge carriers! Provides a means of
telling what sign a charge carrier has. We will
find positive charge carriers when we deal with
semiconductors.
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The Hall Effect

• Since the Hall EMF is directly proportional to
  magnetic field, we can measure the field strength
  by measuring the EMF.
• The device is called a Hall probe.
• Just calibrate EMF vs. B

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Mass Spectrometry

• Use the magnetic force on a moving charged
  particle to separate particles by mass
• Useful for analysis and identification

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Mass Spectrometry
Magnetic fields are out of the page. Between
slits for ions with speed v, forces are balanced
between electric and magnetic fields.
qEqvB. All ions out of slit two have the same
speed vE/B. These ions are subject to a force at
right angles to their velocity
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Mass Spectrometry
22
Ferromagnetism

• Iron can be permanently magnetized
• Due to alignment of atoms orientation

Regions align all atoms. These are called
domains. Normally, domains are randomly
oriented. Can be aligned with an external
magnetic field and they retain alignment.