Sources of Magnetic Field Chapter 28

1
Sources of Magnetic Field Chapter 28

• Study the magnetic field generated by a moving
  charge
• Consider magnetic field of a current-carrying
  conductor
• Examine the magnetic field of a long, straight,
  current-carrying conductor
• Study the magnetic force between current-carrying
  conductors
• Consider the magnetic field of a current loop
• Examine and use Amperes Law

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The magnetic field of a moving charge

• A moving charge will generate a magnetic field
  relative to the velocity of the charge.

3
Magnetic Field of a Moving Charge)
Permeability of free space
Magnitude of B
(28-1)
Direction of B determined by
The vector form
4
Force between two moving protons

• Two protons moving at the same velocity (much
  less than speed of light) in opposite directions.
• The electric force FE is repulsive.
• The right-hand rule indicates the magnetic force
  FM is repulsive. (i x k-j)
• Find the ratio of the magnitude of the forces.

The ratio of the two forces. Where cspeed of
light. Therefore FEgtgtFB
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Magnetic Field of a Current Element
Total magnetic field of several moving charges
vector sum of fields caused by individual charges
Let dQ charge in wire segment dl
Let A cross section area of wire
segment dl
Let n charge density in wire
segment dl
dQ nqAdl
I nqvdA
Figure 28-3
Vector form of Biot-Savart Law
(28-5)
Biot-Savart Law
Direction of dB determined by
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Magnetic field of a straight current-carrying
conductor

• Biot and Savart contributed to finding the
  magnetic field produced by a single
  current-carrying conductor.

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Magnetic Field of a Current-Carrying Conductor
Figure 28-5
If a ?? x
Based upon symmetry around the y-axis the field
will be a circle
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Magnetic Field of a Current-Carrying Conductor
Figure 28-6
where r perpendicular distance from the
current-carrying wire.
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Force between Parallel Conductors
Only field due to I shown
Each conductor lies in the field set up by the
other conductor
Note If I and I are in the same direction, the
wires attract. If I and I are in opposite
directions, the wires repel.
Substitute for B
See Example 28.5 Page 966
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Magnetic Field of a Circular Current Loop
Figure 28-12
By 0
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Magnetic Field of a Circular Current Loop
(on the axis of N circular loops) (x0)
x
Figure 28-13
Figure 28-14
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Amperes Law Ispecific then general
Similar to electric fields if symmetry exists it
is easier to use Gausss law
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Amperes Law II

• The line integral equals the total enclosed
  current
• The integral is the sum of the tangential B to
  line path

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Amperes Law (Chapter 28, Sec 6)
Figure 28-15
For Figure 28-15c
For Figure 28-15a
For Figure 28-15b
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Amperes Law
Figure 28-16
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Applications of Amperes Law Example 28-9
Field of a Solenoid (magnetic field is
concentrated in side the coil)
n turns/meter
Figure 28-20
Figure 28-21
turns/meter
where N total coil turns l total
coil length
(28-23)
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Applications of Amperes Law
Example 28-9 Field of a Solenoid
turns/meter
where N total coil turns l 4a
total coil length
Figure 28-22
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Applications of Amperes Law Example 28-10
Field of a Toroidal Solenoid (field is inside
the toroid)
N turns
Path 1
No current enclosed
Path 3
Figure 28-23
Current cancels
Path 2
(28-24)
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Magnetic materials

• The Bohr magneton will determine how to classify
  material.
• Ferromagnetic can be magnetized and retain
  magnetism
• Paramagnetic will have a weak response to an
  external magnetic field and will not retain any
  magnetism
• Diamagnetic shows a weak repulsion to an
  external magnetic field

Bohr Magneton- In atoms electron spin creates
current a loop, which produce magnetic their own
field
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Ferromagnetism and Hysteresis loops

• The larger the loops the more energy that is lost
  magnetizing and de-magnetizing.
• Soft iron produce small loops and are used for
  transformers, electromagnets, motors, and
  generators
• Material that produces large loops are used for
  permanent magnet applications