Electromagnet

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Electromagnet
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Wire Field

• A moving charge generates a magnetic field.
• Symmetry with experiencing force
• Perpendicular to direction of motion
• Circles around path
• Outside a straight wire the magnetic field is
  cylindrical.
• Decreases inversely with distance

B
I
3
Permeability

• The permeability m defines the strength of the B
  field in a material.
• The vacuum permeability is m0.
• Defined as m0 4p x 10-7 T m / A
• The permeability is constant for most materials.
• Usually close to m0
• Not constant for ferromagnetic materials like
  iron m gt m0

4
Mutual Attraction

• Two parallel wires with current will exert a
  force on each other.
• Wire length l
• Separation d
• Currents in the same direction attract.
• Currents in the opposite direction repel.

I1
d
I2
l
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Wire Force

• Find the force per unit length experienced by
  each of two long parallel wires in avacuum
  separated by 1.0 m carrying currents of 1.0 A.
• This is the official definition of the SI unit of
  the ampere (A).
• 1 A 1 C/s

• Convert the force on the wire into a force per
  unit length.
• F/l (4p x 10-7 Tm/A)(1.0 A)2 / 2p (1.0 m)
• F/l 2 x 10-7 N/m

The ampere is that constant current which, if
maintained in two straight parallel conductors of
infinite length, of negligible circular
cross-section, and placed 1 meter apart in
vacuum, would produce between these conductors a
force equal to 2 x 10-7 newton per meter of
length.
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Loop Field

• Each segment of a loop of current contributes a
  circular field.
• All the same direction inside loop
• Similar to a dipole pattern
• Field strength depends on radius of loop R.

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Solenoid

• Multiple parallel loops form a solenoid.
• Each of N loops contributes a share of the field
• Solenoids create very uniform magnetic fields

Tight, short coil
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Close Loops

• Field in a solenoid varies at the edges from each
  loop of wire.
• Closer loops in a solenoid make a stronger field.
• Turns per length n N/l
• Formula changes for a long coil
• A split coil would have half the field.
• Equivalent to saying half the field leaks out
  between loops.

NI
B
l
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Electromagnet

• An electromagnet is usually a solenoidal coil of
  wire.
• Increasing the permeability will increase the
  field lines.
• Iron core solenoid

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