19'8 Magnetic Field of a long straight wire

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19.8 Magnetic Field of a long straight wire

• Danish scientist Hans Oersted (1777-1851)
  discovered (somewhat by accident) that an
  electric current in a wire deflects a nearby
  compass needle.
• In 1820, he performed a simple experiment with
  many compasses that clearly showed the presence
  of a magnetic field around a wire carrying a
  current.

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Magnetic Field due to Currents

• The passage of a steady current in a wire
  produces a magnetic field around the wire.
• Field form concentric lines around the wire
• Direction of the field given by the right hand
  rule.
• If the wire is grasped in the right hand with the
  thumb in the direction of the current, the
  fingers will curl in the direction of the field
  (second right-hand rule).
• Magnitude of the field

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Magnitude of the field
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r
B
mo called the permeability of free space
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Amperes Law
Consider a circular path surrounding a current,
divided in segments Dl, Ampere showed that the
sum of the products of the field by the length of
the segment is equal to mo times the current.
Andre-Marie Ampere
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r
B
Dl
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Consider a case where B is constant and uniform
Then one finds
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19.9 Magnetic Force between two parallel
conductors
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Force per unit length
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Definition of the SI unit Ampere
Used to define the SI unit of current called
Ampere.

• If two long, parallel wires 1 m apart carry the
  same current, and the magnetic force per unit
  length on each wire is 2x10-7 N/m, then the
  current is defined to be 1 A.

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Example 1 Levitating a wire

• Two wires, each having a weight per units length
  of 1.0x10-4 N/m, are strung parallel to one
  another above the surface of the Earth, one
  directly above the other. The wires are aligned
  north-south. When their distance of separation is
  0.10 mm what must be the current in each in order
  for the lower wire to levitate the upper wire.
  (Assume the two wires carry the same current).

l
1
I1
2
d
I2
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Two wires, each having a weight per units length
of 1.0x10-4 N/m, are strung parallel to one
another above the surface of the Earth, one
directly above the other. The wires are aligned
north-south. When their distance of separation is
0.10 mm what must be the current in each in order
for the lower wire to levitate the upper wire.
(Assume the two wires carry the same current).
F1
1
I1
B2
mg/l
2
d
I2
l
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Example 2 magnetic field between the wires
The two wires in the figure below carry currents
of 3.00A and 5.00A in the direction indicated.
Find the direction and magnitude of the magnetic
field at a point midway between the wires.
5.00 A
3.00 A
20.0 cm
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19.10 Magnetic Field of a current loop

• Magnetic field produced by a wire can be enhanced
  by having the wire in a loop.

Dx1
I
B
Dx2
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19.11 Magnetic Field of a solenoid

• Solenoid magnet consists of a wire coil with
  multiple loops.
• It is often called an electromagnet.

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Solenoid Magnet

• Field lines inside a solenoid magnet are
  parallel, uniformly spaced and close together.
• The field inside is uniform and strong.
• The field outside is non uniform and much weaker.
• One end of the solenoid acts as a north pole, the
  other as a south pole.
• For a long and tightly looped solenoid, the field
  inside has a value

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Solenoid Magnet

• n N/l number of (loop) turns per unit
  length.
• I current in the solenoid.

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Example Magnetic Field inside a Solenoid.

• Consider a solenoid consisting of 100 turns of
  wire and length of 10.0 cm. Find the magnetic
  field inside when it carries a current of 0.500 A.

N 100 l 0.100 m I 0.500 A
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ComparisonElectric Field vs. Magnetic Field
Electric Magnetic Source Charges Moving
Charges Acts on Charges Moving
Charges Force F Eq F q v B
sin(q) Direction Parallel
E Perpendicular to v,B
Field Lines Opposites Charges Attract
Currents Repel