Magnetic Fields due to Current in a Wire

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Magnetic Fields due to Current in a Wire
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A Surprising Discovery

• In 1820, Hans Christian Oersted discovered that
  moving charges create a magnetic field.

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Magnetic Field of a Current Carrying Wire

• Hans Christian Oersted discovered that a wire
  carrying current influenced the needles of
  nearby compasses.
• By applying right-hand-rule 2, the direction of
  the magnetic field can be determined around the
  wire.
• For an infinitely long straight wire
• The constant ?o is the permeability
  of free space (4? x 10-7 T
  m/A).
• Note B is inversely proportional to r.
• Magnetic Field due to a wire.

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Magnetic Force on Current Carrying Wires

• When two current carrying wires have current
  flowing in the same direction, they will be
  attracted to one another (a).
• When two current carrying wires have current
  flowing in opposite directions, they will repel
  (b).

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Magnetic Force on Current Carrying Wires(cont.)
-The influence of the magnetic field of wire (a)
on wire (b). -Using RHR 1, we see that the
force by wire (a) on wire (b) is such that it is
attracted to wire (b). -The same is true for
wire (b) on wire (a). -However, even if the
current is flowing in opposite directions, wont
the conductors be attracted to one another?
(a)
(b)
x
B
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Magnetic Force on Current Carrying Wires(cont.)
-No. Note that the magnetic fields cancel each
other between the conductors while they add
outside for two parallel conductors with current
moving in the same direction. -As a result the
conductors are attracted to one another. -In the
case where the conductors have current flowing in
opposite directions, the field lines add between
them while they cancel outside. This results in
a net repulsion between the two conductors.
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Magnetic Field in a Loop of Wire

• For the center of a circular loop, the magnetic
  field is
• Where
• N number of turns of wire.
• R Radius of loop.

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Magnetic Field of a Solenoid

• For a solenoid, the magnetic field is given by
• B ?oNI
• L
• B ?onI
• Where
• n the number of turns per length of coil N/L

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Key Ideas

• The strength of a magnetic field created by
  current in a wire is inversely proportional to
  the distance from the wire.
• Two current carrying wires will attract each
  other if the current flows in the same direction
• Two current carrying wires will repel each other
  if the current is in opposite directions.
• The strength of the magnetic field of current in
  a loop is proportional the current in the loop
  and the number of loops.