Magnetism and Currents

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Magnetism and Currents
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Magnetism and Currents
In this section we learn that

• A current generates a magnetic field.
• A magnetic field exerts a force on a current.
• Two contiguous conductors, carrying currents,
  will exert forces on each other.

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Magnetic Force on Current-Carrying Wire

• We saw that magnetic fields, exert forces on
  moving charges.
• But moving charges constitute a current
• (either in vacuum or inside a conductor)
• Thus, a current-carrying wire will experience a
  force
• when placed in a magnetic field

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Magnetic Force on Current-Carrying Wire
If a segment of a wire of length L carries a
current I, in a region of space where there is a
magnetic field B, then the wire experiences a
force F given by
The force is perpendicular to the
current according to the right hand rule point
fingers in the direction of the current, rotate
or close towards magnetic filed, ? thumb points
in the direction of the force
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Magnetic Force on Current-Carrying Wire
A cooper rod 0.15 m in length, and 0.05 kg in
mass, is suspended from two thin, flexible wires,
in a magnetic field B 0.550 T, as shown.

• Find
• The direction
• The magnitude
• of the current I needed to levitate the rod

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Magnetic Forces on a Current Loop
A rectangular current loop in a magnetic field
The force on each horizontal segment is zero (I
?? B). The force on each vertical segment is F
I L B The two forces are equal and opposite ?
The loop is not displaced However the forces
exert a torque on the loop ? The loop will rotate
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Magnetic Forces on a Current Loop
The torque exerted by the magnetic force on the
loop is
In general, for an arbitrary field-loop
orientation
For a loop with N turns and area A
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Torque on a Coil
A rectangular coil with 200 turns, is placed in a
magnetic field B 0.35 T.
If the maximum torque is 0.22 N m, what is the
current I on the coil?
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Magnetic Field Produced by a Current
It was experimentally found that currents produce
magnetic fields
For a straight long wire, that carries a current
I, the lines of the magnetic field B created by
the current, are circles, centered at the wire,
and perpendicular to it. The direction of the
magnetic field is given by the right hand rule,
as shown above.
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Magnetic Field Produced by a Current
Amperes Law is used to calculate the magnetic
field produced by a current (or current-carrying
wire)
Calculated along a closed path ?0 4?x10-7 T m
/ A permeability of free space B is the
magnetic field parallel to the path
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Magnetic Field Produced by a Current
Amperes Law
For an infinite straight wire with current I

• Path is circular loop with radius r
• centered at wire and perpendicular to it
• 2. Segments are ?L all around the loop
• 3. B lines are circles around the loop
• (empirical) so B B all around, and
• ?B?L B 2?r
• Ienclosed I ? B 2?r ?0 I

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Magnetic Field Produced by a Current
For a long straight wire, that carries a current
I, the lines of the magnetic field B created by
the current, are circles, centered at the wire,
and perpendicular to it. The direction of the
magnetic field is given by the right hand rule,
as shown below.
The magnitude of the magnetic field is
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The wire carries a current of 2.4 Amp. The
particle has a charge of 52 ?C, moves with a
speed of 720 m/s and is at a distance of 13 cm
from the wire.
Find the force on the particle
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Force between two current-carrying wires

We know that a current I produces a magnetic
field B, at a distance r, given by
We know that a current I, in a magnetic field B,
experiences a force F, given by
Calculate the force exerted on each other, by two
parallel conductors (length L, current I),
separated by a distance d. Is the force
attractive or repulsive? What happens if one
current is reversed?
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Magnetic Field of a Current Loop
Note that the magnetic field of a loop is similar
to the magnetic field of a magnet bar
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Magnetic Forces Between Current Loops
If the currents are in the same direction the
two loops attract each other
If the currents are in opposite directions the
two loops repel
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Magnetic Field of a Solenoid
A solenoid is a long wire wound into a
succession of closely spaced loops
The magnetic field inside the solenoid is
Ideally, for a very long solenoid, the magnetic
field is zero outside the solenoid, and parallel
to the axis, and uniform in strength, inside.
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Magnetic Field of a Solenoid
What would happen if we place a magnet bar near
the solenoid?
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A Solenoid
.. is a closely wound coil having n turns per
unit length.
current flows into plane
current flows out of plane
What direction is the magnetic field?
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A Solenoid
.. is a closely wound coil having n turns per
unit length.
current flows into plane
current flows out of plane
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A Solenoid
Consider longer and longer solenoids.
Fields get weaker and weaker outside.
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Apply Amperes Law to the loop shown. Is there a
net enclosed current? In what direction does the
field point? What is the magnetic field inside
the solenoid?
current flows into plane
current flows out of plane
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Apply Amperes Law to the loop shown. Is there a
net enclosed current? In what direction does the
field point? What is the magnetic field inside
the solenoid?
current flows into plane
current flows out of plane
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Magnetic Materials
The phenomenon of magnetism is due mainly to the
orbital motion of electrons inside materials, as
well as to the intrinsic magnetic moment of
electrons (spin).
There are three types of magnetic behavior in
bulk matter Ferromagnetism Paramagnetism Diama
gnetism
Remind me to ask you why does the magnet stick
to the refrigerator?