Lecture 7 Magnetic Field and Magnetic Force

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Lecture 7Magnetic Field and Magnetic Force
Chapter 19.1 ? 19.6
Outline

• Magnets
• Magnetic Field
• Magnetic Force
• Motion in a Magnetic Field

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Magnets
The simplest magnet is a somehow magnetized bar
of iron. It attracts and holds other pieces of
iron. Most of the force a magnet exerts from its
ends.
A magnets ends point north and south. The
north-pointing end is called the north pole. The
south-pointing end is called the south pole.
Like magnet poles repel one another, unlike poles
attract one another.
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Magnetic Poles
Positive and negative charges in neutral matter
can be separated from each other. The north and
south magnetic poles cannot be separated.
Every time we saw a magnet in half, it gets the 2
poles.
Magnetic properties have all substances, but to a
different extent. Iron is one of the best magnets.
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Magnetic Field
The presence of a magnet alters properties of
space near it.
The altered space is called a force field. We
cannot see a force field, but can detect its
presence by its effects. The form of the magnetic
field can be traced by a pattern of iron
filings. They line up in the direction in which a
piece of iron would move if put there (field
lines). They gather most thickly where the force
on the iron would be the greatest (larger field
line density).
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Origin of the Magnetic Field
Every electric current has a magnetic field
around it. This was first shown by Oersted in
1820.
The current and the field are perpendicular to
each other. The direction of the magnetic field
can be found by encircling the wire with the
fingers of the right hand. The direction of the
current along the wire is then shown by the thumb.
All magnetic fields originate from moving
electric charges.
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The Electromagnetic Field
An electric charge at rest is surrounded by only
an electric field. When it is moving, a magnetic
field around it appears.
The relative motion between the charge and
observer is needed to produce a magnetic field.
Both an electric and magnetic field are aspects
of a single electromagnetic field that surrounds
every electric charge.
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Magnetic Field
A charged object, moving through a magnetic
field, experiences a magnetic force. The force
has a maximum strength when the charge moves
perpendicularly to the magnetic filed lines.
The magnetic force is experimentally defined as
q is the magnitude of a test charge v is the
charge velocity B is the strength of the external
magnetic filed ? is the angle between the
directions of v and B
F q v B sin ?
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Units of Magnetic Field
The SI unit of magnetic fields is tesla (T)
F B ???? q v sin ?
F q v B sin ?
?
N N T ???? ??
C m / s A m
If v B ? F 0 If v ? B ? F q v B
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Magnetic Field
Problem A proton moves perpendicularly to a
uniform magnetic field B at 107 m/s and
experiences an acceleration of 2 1013 m/s2 in the
x direction when its velocity is in z
direction. Find the magnitude and direction of
the field.
F B ???? q v sin ?
F m a
m 1.67 10?27 kg F 3.34 10?14 N q 1.6 10?19
C sin ? 1 B 0.02 T
Direction of B is ?y
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Magnetic Force on a Current-Carrying Conductor
Current is a collection of moving charges ? the
resultant force on the wire (conductor) is the
sum of the individual forces on the charged
particles.
Let us calculate a force acting on a piece of
wire of length l and cross-sectional area A in a
uniform external magnetic field B, perpendicular
to the wire.
vd ? drift velocity of the charge n ? total
number of charges per volume
Fmax (q vd B) (n A l)
I n q vd A
Fmax B I l
F B I l sin ?
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Motion of a Charged Particle in a Magnetic Field
The magnetic force is always toward the center of
the circular path ? the magnetic force causes a
centripetal acceleration, changing the direction
of v.
mv2 F q v B ??
r
m v r ?? q B
?
The radius of the path is proportional to the
momentum of and is inversely proportional to the
magnetic field.
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Summary

• Gravity, electric, and magnetic forces alter
  properties of the surrounding space.
• These properties are called force fields.

• Electromagnetic forces is one of the 4
  fundamental forces which exist in the Universe.

• A single electromagnetic field surrounds every
  moving electric charge.