Download Magnetism

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Magnetism
Magnetic Material
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Very few materials exhibit strong magnetism. These
materials are called ferromagnetic.
Examples include iron, cobalt, nickel, and gadolinium.
Magnets
Magnets have two
ends – poles – called
north and south.
Like poles repel;
unlike poles attract.
This attraction or
repulsion is the
magnetic force.
These are examples of bar magnets.
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Magnetic Poles
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Since magnets have two poles they are said to be dipoles.
No magnet with a monopole has ever been found,
therefore, when a magnet is cut in half, the two resulting
magnets both have two poles.
Magnetic Fields
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Magnetic fields can be visualized using magnetic field
lines, which are always closed loops.
Magnetic fields are always
drawn coming out of the
north pole and going into
the south pole.
The more lines per unit
area, the stronger the field.
The Earth's Magnetic Field
The Earth’s magnetic field is similar to that of a bar magnet.
Note two things:
· the Earth’s “North
Pole” is really a south
magnetic pole as the
north ends of magnets
are attracted to it
· the Earth's poles are
not located along the
rotation axis
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Uniform Magnetic Fields
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A uniform magnetic field is constant in magnitude and direction.
How can we create a uniform magnetic field?
Aligning the opposite
poles of two bar magnets
will create a field which is
almost uniform.
Which areas in the
diagram are non-uniform?
Definition of B
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The magnetic field is often expressed as B. The field is a vector
and has both magnitude and direction.
Often the magnetic field will be referred to as a "B-field".
The unit of B is the tesla, T.
1T= 1 N
Am
Another unit sometimes used: the gauss (G).
1 G = 10-4 T
To gain perspective, the weak magnetic field of the Earth at its
surface is around 0.5 x 10-4 T or simply 0.5 G.
Electric Currents Produce Magnetic Fields
Experiment shows that an electric current
produces a magnetic field.
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Electric Currents Produce Magnetic Fields
The direction of the field
is given by a right-hand
rule.
First, orient your right
hand thumb in the
direction of the current...
Then wrap your fingers in
the direction of the B
Field.
Direction of Magnetic Fields
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Because we need three dimensions to describe
magnetic field and our paper is essentially two
dimensional, we need to represent the third
dimension somehow.
We have left / right :
Up / down :
What is the third dimension?
Magnetic Fields
Picture the field line like an arrow. The head of the arrow is the
direction of the field.
If the magnetic field is into the page, you will see the tail of the
arrow.
If the magnetic field is out of the page, you will see the front of the
arrow.
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1
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Which diagram correctly shows
the magnetic field (red) around a
current carrying wire (blue)?
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A
C
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B
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2
Which diagram correctly
shows the magnetic field
(red) around a current
carrying wire (blue)?
C
A
D
B
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3
Which diagram correctly
shows the magnetic field
(black) around a current
carrying wire (red)?
A
C
B
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D
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Which diagram correctly
shows the magnetic field
inside and outside a
current carrying loop of
wire?
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5
Which diagram correctly
shows the magnetic field
around a current carrying
wire?
A
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B
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Which diagram correctly
shows the magnetic field
around a current carrying
wire?
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B
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Force on an Electric Current in a Magnetic
Field; Definition of B
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A magnet exerts a force on a current-carrying wire.
The direction of the force is given by another different
right-hand rule, we will call this the right-arm rule to
avoid confusion.
Force on an Electric Current in a Magnetic
Field; Definition of B
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The force on the wire depends on the current,
the length of the wire, the magnetic field, and
its orientation.
FB = I L B sin #
This equation defines the magnetic field, B.
I is the current
L is the length of wire
B is the magnetic field
Force on an Electric Current in a Magnetic
Field; Definition of B
As you can see from the equation, the
magnetic force depends on the angle the
magnetic field makes with the current.
FB = I L B sin #
The force is the greatest when the magnetic field is
perpendicular the the current and zero when it is
parallel to the current.
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7
A wire carries a current of 2 A in a direction
perpendicular to a 0.3 T magnetic field. What is
the magnitude of the magnetic force acting on the
0.5 m long wire?
A
0.8 N
B
0.5 N
C
0.3 N
D
0.1 N
E
1.23 N
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8
A uniform magnetic field exerts a maximum force
of 20 mN on a 0.25 m long wire, carrying a current
of 2 A. What is the strength of the magnetic field?
A
0.1 T
B
0.2 T
C
0.3 T
D
0.4 T
E
0.5 T
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9
A 0.05 N force acts on a 10 cm wire as a result of it
being located in a 0.3 T, perpendicularly oriented,
magnetic field. What is the electric current
through the wire?
A
1.67 A
B
1.25 A
C
2.13 A
D
3.95 A
E
3.32 A
Force on an Electric Current in a Magnetic
Field; Definition of B
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To make sure we have the right direction for B, we
use the right-arm rule:
Orient your arm in the direction of the current.
Rotate your wrist until your thumb is in the
direction of the force.
Bend your fingers 90o for the direction of the
magnetic field.
All three vectors are now perpendicular
10
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What is the direction of the force
on the current carrying wire
(green) in the magnetic field (red)?
A
B
D
C
F
E
G zero
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11
What is the direction of the force
on the current carrying wire
(green) in the magnetic field (red)?
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B
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E
F
G zero
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12
A
What is the direction of the force
on the current carrying wire
(green) in the magnetic field (red)?
B
C
D
E
F
G zero
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13
A
What is the direction of the force
on the current carrying wire
(green) in the magnetic field (red)?
B
C
D
E
F
G zero
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14
A
What is the direction of the force
on the current carrying wire
(green) in the magnetic field (red)?
B
C
D
E
F
G zero
Force on Electric Charge Moving
in a Magnetic Field
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The force on a moving charge is related to the force
on a current:
F = qvB sin #
Once again, the
direction is given by a
right-arm rule.
Force on a Moving Charge
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v (velocity)
B
v (velocity)
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F
Force on a Moving Charge
F
v (velocity)
B
v (velocity)
F
For a negative charge, negate the force.
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15
An electron experiences a maximum upward force
of 2.8x10-12 N when it is moving at a speed of
5.1x106 m/s towards the north. What is the
direction and magnitude of the magnetic field?
A
3.43 N west
B
3.43 N east
C
4.74 N west
D
4.74 N east
E
6.56 N west
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16
What is the direction of the
force on the proton shown
below?
A
B
C
v
D
E
F
G
Zero
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17
What is the direction of the
force on the proton shown
below?
A
B
C
v
D
E
F
G
Zero
18
What is the direction of the
force on the electron shown
below?
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A
B
C
v
D
E
F
G
Zero
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19
What is the direction of the
force on the electron shown
below?
A
B
C
v
D
E
F
G
Zero
Force on Electric Charge Moving in a
Magnetic Field
If a charged particle is
moving perpendicular to
a uniform magnetic
field, its path will be a
circle.
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Magnetic Field Due to a Long Straight Wire
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Recalling our current carrying wire, it is
obvious that the field is inversely proportional
to the distance from the wire:
The constant μ0 is called the permeability of
free space, and has the value:
μ0 = 2 x10-7 Tm/A
2#
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20
A long straight wire carries a current of 12 A
towards the west. What is the direction and
magnitude of the magnetic field 10 cm to the
south of the wire?
A
1.2 x 10-5 T out of the page
B
2.4 x 10-5 T into the page
C
2.4 x 10-5 T out of the page
D
2.9 x 10--5 T into the page
E
2.9 x 10-5 T out of the page
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21
A long straight wire carries a current of 30 A
towards the west. What is the direction and
magnitude of the magnetic field 5 m to the south
of the wire?
A
1 x 10-6 T into the page
B
1 x 10-6 T out of the page
C
2.5 x 10-6 T into the page
D
2.5 x 10-6 T out of the page
E
3 x 10-6 T out of the page
Force between Two Parallel Wires
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Two current carrying wires will
interact with each other.
The magnetic field produced at
the position of wire 2 due to the
current in wire 1 is:
The force this field exerts on a
length l2 of wire 2 is:
Force between Two Parallel Wires
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Parallel currents in the same direction attract.
Parallel currents in opposite directions repel.
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22
What is the magnitude and direction of the
magnetic force between two parallel wires, 5 m
long and 2 cm apart, if each carries a current of 15
A in the opposite direction?
A
1.1 x 10-2 F towards each other
B
1.1 x 10-2 F away from each other
C
1.8 x 10-2 F towards each other
D
1.8 x 10-2 F away from each other
E
2.6 x 10-2 F away from each other
Mass Spectrometer
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All the atoms passing
through the second slit
will have the same
speed.
FE
FB
FE = FB
qE = qvB
E = vB
Mass Spectrometer
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Atoms reaching the second magnetic field will have the
same speed; their radius of curvature will depend on
their mass.
FB = ma
qvB = mv2
r
qB = mv
r
qBr = mE
B
m = qrB2
E
Summary
·
·
·
·
·
Magnets have north and south poles
Like poles repel, unlike attract
Unit of magnetic field: Tesla
Electric currents produce magnetic fields
A magnetic field exerts a force on an electric current:
F = ILBperpendicular
· A magnetic field exerts a force on a moving charge:
F = qvBperpendicular
· Magnitude of the field of a long, straight current-carrying
wire:
· Parallel currents attract; antiparallel currents repel
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