Download Physics 112 Magnetism

Physics 152
Magnetism
Walker, Chapter 22
Magnetism
• Known since antiquity
– Pieces of Magnetite, also called lodestone
(Fe3O4) known by Greeks to exert both forces
of attraction and repulsion on each other
• Chinese invented compass for navigation
– The earth exerts a force on magnetite.
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Basic model of Magnetic
Materials
• All magnetic materials
have two poles
– Labeled: North and South
poles
• Just as in electrostatics,
Like repels like and
opposites attract.
N repels N, S repels S, N
attracts S
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Magnetic Monopoles
• Unlike electrostatics:
Magnetic monopoles have
never been detected.
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Modern View of Magnetism
(Oersted, Faraday, Maxwell, 19th Century
plus Quantum Mechanics – 20th Century)
• Magnetism is associated with charges in
motion
• These currents can be microscopic currents
in the atoms of magnetic materials.
• These currents can be macroscopic currents
in the windings of an electromagnet.
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Magnetic Field Lines
Magnetic field lines
(outside the object)
always go from the N
pole to the S pole
N
S
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The Earth’s Magnetic Field
The spinning iron core of the
earth produces a magnetic
field.
The magnetic north pole
corresponds to the
geographic south pole...
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Magnetic Fields
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Magnetic Forces
1. Forces on moving charges
2. Forces on currents in wires or fluids
• A charged particle in a static (not changing with
time) magnetic field will experience a magnetic
force only if the particle is moving.
• If a charge q with velocity v moves in a magnetic
field B and v makes an angle q w.r.t. B, then the
magnitude of the force on the charge is:
|F| = | q v B sinq | = q vB
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Magnetic Units
We can determine the magnetic field by measuring the
force on a moving charge:
F
B
qv sin q
The mks unit of magnetic field is the Tesla (T).
Dimensional analysis: 1 T = 1 N·s / (C·m) = 1 V ·s /
m2
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Direction of Magnetic Forces
The magnetic force is in a direction perpendicular to
the plane formed by B and v.
To determine the direction, you must apply the right
hand rule.
F
B
v
x
= negative z direction
(into the plane of paper)
= positive z direction
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Direction of Magnetic Forces
F
x
B
q+
v
palm: B
fingers: v
thumb: F
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Right Hand
Rule


•
•
•
•

F = qv  B
Draw vectors v and B with their
tails at the location of the charge
q.
Point fingers of right hand along
velocity vector v.
Curl fingers towards Magnetic
field vector B.
Thumb points in direction of
magnetic force F on q,
perpendicular to both v and B.
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Walker, Problem 22-6
A particle with a charge of 14 µC experiences a force of 2.1x10-4 N
when it moves at right angles to a magnetic field with a speed of 28.1
m/s. What force does this particle experience when it moves with a
speed of 7.0 m/s at an angle of 24.6° relative to the magnetic field?
answer: 2.17x10-5 N.
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y
Question
•
•
•
v
A negative charge q is moving in the +y
direction with velocity v.
The magnetic field B is in the +x direction
What is the direction of the force on q?
B
x
a.
b.
c.
d.
-y direction
Force is zero
+z direction
-z direction
+z
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Force on a Current Carrying Wire
Recall that a current in a wire is a collection
of moving charges; therefore, a current
carrying wire in a magnetic field also
experiences a force.
If a wire of length L, carrying a current I,
makes an angle q with a magnetic field B,
then the total force on the wire is:
|F| = |I L B sin q|
B
q
F
I
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Right-Hand-Rule for
Magnetic Force on a Wire
• Direction of magnetic force
|I L B sinq | on wire is
perpendicular to direction
of I and to direction of B.
• Orientation of Force is
determined by curling
fingers from direction to I
to direction of B.
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Motion of Charges in B Fields
If a charged particle is moving in a
direction perpendicular to a uniform
magnetic field, then its trajectory will
be a circle because the force F=qvB is
always perpendicular to the motion,
and therefore centripetal.
Recall that
mv
Fc = ma =
r
2
so
mv 2
F = qvB =
r
From which we find the radius of the circular trajectory
is:
mv
r=
qB
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Mass Spectrometer
Magnetic
Field
 to
drawing
EB
Velocity
Selector
    
    
   
    
    
   
 -   +
 -    +
  Ionsource
 
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         
         
        
        
        
        

Position Sensitive Detector


mv
radius of ion orbit r =
qB
sample
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Mass Spectrometer
Measures m/q of ions
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