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Chapter 19: Magnetism
The nature of magnetism
Iron ore found near Magnesia
Compass needles align N-S: magnetic Poles
North (South) Poles attracted to geographic North (South)
Like Poles repel, Opposites Attract
No Magnetic Monopoles
Define magnetic field lines = direction of compass deflection.
Electric Currents produce deflections in compass direction.
Electric Currents interact magnetically I
I
F
I
F
F
F
I
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Magnetic Fields in analogy with Electric Fields
Electric Field:
– Distribution of charge creates an electric field E in the
surrounding space.
– Field at charges location exerts a force F=q E on a
charge q
Magnetic Field:
– Moving charge or current creates a magnetic field B in
the surrounding space.
– Field exerts a force F on a charge moving q
F = qvB sin
 is angle between B and v.
– F is perpendicular to B an v
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F
F = |q| v B sin
= |q| v B (v  B)
B
+
v
F
F = |q| v B sin
F = |q| v B
B
+
v
v
F
F = |q| v B sin
F = |q| v B
+
B
v
B
Right Hand Rule (1-2-3) : v, B, F
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Units of Magnetic Field Strength:
[B]
= [F]/([q][v])
= N/(C m s-1)
= Tesla
actually defined in terms of force on standard current
CGS Unit 1 Gauss = 10-4 Tesla
Earth's field strength ~ 1 Gauss
Direction = direction of velocity which generates no force
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J. J. Thomson’s Measurement of e/m
Electron Gun


E
V
Example 19.2: Electrons are accelerated through a potential difference of 1000 V. The
electrons then enter a region where there is a magnetic field and a “crossed” electric
field (E and B are perpendicular), both of which are perpendicular to the beam. What
magnitude magnetic field must be applied to exactly cancel the effect of the Electric
field of 104 V/m?
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I
Field of a long straight wire
oI
B
2 s
 o  4  1  10 7 T  m A
B
s
Magnetic field circulates around the
wire; use Right hand rule for
direction
Thumb in direction of the current,
fingers curl around in direction of B
Example 19.2: Find the magnetic field 10 mm from a wire that carries a
current of 1.0 A.
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Bx 
o I
at center
2r
using N turns of wire
 o NI
Bx 
at center
2r
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Magnetic Field in a Solenoid
Close packed stacks of coils form cylinder
I
B
Fields tend to cancel in region right between wires.
Field Lines continue down center of cylinder
Field is negligible directly outside of the cylinder
B   o nI (n turns per unit length)
B
N
B   o I (for finite solenoid)
L
I
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Example 19.3: A solenoid 20 cm long and 40 mm in diameter with an air core is
wound with a total of 200 turns of wire. The solenoid is to be used to exactly cancel
the Earth's magnetic field where it is 3.0x10-5 T in magnitude. What should the
current in the solenoid be for its field to exactly cancel the earth’s field inside the
solenoid?
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Magnetic Materials
Microscopic current loops:
L
electron “orbits”

electron “spin”

Quantum Effects: quantized angular momentum L, Pauli Exclusion Principle, etc. are
important in macroscopic magnetic behavior.
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Magnetic Materials: Microscopic magnetic moments
interact with an external (applied) magnetic field and each
other, producing additional contributions to the net
magnetic field B.
Types of Materials
Diamagnetic: Magnetic field decreases in strength.
Paramagnetic: Magnetic field increases in strength.
Ferromagnetic: Magnetic field increases in strength!
Diamagnetic and Paramagnetic are often approximately
linear with a relative permeability KM,  = KM  0
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Ferromagnetism:
Bnet
Greatly increases field
Saturation
Highly nonlinear, with Hysteresis:
Bo
Hysteresis= magnetic record
Permanent Magnetization
Magnetization forms in Magnetic Domains
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More on the magnetic force on a moving charge
For a charged particle moving perpendicular to the
Magnetic Field
– Circular Motion!
F
+
mv 2
F | q | vB 
R
mv
R
|q|B
v
F
+
v
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Example 19.5 A mass spectrometer:
R2
 R1

E
velocity selector + circular trajectory
E = 40.0 kV/m
B = .0800 T
Velocity Selector: uses crossed E and B, so that Electric and Magnetic Forces cancel
for a particular velocity.
(a)What is the speed of the ions pass through the velocity selector?
(b) If the radius of the path of the ions is 390 mm, what is the mass of the ions?
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In a non-uniform field: Magnetic Mirror
v
F
B
Net component of force away from concentration of
field lines.
Magnetic Bottle
Van Allen Radiation Belts
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Magnetic Force on a Current Carrying Wire
B
I
A
vd
L
Fi


F   Fi
Fi  qvB sin 
L  vt
F
I
ILB sin 
F  QvB sin 
Q
t
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Example 19.6 (almost) A wire carries 100 A due west, suspended between two poles 50
m apart. The Earth’s field is 5.0 x 10-5 T, directed north. What is the magnitude and
direction of the magnetic force on the wire.
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Force between two long parallel current carrying wires
(consider, for this example, currents in the same direction)
I2
I1
F12 = I1 Bdue to I2 L
= I1 (oI2/(2r)) L
F/L = oI1 I2 /(2 r)
force on I1 is towards I2
force is attractive (force is
repulsive for currents in
opposite directions!)
Bdue to I2
Fdue to I2
Example: Two 1m wires separated by 1cm each carry 10 A in the same direction.
What is the force one wire exerts on the other
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Torque on a Current Loop (from force on wire segments)
Rectangular loop in a magnetic field (directed along z axis)
short side length a, long side length b, tilted with short sides
at an angle with respect to B, long sides still perpendicular to
B.
B
Fb
Fa
Fb
Fa
Forces on short sides cancel: no net force or torque.
Forces on long sides cancel for no net force but there is a net
torque.
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Torque calculation: Side view
moment arm
a/2 cos 
Fb = IBb

Fb
= Fb a/2 cos Fb a/2 cos 
Iab B cos  = I A B cos 
 I N A B cos  with N loops
magnetic moment


B
Magnetic Dipole ~ Electric Dipole
Switch current direction every 1/2 rotation => DC motor
Torque for armature of Galvanometer
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Magnetic Poles:
Magnetic “dipoles” from electric current
No isolate magnetic poles, they are always present in pairs!
No magnetic monopoles!
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