MAGNETIC FIELD
Magnetic Force
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For centuries, humans observed “strange” force
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Force couldn't be gravity or electric
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Between iron and special stones called “lodestones”
Not enough mass or electric charge to explain force
Iron and lodestones must have something else
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Humans called these magnetic “poles”
Two varieties: “North” and “South” (like + and –)
Magnetic Poles
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Like poles repel; opposite poles attract
S
N
S
N
S
N
N
S
Repulsive force
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Attractive force
Note: “North” and “South” always come in pairs
(unlike + and –)
Magnetic Field
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Magnetic Force → Action-at-a-distance
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The “magnetic field”
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Just like gravity and the electric force → requires a “field”
Represented by symbol B (“B field”)
Units: Tesla (T) or Gauss (G)
Magnetic poles affect the space around them
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If another pole comes into this space, it feels a force
This still doesn't explain the origin of the magnetic field...
Magnetic Materials
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Experiments → possible to “magnetize” iron
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Most other metals don't show this behavior
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By touching an unmagnetized piece of iron to a lodestone
The iron holds its magnetism permanently
Iron can be “de-magnetized” by heating it
Iron must be magnetically “special”
For centuries, iron was used to make:
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Compasses
Bar magnets
Atoms and Magnetism
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Individual atoms act like tiny bar magnets
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Usually pointing in random directions
When many atomic magnets “line up”:
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An object is “magnetized”
Requires special conditions
Only iron and a few other materials are easily magnetized
Earth's Magnetic Field
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Earth itself acts like a huge “bar magnet”
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Lodestones
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Humans have observed the magnetic field for centuries
Naturally-formed magnetic rocks
Made as iron-rich lava cooled
Earth magnetized the iron inside the rocks
Origin of magnetic field not fully understood
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Can NOT be due to Earth's iron core (too HOT!)
Must be due to electric currents in molten core
Magnets and Electric Current
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Experiments on magnets in 1800's
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Found that electric current can deflect a compass needle
Must be a link between electricity and magnetism!
creates
Electric
Magnetic Field
Current exerts force
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exerts force
creates
Electric
Current
Currents create magnetic fields of many sizes
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Atoms (due to current produced by orbiting electron)
Medium size (e.g. coil of wire → electromagnet)
Huge (Sun is made of rotating plasma → magnetic field)
Charged Particles in Magnetic Fields
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Need a magnetic equation similar to F = qE
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i.e. an E field pushes a + charge, but pulls a – charge
B field → affects electric current (moving charges)
Direction of F determined
by the “right hand rule”
F = ∣q∣ v ⊥ B = ∣q∣ v B sin 
1) Fingers = v
B
B
v
v
No Force
2) Curl fingers toward B
B
×F
F = qvB
(directed into page)
(switch for – charge)
F•
ϕ
v
F = qvBsin(ϕ)
(directed out of page)
(switch for – charge)
3) Thumb = F
• = “out”
× = “in”
Charged Particle Motion
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Right-hand rule → F always perpendicular to v
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This means B field can never affect speed of particle
It can only affect the direction of the particle's motion
Magnetic force acts as centripetal force
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B
Charged particles tend to loop around B field lines
× ×
×
× F
× ×
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v
mv
∣q∣ v B =
R
2
R=
mv
∣q∣ B
General motion: a “helix”
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+ and – charges “corkscrew” in opposite directions
∣q∣ B
=
m
Cosmic Radiation
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Dangerous high-energy particles hit Earth
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From the Sun and from deep space
Charged particles are “trapped” by the magnetic field
The captured charged
particles produce the
aurora borealis
(Uncharged particles
must be stopped by
the atmosphere)
Electric Currents in Straight Wires
Acting as a “test”
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Acting as a “source”
Wire is basically a line of
moving point charges
A new “right hand rule” gives
the direction of the B field
B field produced by some
external source
Right hand rule still applies
B
I
ϕ
F = I l B ⊥ = I l B sin 
0 I
B=
2r
−7
0 = 4×10
T
A⋅m
Attraction / Repulsion of Straight Wires
If 2 current-carrying wires are near each other:
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They each act as a source current and a test current
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For parallel wires:
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Current in same direction → wires attract
Current in opposite direction → wires repel
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Force per unit length of wire
I
F 0 I I '
=
l
2 r
I'
r
This is a major issue in small circuits with
large currents – e.g. computer chips
Electric Currents in Wire Loops
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Acting as a “test”
Acting as a “source”
Each piece of the loop has a
magnetic force on it
Another “right hand rule” gives
the direction of the B field
Forces produce a torque
Torque turns loop so B field
points through it
F
 = I A B sin 
 = IA
F “Magnetic Moment”
Curled fingers = current
Thumb = B field
0 I
B center =
2R
Wire Coils
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Magnetic effects of wire loops can be amplified
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By using wire coils rather than a single loop
 = N I A B sin 
F
0 N I
B center =
2R
F
B center = 0 n I
“Solenoid”
n=
number of loops
length of coil
DC Motors
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Convert electric current to kinetic energy
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Ingredients: A wire coil and a permanent magnet
Must switch the direction of current every half-cycle
Coil is perpetually trying to “line up” with magnet's B field
Wide range of sizes
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Micro-mechanical devices
Hand-held drills
Electric car motors