Download Magnetism

Magnetism
A Whole New Topic
October 23, 2006
Magnetism
1
This Week


Today we begin magnetism – a topic that
will occupy us for most of the remainder
of the semester.
Wednesday – Examination #2
• Potential, Capacitors, Resisters and DC
Circuits.



There is a new, SHORT WebAssign on
board on RC. (2 problems)
No quiz on Friday. We continue with
Magnetism.
Watch for new WA popping up after the
exam.
Magnetism
2
What did you think about the quiz on
Friday? Both answers = 3 points.


It was fair.
It was unfair.
Magnetism
3
Magnetism was known
long ago.
Magnetism
4
Lodestone (Mineral)
• Lodestones attracted iron
filings.
• Lodestones seemed to
attract each other.
• Used as a compass.
– One end always pointed
north.
– Called the “North Pole”
• Lodestone is a natural
magnet.
Magnetism
5
Magnetism
• Refrigerators are attracted to magnets!
Magnetism
6
Where is Magnetism Used??
• Motors
• Navigation – Compass
• Magnetic Tapes
– Music, Data
• Television
– Beam deflection Coil
• Magnetic Resonance Imaging
• High Energy Physics Research
Magnetism
7
Magnet Demo – Compare to
Electrostatics
N
Magnet
What Happens??
S
Pivot
Magnetism
8
Results - Magnets
S N
Shaded End is NORTH Pole
Shaded End of a compass points
to the NORTH.
Magnetism
• Like Poles Repel
• Opposite Poles
Attract
• Magnetic Poles are
only found in pairs.
– No magnetic
monopoles have
ever been
observed.
9
Bring a magnet to a wooden rod
• The wooden rod is
attracted to the
magnet.
• The wooden rod is
repelled by the
magnet.
• Nothing happens.
Magnetism
10
Bring a magnet to an aluminum
rod.
• Nothing happens.
• The magnet attracts
the rod.
• The magnet repels the
rod.
• It depends on whether
the N or S pole is
closest to the rod.
• Nothing happens.
Magnetism
11
Bring a neutral Teflon rod to a
magnet…
• The rod attracts the
magnet.
• The rod repels the
magnet.
• Nothing happens.
Magnetism
12
Bring a charged Teflon rod to a
magnet ..
• It will attract the NORTH
pole and repel the
SOUTH pole.
• It will repel the NORTH
pole and will attract the
SOUTH pole.
• It will repel both poles.
• It will attract both poles.
• Nothing will happen.
Magnetism
13
Observations
• Bring a magnet to an electrically charged object and
the observed attraction will be a result of charge
induction.
• Magnetic poles do not interact with stationary
electric charges.
• Bring a magnet near some metals (Co, Fe, Ni …) and it
will be attracted to the magnet.
– The metal will be attracted to both the N and S poles
independently.
– Some metals are not attracted at all. (Al, Cu, Ag, Au)
– Wood is NOT attracted to a magnet.
– Neither is water.
• A magnet will force a compass needle to align with it.
(No big Surprise.)
Magnetism
14
Magnets
Cutting a bar magnet in half produces TWO bar
magnets, each with N and S poles.
Magnetism
15
Consider a Permanent Magnet

B
N
Magnetism
S
16
Introduce Another Permanent Magnet

B
N
N
S
pivot
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
17
Field of a Permanent Magnet

B
N
N
S
S
The south pole of the small bar magnet is attracted towards the north pole of the big
magnet.
The North pole of the small magnet is repelled by the north pole of the large magnet.
The South pole pf the large magnet creates a smaller force on the small magnet than
does the North pole. DISTANCE effect.
The field attracts and exerts a torque on the small magnet.
Magnetism
18
Field of a Permanent Magnet

B
N
N
S
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
19
The Magnetic Field
• Similar to Electric Field … exists in
space.
– Has Magnitude AND Direction.
• The “stronger” this field, the greater is
the ability of the field to interact with
a magnet.
Magnetism
20
Convention For Magnetic Fields
X
Field INTO Paper
Magnetism
B

Field OUT of Paper
21
Experiments with Magnets Show
• Current carrying wire produces a
circular magnetic field around it.
• Force on Compass Needle (or magnet)
increases with current.
Magnetism
22
Current Carrying Wire
Current into
the page.
B
Right hand RuleThumb in direction of the current
Fingers curl in the direction of B
Magnetism
23
Current Carrying Wire
• B field is created at ALL POINTS in space
surrounding the wire.
• The B field has magnitude and direction.
• Force on a magnet increases with the
current.
• Force is found to vary as ~(1/d) from the
wire.
Magnetism
24
Compass and B Field
• Observations
– North Pole of magnets
tend to move toward
the direction of B while
S pole goes the other
way.
– Field exerts a
TORQUE on a
compass needle.
– Compass needle is a
magnetic dipole.
– North Pole of
compass points
toward the NORTH.
Magnetism
25
Planet Earth
Magnetism
26
Inside it all.
8000
Miles
Magnetism
27
On the surface it looks like this..
Magnetism
28
Inside: Warmer than Floriduh
Magnetism
29
Much Warmer than Floriduh
Magnetism
30
Finally
Magnetism
31
In Between






The molten iron core exists in a magnetic
field that had been created from other
sources (sun…).
The fluid is rotating in this field.
This motion causes a current in the molten
metal.
The current causes a magnetic field.
The process is self-sustaining.
The driving force is the heat (energy) that
is generated in the core of the planet.
Magnetism
32
After molten lava emerges from a volcano, it solidifies to a rock. In
most cases it is a black rock known as basalt, which is faintly
magnetic, like iron emerging from a melt. Its magnetization is in the
direction of the local magnetic force at the time when it cools down.
Instruments can measure the magnetization of basalt. Therefore, if
a volcano has produced many lava flows over a past period, scientists
can analyze the magnetizations of the various flows and from them
get an idea on how the direction of the local Earth's field varied in
the past. Surprisingly, this procedure suggested that times existed
when the magnetization had the opposite direction from today's. All
sorts of explanation were proposed, but in the end the only one
which passed all tests was that in the distant past, indeed, the
magnetic polarity of the Earth was sometimes reversed.
Magnetism
33
Ancient Navigation
Magnetism
34
This planet is really screwed up!
NORTH
POLE
Magnetism
SOUTH POLE
35
Repeat
Navigation
DIRECTION
N
S
If N direction
is pointed to by
the NORTH pole
of the Compass
Needle, then the
pole at the NORTH
of our planet must
be a SOUTH MAGNETIC
POLE!
Compass
Direction
Navigation
DIRECTION
S
N
And it REVERSES from time to time.
Magnetism
36
Rowland’s Experiment
Field is created by
any moving charge.
Rotating
INSULATING
Disk
which is
CHARGED
+ or –
on exterior.
++
Magnetism
+ +
++
xxx
xxx B
xxx
Increases with
charge on the
disk.
Increases with
angular velocity of
the disk.
Electrical curent is a
moving charge.
37
So much for the
observations.
Let’s do the physics!
Magnetism
38
A Look at the Physics

B
q

v

q B
There is NO force on
a charge placed into a
magnetic field if the
charge is NOT moving.
There is no force if the charge
moves parallel to the field.
• If the charge is moving, there
is a force on the charge,
perpendicular to both v and B.
F=qvxB
Magnetism
39
WHAT THE HECK IS
THAT???
• A WHAT PRODUCT?
• A CROSS PRODUCT – Like an
angry one??
• Alas, yes ….
• F=qv X B
Magnetism
40
The Lorentz Force
This can be summarized as:

 
F  qv  B
F
or:
F  qvBsin 
v
B
mq
 is the angle between B and V
Magnetism
41
Nicer Picture
Magnetism
42
VECTOR CALCULATIONS
Magnetism
i
a  b  ax
j
ay
k
az
bx
by
bz
43
Note
See proof of previous
approach on the website.
Magnetism
44
Practice
B and v are parallel.
Crossproduct is zero.
So is the force.
Which way is the Force???
Magnetism
45
Units
F  Bqv Sin(θ )
Units :

F
N
N
B


qv Cm / s Amp  m
Magnetism
1 tesla  1 T  1 N/(A - m)
46
teslas are
Magnetism
47
The Magnetic Force is Different
From the Electric Force.
Whereas the electric force
acts in the same direction as
the field:
The magnetic force acts in a
direction orthogonal to the
field:


F  qE



F  qv  B
(Use “Right-Hand” Rule to
determine direction of F)
And
--the
charge
must
be
moving
!!
Magnetism
48
So…
A moving charge can create a magnetic
field.
A moving charge is acted upon by a
magnetic field.
In Magnetism, things move.
In the Electric Field, forces and the
field can be created by stationary
charges.
Magnetism
49
Wires
• A wire with a current
contains moving charges.
• A magnetic field will
apply a force to those
moving charges.
• This results in a force
on the wire itself.
– The electron’s sort of
PUSH on the side of the
wire.
F
Remember: Electrons go the “other way”.
Magnetism
50
The Wire in More Detail
Assume all electrons are moving
with the same velocity vd.
q  it  i
L
vd
F  qvd B  i
L
vd B  iLB
vd
vector :
F  iL  B
L in the direction of the motion
of POSITIVE charge (i).
B out of plane of the paper
Magnetism
51
Magnetic Levitation
Magnetic Force
mg
Current = i
iLB  mg
Where does B point????
Into the paper.
mg
B
iL
Magnetism
52
MagLev
Magnetism
53
Motion of a charged
particle in a magnetic
Field
Magnetism
54
There was a crooked man who lived in
a crooked house that was wired with
crooked wires
Magnetism
55
Crooked Wire (in a plane) in
a constant B field
dFB  Ids  B
b 
Fb  I  ds  B  I  ds   B
a
a 
b
Magnetism
56
Case 1
dFB  Ids  B
b 
Fb  I  ds  B  I  ds   B
a
a 
Fb  IL'B
b
The magnetic force on a curved current carrying conductor in a uniform
magnetic field is the same as that of a straight conductor carrying the
same current between the two points a and b.
Magnetism
57
Case 2
dFB  Ids  B
b
 
Fb  I  ds  B  I  ds  B  0
a
The net magnetic force on a closed
current carrying loop is ZERO!
Magnetism
58
Current Loop
What is force
on the ends??
Loop will tend to rotate due to the torque the field applies to the loop.
Magnetism
59
The Loop
OBSERVATION
Force on Side 2 is out
of the paper and that on
the opposite side is into
the paper. No net force
tending to rotate the loop
due to either of these forces.
The net force on the loop is
also zero,
pivot
Magnetism
60
An Application
The Galvanometer
Magnetism
61
The other sides
t1=F1 (b/2)Sin()
=(B i a) x (b/2)Sin()
total torque on
the loop is: 2t1
Total torque:
t=(iaB) bSin()
=iABSin()
(A=Area)
Magnetism
62
A Coil
For a COIL of N turns, the net
torque on the coil is therefore :
Normal to the
coil
τ  NiABSin(θ )
RIGHT HAND RULE TO FIND NORMAL
TO THE COIL:
“Point or curl you’re the fingers of your right
hand in the direction of the current and your
thumb will point in the direction of the normal
to the coil.
Magnetism
63
Dipole Moment Definition
Define the magnetic
dipole moment of
the coil m as:
m=NiA
t=m X B
Magnetism
We can convert this
to a vector with A
as defined as being
normal to the area as
in the previous slide.
64
Trajectory of Charged Particles
in a Magnetic Field
(B field points into plane of paper.)
+
+B
+
v+
+
+
+
+
+
+
+
+ F
+
+
+
+ F +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
+
+
+
+
+
Magnetism
v
65
Trajectory of Charged Particles
in a Magnetic Field
(B field points into plane of paper.)
+
+B
+
v+
+
+
+
+
+
+
+
+ F
+
+
+
+ F +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
+
+
+
+
+
Magnetism
v
Magnetic Force is a centripetal force
66
Review of Rotational Motion

 = s / r  s =  r  ds/dt = d/dt r  v =  r
s
r
 = angle,  = angular speed,  = angular acceleration

at
ar
at = r 
tangential acceleration
ar = v2 / r radial acceleration
The radial acceleration changes the direction of motion,
while the tangential acceleration changes the speed.
Uniform Circular Motion
ar
 = constant  v and ar constant but direction changes

v
Magnetism
ar = v2/r = 2 r
KE = ½ mv2 = ½ mw2r2
F = mar = mv2/r = m2r
67
Magnetism
68
Radius of a Charged Particle
Orbit in a Magnetic Field
+B
+
+
v+
+
+
+
+
+
+
+
+
+
r
+
+
+
+
+
+
F
+
Magnetism
Centripetal
Force
=
Magnetic
Force
mv 2

 qvB
r

mv
r
qB
 
Note: as Fv , the magnetic
force does no work!
69
Cyclotron Frequency
+B
+
+
v+
+
+
+
+
+
+
+
+
+
r
+
+
+
+
+
+
F
+
Magnetism
The time taken to complete one
orbit is:
2r
v
2 mv

v qB
T 
1
qB
f  
T 2 m
qB
 c  2f 
m
70
More Circular Type Motion in a
Magnetic Field
Magnetism
71
Mass Spectrometer
Smaller Mass
Magnetism
72
Magnetism
73
An Example
A beam of electrons whose kinetic energy is K emerges from a thin-foil
“window” at the end of an accelerator tube. There is a metal plate a distance d
from this window and perpendicular to the direction of the emerging beam. Show
that we can prevent the beam from hitting the plate if we apply a uniform
magnetic field B such that
2mK
B
2 2
ed
Magnetism
74
Problem Continued
r
From Before
mv
r
qB
1 2
2K
K  mv so v 
2
m
m 2K
2mK
r

d
2 2
eB m
e B
Solve for B :
2mK
B
e2d 2
Magnetism
75
Let’s Look at the effect of crossed E and B Fields:
x x x B
E
x x x
v
q , m
Magnetism
•
76
What is the relation between the intensities of the electric and
magnetic fields for the particle to move in a straight line ?.
x x x B
E
x x x
v
q• m
FE = q E and FB = q v B
If FE = FB the particle will move
following a straight line trajectory
qE=qvB
v=E/B
FB FE
•
Magnetism
77