Download Magnetism

Magnetism
A Whole New Topic
March 8, 2006
Magnetism
1
Introductory Material
Magnetism
2
Dis Here Week

Today we begin magnetism – a topic that
will occupy us for most of the remainder
of the semester.
• I do not yet have the exam papers (Tuesday
PM) but I will return them if I get them.



Friday – Quiz on DC Circuits
New material on the web
New WebAssign on board – READ THE
CHAPTER!!
Magnetism
3
DEMO ON Magnetism
Magnetism
4
Lodestone (Mineral)
• Lodestones attracted
iron filings.
• Lodestones seemed to
attract each other.
• Used as a compass.
– One end always
pointed north.
• Lodestone is a natural
magnet.
Magnetism
5
Magnetism
• Refrigerators are attracted to magnets!
Magnetism
6
Applications
• Motors
• Navigation – Compass
• Magnetic Tapes
– Music, Data
• Television
– Beam deflection Coil
• Magnetic Resonance Imaging
• High Energy Physics Research
Magnetism
7
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.
8
Observations
• Bring a magnet to an electrically charged
object and nothing happens. No forces.
• 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.
– 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
9
Magnets
Cutting a bar magnet in half produces TWO bar
magnets, each with N and S poles.
Magnetism
10
Consider a Permanent Magnet

B
N
Magnetism
S
11
Introduce Another Permanent Magnet

B
N
N
S
pivot
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
12
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.
Also, the small bar magnet (a magnetic dipole) wants to align
with the B-field.
The
field attracts and exerts a torque on the small magnet.
Magnetism
13
Field of a Permanent Magnet

B
N
N
S
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
14
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
15
Convention For Magnetic Fields
X
Field INTO Paper
Magnetism
B

Field OUT of Paper
16
Experiments with Magnets Show
• Current carrying wire produces a
circular magnetic field around it.
• Force on Compass Needle (or magnet)
increases with current.
Magnetism
17
Current Carrying Wire
Current into
the page.
B
Right hand RuleThumb in direction of the current
Fingers curl in the direction of B
Magnetism
18
Current Carrying Wire
• B field is created at ALL POINTS in space
surrounding the wire.
• The B field had magnitude and direction.
• Force on a magnet increases with the
current.
• Force is found to vary as ~(1/d) from the
wire.
Magnetism
19
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
20
Planet Earth
Magnetism
21
Inside it all.
8000
Miles
Magnetism
22
On the surface it looks like this..
Magnetism
23
Inside: Warmer than Floriduh
Magnetism
24
Much Warmer than Floriduh
Magnetism
25
Finally
Magnetism
26
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
27
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
28
Ancient Navigation
Magnetism
29
This planet is really screwed up!
NORTH
POLE
Magnetism
SOUTH POLE
30
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
31
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.
32
So much for the
observations.
Let’s do the physics!
Magnetism
33
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
34
WHAT THE HECK IS
THAT???
• A WHAT PRODUCT?
• A CROSS PRODUCT – Like an
angry one??
• Alas, yes ….
• F=qv X B
Magnetism
35
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
36
Nicer Picture
Magnetism
37
VECTOR CALCULATIONS
Magnetism
i
a  b  ax
j
ay
k
az
bx
by
bz
38
Note
See proof of previous
approach on the website.
Magnetism
39
Practice
B and v are parallel.
Crossproduct is zero.
So is the force.
Which way is the Force???
Magnetism
40
Units
F  Bqv Sin(θ )
Units :

F
N
N
B


qv Cm / s Amp  m
Magnetism
1 tesla  1 T  1 N/(A - m)
41
teslas are
Magnetism
42
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
43
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
44
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
45
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
46
Magnetic Levitation
Magnetic Force
mg
Current = i
iLB  mg
Where does B point????
Into the paper.
mg
B
iL
Magnetism
47
MagLev
Magnetism
48
WELCOME BACK!
Magnetism
49
SCHEDULE
10
13-Mar
BREAK
BREAK
BREAK
11
20-Mar
Magnetic Field
Sources of B
Sources of B
12
27-Mar
Ampere’s Law
Faraday's Law
Faraday’s Law
13
3-Apr
Inductance
Inductance
EXAM #3
14
10-Apr
Inductance - Finish
AC Circuits
AC Circuits
15
17-Apr
AC Circuits
EM FIELDS
Light Topics
16
24-Apr
Light Topics
No Class
FINAL EXAM
17
1-May
No Class
No Class
No Class
Magnetism
50
What’s are we doing??

This week
• Finish B Fields and the motion of
Particles
• Sources of Magnetic Fields

Friday
• QUIZ – materials from the week before
the break through this Wednesday
Magnetism
51
What in the world were we doing
before the binge???



F  qv  B
Magnetism
52
AND …..
L
q  it  i
vd
L
F  qvd B  i vd B  iLB
vd
vector :
F  iL  B
L in the direction of the motion
of POSITIVE charge (i).
Magnetism
53
Motion of a charged
particle in a magnetic
Field
March 20, 2006
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
Magnetism
65
Trajectory of Charged Particles
in a Magnetic Field
(B field points into plane of paper.)
+
+B
+
v+
+
+
+
+
+
+
+
+ F
+
+
+
+ F +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
+
+
+
+
+
Magnetism
v
66
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
67
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
68
Magnetism
69
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!
70
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
71
More Circular Type Motion in a
Magnetic Field
Magnetism
72
Mass Spectrometer
Smaller Mass
Magnetism
73
Magnetism
74
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
75
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
76
Let’s Look at the effect of crossed E and B Fields:
x x x B
E
x x x
v
q , m
Magnetism
•
77
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
78