Download Magnetism and Magnetic Forces

Magnetism
A Whole New Topic
Magnetism
1
Bad Week …..


Examination #2 on Friday
Don’t miss the WebAssign on RC
• RC will not be on the exam (you’re welcome!)




Problem session on Wednesday Morning –
7:30 AM – Rm 306 – for BOTH sections.
Spring Break Cancelled.
Today we start on a new topic
MAGNETISM.
Check the two files on the website
concerning vector products.
• They may be helpful in this topic.
Magnetism
2
Magnetism was known
long ago.
Magnetism
3
Lodestone (Mineral)
• Lodestones attracted
iron filings.
• Lodestones seemed to
attract each other.
• Lodestone is a natural
magnet.
Magnetism
4
New Concept
The Magnetic Field
– We give it the symbol B.
– A compass will line up
with it.
– It has Magnitude and
direction so it is a
VECTOR.
• There are some
similarities with the
Electric Field but also
some significant
differences.
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
Observations
• Bring a magnet to an electrically charged object and
the observed attraction will be a result of charge
induction or polarization.
• 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
10
Magnets
Cutting a bar magnet in half produces TWO bar
magnets, each with N and S poles.
Magnetism
11
Consider a Permanent Magnet

B
N
S
The magnetic Field B goes from North to South.
Magnetism
12
Introduce Another Permanent Magnet

B
N
N
S
pivot
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
13
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
14
Field of a Permanent Magnet

B
N
N
S
S
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism
15
Convention For Magnetic Fields
X
Field INTO Paper
Magnetism
B

Field OUT of Paper
16
Typical Representation
Magnetism
17
Experiments with Magnets Show
• Current carrying wire produces a
circular magnetic field around it.
• Force (actually torque) on a Compass
Needle (or magnet) increases with
current.
Magnetism
18
Current Carrying Wire
Current into
the page.
B
Right hand RuleThumb in direction of the current
Fingers curl in the direction of B
Magnetism
19
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
20
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
21
Planet Earth
Magnetism
22
Inside it all.
8000
Miles
Magnetism
23
On the surface it looks like this..
Magnetism
24
Inside: Warmer than Floriduh
Magnetism
25
Much Warmer than Floriduh
Magnetism
26
Finally
Magnetism
27
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
28
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
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
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
33
WHAT THE HECK IS
THAT???
• A WHAT PRODUCT?
• A CROSS PRODUCT – Like an
angry one??
• Alas, yes ….
• F=qv X B
Magnetism
34
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
35
Nicer Picture
Magnetism
36
Another Picture
Magnetism
37
VECTOR CALCULATIONS
Magnetism
i
a  b  ax
j
ay
k
az
bx
by
bz
38
Practice
B and v are parallel.
Crossproduct is zero.
So is the force.
Which way is the Force???
Magnetism
39
Units
F  Bqv Sin(θ )
Units :

F
N
N
B


qv Cm / s Amp  m
Magnetism
1 tesla  1 T  1 N/(A - m)
40
teslas are
Magnetism
41
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
42
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
43
The Wire in More Detail
Assume all electrons are moving
with the same velocity vd.
L
L
q  it  i
vd
F  qvd B  i
L
vd B  iLB
vd
vector :
F  iL  B
B out of plane of the paper
Magnetism
Vector L in the direction of the
motion of POSITIVE charge (i).
44
Magnetic Levitation
Magnetic Force
mg
Current = i
iLB  mg
Where does B point????
Into the paper.
mg
B
iL
Magnetism
45
MagLev
Magnetism
46
A conductor suspended by two flexible wires as shown in
the diagram has a mass per unit length of 0.040 0 kg/m.
What current must exist in the conductor in order for the
tension in the supporting wires to be zero when the
magnetic field is 3.60 T into the page? What is the
required direction for the current?
Concrete Insulator
Magnetism
47
There was a crooked man who lived in
a crooked house that was wired with
crooked wires
Magnetism
48
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
49
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
50
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
51
Current Loop
What is force
on the ends??
Loop will tend to rotate due to the torque the field applies to the loop.
Magnetism
52
The Loop (From the top)
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
53
An Application
The Galvanometer
Magnetism
54
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
55
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
56
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.
57
A 40.0-cm length of wire carries a current of
20.0 A. It is bent into a loop and placed with
its normal perpendicular to a magnetic field
with a magnitude of 0.520 T. What is the
torque on the loop if it is bent into
(a)an equilateral triangle?
(b)What is the torque if the loop is
(c) a square or
(d) a circle?
(e) Which torque is greatest?
Magnetism
58
Motion of a charged
particle in a magnetic
Field
Magnetism
59
Trajectory of Charged Particles
in a Magnetic Field
(B field points into plane of paper.)
+
+B
+
v+
+
+
+
+
+
+
+
+ F
+
+
+
+ F +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
+
+
+
+
+
Magnetism
v
60
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
61
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
62
Magnetism
63
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!
64
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
65
More Circular Type Motion in a
Magnetic Field
Magnetism
66
Review Problem. An electron moves in a circular path
perpendicular to a constant magnetic field of magnitude 1.00
mT. The angular momentum of the electron about the center
of the circle is 4.00 × 10–25 J · s.
Determine:
(a)the radius of the circular path and
(b)the speed of the electron.
Magnetism
67
Mass Spectrometer
Smaller Mass
Magnetism
68
Magnetism
69
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
70
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
71
Let’s Look at the effect of crossed E and B Fields:
x x x B
E
x x x
v
q , m
Magnetism
•
72
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
73