1. An Attractive New Topic
Magnetism
An Attractive New Topic
Magnetism

2. EXAMS RETURNED
WELCOME BACK
Magnetism

3. What’s Up? Return Exam#2 papers Begin study of magnetism.
Watch for WebAssign shortly
Magnetism

4. How Did You Do?? A. 80-100 B. 60-79 C. 40-59 D. 20-39 E. 0-19
F. Less than 0
Magnetism

5. EXAM #2
High = 95%
Low = 9%
50-59
Magnetism

6. Did the Card Help?
A Lot
A Little
Not really No
Magnetism

7. Magnetism was known long ago.

8. Lodestone (Mineral) Lodestones attracted iron filings.
Lodestones seemed to attract each other.
Lodestone is a natural magnet.
Magnetism

9. 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

10. Magnetism
Refrigerators are attracted to magnets!
Magnetism

11. Where is Magnetism Used??
Motors
Navigation – Compass
Magnetic Tapes
Music, Data
Television
Beam deflection Coil
Magnetic Resonance Imaging
High Energy Physics Research
Magnetism

12. Magnet Demo – Compare to Electrostatics
Magnetism
Magnet Demo – Compare to Electrostatics N S
Magnet
What Happens??
Pivot

13. Results - Magnets Like Poles Repel Opposite Poles Attract
Magnetism
Results - Magnets
Like Poles Repel
Opposite Poles Attract
Magnetic Poles are only found in pairs.
No magnetic monopoles have ever been observed.
S N
Shaded End is NORTH Pole
Shaded End of a compass points
to the NORTH.

14. Magnetism
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.)

15. Magnetism
Magnets
Magnetic Field
N S
N S
Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles.

16. Consider a Permanent Magnet
Magnetism
Consider a Permanent Magnet N S
The magnetic Field B goes from North to South.

17. Introduce Another Permanent Magnet
Magnetism
Introduce Another Permanent Magnet N S
pivot
The bar magnet (a magnetic dipole) wants to align with the B-field.

18. Field of a Permanent Magnet
Magnetism
Field of a Permanent Magnet N 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 of 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.

19. Field of a Permanent Magnet
Magnetism
Field of a Permanent Magnet N S
Show disk 19, demo 6 (minimum energy configuration of magnets)
The bar magnet (a magnetic dipole) aligns with the B-field.
It is now happy!

20. Talk about Torque – back to the past
Magnetism
Talk about Torque – back to the past
If the two charges are rigidly held together in this way, the Charges behave similarly to a magnet in a magnetic field.
This structure is referred to as a DIPOLE.
Usually, “a” is very small.

21. Important: the electric dipole aligns itself with the electric field
Magnetism
Important: the electric dipole aligns itself with the electric field
(- To +) p
p is the electric dipole moment

22. Electric field of an electric dipole
Magnetism
Electric field of an electric dipole
Electric Field
Magnetic Field
The magnet behaves just like the
Electric dipole and aligns itself with
A MAGNETIC field.
Similarities will continue.

23. Convention For Magnetic Fields
Magnetism
Convention For Magnetic Fields B
X 
Field INTO Paper Field OUT of Paper

24. Typical Representation
Magnetism B
B is a vector!

25. for an electric dipole moment p (in coulomb-meters), or
Magnetism
When placed in an electric or magnetic field, equal but opposite forces arise on each side of the dipole creating a torque τ:
for an electric dipole moment p (in coulomb-meters), or
for a magnetic dipole moment m (in ampere-square meters).
The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of .
The energy of a magnetic dipole is similarly

26. Experiments with Magnets Show
Magnetism
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.

27. Current Carrying Wire B Right hand Rule-
Magnetism
Current Carrying Wire B
Current into
the page.
Right hand Rule-
Thumb in direction of the current
Fingers curl in the direction of B

28. Magnetism
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.

29. Compass and B Field Observations
Magnetism
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.
The NORTH geographic pole of the planet is therefore a magnetic South pole!

30. Magnetism
Planet Earth

31. Magnetism
Inside it all.
8000
Miles

32. On the surface it looks like this..
Magnetism
On the surface it looks like this..

33. Inside: Warmer than Floriduh
Magnetism
Inside: Warmer than Floriduh

34. Much Warmer than Floriduh
Magnetism
Much Warmer than Floriduh

35. Magnetism
Finally
Hot Hot Hot

36. Magnetism
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.

37. Magnetism
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.

38. Repeat And it REVERSES from time to time. Navigation DIRECTION N S
Magnetism
Repeat
Navigation
DIRECTION N S
Navigation
DIRECTION S N
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
And it REVERSES from time to time.

39. Rowland’s Experiment xxx xxx B INSULATING Field is created by
Magnetism
Rowland’s Experiment
Field is created by
any moving charge.
Increases with
charge on the
disk.
angular velocity of
the disk.
Electrical curent is a
moving charge.
Rotating
INSULATING
Disk
which is
CHARGED
+ or –
on exterior.
xxx
xxx B ++

40. A Look at the Physics q If the charge is moving, there
Magnetism
A Look at the Physics
There is NO force on
a charge placed into a
magnetic field if the
charge is NOT moving. q
There is no force if the charge
moves parallel to the field. q
If the charge is moving, there
is a force on the charge,
perpendicular to both v and B.
F = q v x B

41. WHAT THE HECK IS THAT??? A WHAT PRODUCT?
Magnetism
WHAT THE HECK IS THAT???
A WHAT PRODUCT?
A CROSS PRODUCT – Like an angry one??
Alas, yes ….
F=qv X B

42. The Lorentz Force This can be summarized as: F or: v q m B
Magnetism
The Lorentz Force
This can be summarized as: F
or: v q m B
q is the angle between B and V

43. Magnetism
Nicer Picture

44. Magnetism
Another Picture

45. Magnetism
VECTOR CALCULATIONS

46. Practice B and v are parallel. Crossproduct is zero. So is the force.
Magnetism
Practice
B and v are parallel.
Crossproduct is zero.
So is the force.
Which way is the Force???

47. Magnetism
Units

48. teslas are
HUGE!
Magnetism

49. The Magnetic Force is Different From the Electric Force.
Magnetism
Whereas the electric force acts in the same direction as the field:
The magnetic force acts in a direction orthogonal to the field:
(Use “Right-Hand” Rule to
determine direction of F)
And --- the charge must be moving !!

50. 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

51. The Wire in More Detail Assume all electrons are moving
Magnetism
The Wire in More Detail
Assume all electrons are moving
with the same velocity vd. L
B out of plane of the paper

52. Magnetic Levitation Magnetic Force Current = i mg
Magnetism
Magnetic Levitation
Magnetic Force
Current = i mg
Where does B point????
Into the paper.

53. Magnetism
MagLev
                                                                                     

54. Magnetism
A conductor suspended by two flexible wires as shown in the diagram has a mass per unit length of 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

55. Magnetism
There was a crooked man who lived in a crooked house that was wired with crooked wires

56. Crooked Wire (in a plane) in a constant B field
Magnetism
Crooked Wire (in a plane) in a constant B field

57. Magnetism
Case 1
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.

58. The net magnetic force on a closed current carrying loop is ZERO!
Magnetism
Case 2
The net magnetic force on a closed current carrying loop is ZERO!

59. Magnetism
Current Loop
What is force
on the ends??
Loop will tend to rotate due to the torque the field applies to the loop.

60. The Loop (From the top) OBSERVATION Force on Side 2 is out
Magnetism
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

61. An Application The Galvanometer
Magnetism
An Application The Galvanometer

62. The other sides t1=F1 (b/2)Sin(q) =(B i a) x (b/2)Sin(q)
Magnetism
The other sides
t1=F1 (b/2)Sin(q)
=(B i a) x (b/2)Sin(q)
total torque on
the loop is: 2t1
Total torque:
t=(iaB) bSin(q)
=iABSin(q)
(A=Area)

63. Don't hurt yourself doing this!
Magnetism
A Coil
Normal to the
coil
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.
Don't hurt yourself doing this!

64. Dipole Moment Definition
Magnetism
Dipole Moment Definition
Define the magnetic
dipole moment of
the coil m as:
=NiA
t=m X B
We can convert this
to a vector with A
as defined as being
normal to the area as
in the previous slide.

65. an equilateral triangle? What is the torque if the loop is a square or
Magnetism
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 T. What is the torque on the loop if it is bent into
an equilateral triangle?
What is the torque if the loop is
a square or
a circle?
Which torque is greatest?

66. Motion of a charged particle in a magnetic Field
Magnetism
Motion of a charged particle in a magnetic Field

67. Trajectory of Charged Particles in a Magnetic Field
Magnetism
Trajectory of Charged Particles in a Magnetic Field
(B field points into plane of paper.) B v B F v F

68. Trajectory of Charged Particles in a Magnetic Field
Magnetism
Trajectory of Charged Particles in a Magnetic Field
(B field points into plane of paper.) v B B v F F
Magnetic Force is a centripetal force

69. Review of Rotational Motion
Magnetism
Review of Rotational Motion r  s
 = s / r  s =  r  ds/dt = d/dt r  v =  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
 = constant  v and ar constant but direction changes
ar = v2/r = 2 r
F = mar = mv2/r = m2r
KE = ½ mv2 = ½ mw2r2 v  ar

70. You have to remember this stuff.
Magnetism
YES !
You have to remember this stuff.

71. Radius of a Charged Particle Orbit in a Magnetic Field
Magnetism
Radius of a Charged Particle Orbit in a Magnetic Field
Centripetal Magnetic
Force Force = v B F r
Note: as , the magnetic
force does no work!

72. Cyclotron Frequency V cancels ! B The time taken to complete one v
Magnetism
Cyclotron Frequency v B F r
The time taken to complete one
orbit is:
V cancels !

73. More Circular Type Motion in a Magnetic Field
Magnetism
More Circular Type Motion in a Magnetic Field

74. the radius of the circular path and the speed of the electron.
Magnetism
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:
the radius of the circular path and
the speed of the electron.

75. Magnetism
Mass Spectrometer
Smaller Mass

76. Magnetism

77. Magnetism
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

78. Magnetism
Problem Continued r

79. • x x x x x x Let’s Look at the effect of crossed E and B Fields: B E
Magnetism
Let’s Look at the effect of crossed E and B Fields: x x x B E x x x v •
q , m

80. • • x q m B v E FE = q E and FB = q v B
Magnetism
What is the relation between the intensities of the electric and
magnetic fields for the particle to move in a straight line ?. x •
q m B v E
FE = q E and FB = q v B
If FE = FB the particle will move
following a straight line trajectory
q E = q v B
v = E / B FB FE •