1. Magnetism
A Whole New Topic
March 5, 2007
Magnetism

2. This Week Exam #2 Returned
Today we begin magnetism – a topic that will occupy us for most of the remainder of the semester.
Quiz on Friday
Watch for WebAssignment
Next week: Spring Break – Enjoy!
Magnetism

3. SEE JBB
Average Grade = 54%
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4. What did you think about the exam last Friday? All answers = 3 points.
It was too difficult.
It was fair.
It was easy.
I should have studied more.
Magnetism

5. Magnetism was known long ago.

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

7. 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

8. Magnetism
Refrigerators are attracted to magnets!
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9. Where is Magnetism Used??
Motors
Navigation – Compass
Magnetic Tapes
Music, Data
Television
Beam deflection Coil
Magnetic Resonance Imaging
High Energy Physics Research
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10. Magnet Demo – Compare to Electrostatics
What Happens??
Pivot
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11. 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.
Magnetism

12. 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

13. Magnets
Magnetic Field
Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles.
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14. Consider a Permanent Magnet
The magnetic Field B goes from North to South.
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15. Introduce Another Permanent MagnetS
pivot
The bar magnet (a magnetic dipole) wants to align with the B-field.
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16. Field of a Permanent MagnetS
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

17. Field of a Permanent MagnetS
Show disk 19, demo 6 (minimum energy configuration of magnets)
The bar magnet (a magnetic dipole) wants to align with the B-field.
Magnetism

18. Convention For Magnetic FieldsB
X 
Field INTO Paper Field OUT of Paper
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19. Typical Representation
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20. 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.
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21. Current Carrying Wire B Right hand Rule-
Current into
the page.
Right hand Rule-
Thumb in direction of the current
Fingers curl in the direction of B
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22. 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

23. 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

24. Planet Earth
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25. Inside it all.
8000
Miles
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26. On the surface it looks like this..
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27. Inside: Warmer than Floriduh
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28. Much Warmer than Floriduh
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29. Finally
Hot Hot Hot
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30. 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

31. After molten lava emerges from a volcano, it solidifies to a rock
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

32. This planet is really screwed up!
NORTH
POLE
SOUTH POLE
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33. Repeat And it REVERSES from time to time. 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
And it REVERSES from time to time.
Magnetism

34. Rowland’s Experiment xxx xxx B INSULATING 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 ++
Magnetism

35. A Look at the Physics q If the charge is moving, there
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
Magnetism

36. WHAT THE HECK IS THAT??? A WHAT PRODUCT?
A CROSS PRODUCT – Like an angry one??
Alas, yes ….
F=qv X B
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37. The Lorentz Force This can be summarized as: F or: v q m B
q is the angle between B and V
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38. Nicer Picture
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39. Another Picture
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40. VECTOR CALCULATIONS
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41. Practice B and v are parallel. Crossproduct is zero. So is the force.
Which way is the Force???
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42. Units
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43. teslas are
HUGE!
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44. 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:
(Use “Right-Hand” Rule to
determine direction of F)
And --- the charge must be moving !!
Magnetism

45. 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”.
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46. The Wire in More Detail Assume all electrons are moving
with the same velocity vd. L
B out of plane of the paper
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47. Magnetic Levitation Magnetic Force Current = i mg
Where does B point????
Into the paper.
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48. MagLev
                                                                                     
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49. 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
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50. There was a crooked man who lived in a crooked house that was wired with crooked wires
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51. Crooked Wire (in a plane) in a constant B field
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52. 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.
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53. The net magnetic force on a closed current carrying loop is ZERO!
Case 2
The net magnetic force on a closed current carrying loop is ZERO!
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54. Current Loop
What is force
on the ends??
Loop will tend to rotate due to the torque the field applies to the loop.
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55. 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
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56. An Application The Galvanometer
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57. 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)
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58. Don't hurt yourself doing this!
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!
Magnetism

59. 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.
Magnetism

60. an equilateral triangle? What is the torque if the loop is a square or
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?
Magnetism

61. Motion of a charged particle in a magnetic Field
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62. Trajectory of Charged Particles in a Magnetic Field
(B field points into plane of paper.) v B F B v F
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63. 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
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64. Review of Rotational Motion 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
Magnetism

65. You have to remember this stuff.
YES !
You have to remember this stuff.
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66. 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!
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67. Cyclotron Frequency V cancels ! B The time taken to complete one v v B F r
The time taken to complete one
orbit is:
V cancels !
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68. More Circular Type Motion in a Magnetic Field
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69. the radius of the circular path and the speed of the electron.
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.
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70. Mass Spectrometer
Smaller Mass
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71. Magnetism

72. 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
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73. Problem Continued r
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74. • x x x x x x Let’s Look at the effect of crossed E and B Fields: B Ev •
q , m
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75. • • x q m B v E FE = q E and FB = q v B
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 •
Magnetism