1. Magnetism

2. Magnetism Unit Plan Per 1/2 Per 7/8 Intro Thurs 4/4
Magnetic Fields Lab
Mag Forces (qvb)
Fri 4/5
Induction
Mon 4/8
Coils Lab
Fields in Wire
Tues 4/9
Generator Lab
Wed 4/10
Review
Thurs 4/11
Test
Thurs or Friday 4/11
R&A
WebAssign
Wed 4/

3. History of Magnets
(~800 BC) Ancient Chinese and Greeks discovered that certain stones would attract and magnetize iron.
Small slivers of the stone were found to align themselves with the North Pole.
Chinese were the first to use magnets for navigation.
The orienting properties were used to align streets in cities in the North-South / East-West direction.

4. Applications Computer disc drives (hard and floppy)
VCR and cassette tape
Credit cards
Speakers
Motors (Both AC and DC)
Speed sensors
Solenoids for relays, valves, etc.

5. Poles of a Magnet Magnets have a North and South Pole.
Like poles repel.
Unlike poles attract.
What happens if you break a magnet in half? Will you get two monopoles?
No.
N S
N S +

6. Magnetic Field Lines
Characteristically similar to electric field lines.
Magnetic field lines point away from the north pole and towards the south pole.
Magnetic field lines are continuous (They do not terminate on the surface!).
Magnetic field lines never cross.
The magnetic field is strongest where the field lines are most concentrated (North and South Pole).

7. Magnetic Flux What is magnetic flux? =BAcos Like electric flux
A measure of the strength of the magnetic field, B, passing through a surface perpendicular to the field.
For a bar magnet, the flux is maximum at the poles.
The more magnetic field lines, the higher the flux.
=BAcos

8. Oddly shaped magnets still have a north and a south
Magnets either attract or repel each other
South poles are attracted to north poles

9. Magnetic Field Lines vs. Electric Field Lines
Electric Dipole
Magnetic Dipole

10. Magnets either attract or repel each other
Like poles repel
South poles are attracted to north poles
Unlike poles attract

11. The Earth’s Magnetic Field
The earth has a magnetic field that scientist believe is a result of the dynamo effect due to electrical currents created in the molten iron and nickel outer core.
PHET Magnet and Compass
The Earth's Magnetic Field
Bar Magnet - 3D

12. Sometimes the field completely flips
Sometimes the field completely flips. The north and the south poles swap places. Such reversals, recorded in the magnetism of ancient rocks, are unpredictable. 
They come at irregular intervals averaging about 300,000 years; the last one was 780,000 years ago. Are we overdue for another? No one knows.

13. Magnetic Domains
A: Iron absent of a magnetic field. This material is magnetic but not a magnet.
B: Iron in the presence of a magnetic field. This is a magnet, either temporary or permanent.
C: A non-magnetic material. No domains.

14. Magnetic Domains = groups of atoms with aligned poles
Magnets can be temporary (like the needle used in the compass).
This nail has its atoms aligned, but the effect is only temporary.  You can get this affect by rubbing the nail on a magnet.
Neat fact:  Hitting the nail can demagnetize it, you are basically scrambling the atoms.

15. Ferromagnetism
Soft Ferromagnets: (Silicon-steels and Iron-Nickel alloys) When the domains align themselves when exposed to an external magnetic field and re-randomize in its absence.
Hard Ferromagnets: (ALNICO, ferrite and neodymium iron boron) Magnetic field persists even in the absence of an external field.
Domains may realign themselves when exposed to an external magnetic field.
Shocking them may re-randomize the domains, such as by dropping.
Heat at or above the Curie point will re-randomize the domains. Ferromagnets lose their ferromagnetism when heated above a specific temperature , because the thermal energy melts the magnetic alignment.

16. Metals that are ferromagnetic: nickel, iron, cobalt
Things that are not magnetic:  aluminum, plastic, glass

17. The Earth’s Magnetic Field
How does a compass behave in Earth’s Magnetic field? N
Earth’s Magnetic Field

18. Magnetism of Soft Ferromagnetic Materials
How does a magnet attract screws, bolts nails, paperclips, etc. when they are not magnetic to start with?
Soft ferromagnetic material align their domains in the presence of an external magnetic field creating a magnetic dipole.
When the magnetic field is removed, the domains re-randomize resulting in no magnetic attraction. They are temporary
Soft ferromagnetic material is attracted to both the North pole and South pole.
N S S

19. Example 1: Application of Magnetism
What type of ferromagnetic material would you use for video cassette tapes, audio cassette tapes, credit card strips, hard drives or floppy discs?
Soft Ferromagnetic
Hard Ferromagnetic
Diamagnetic
Paramagnetic
Diamagnetism and paramagnetism are too weak, and soft ferromagnetic material is temporary while the external field exists.

20. Types of Magnets
Temporary: When charged particles move through space, they induce a magnetic field (Electromagnets).
Permanent: Electrons have an intrinsic magnetic field that may add together in certain matter to create a magnetic field (Speakers).
Temporary
Permanent

21. Types of Magnetism
Ferromagnetism: Ferromagnetic materials (Iron, Cobalt, Nickel) exhibit a long-range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain. (Bind ~ Bapp x 105)
Paramagnetism: Paramagnetic materials (Aluminum, Tungsten, Oxygen) form weak magnetic dipoles at the atomic level when exposed to a magnetic field (Bind ~ Bapp x 10-5). Thermal motion results in randomization of the dipoles and a weak net magnetic field.
Diamagnetism: Diamagnetic materials (Gold, Copper, Water) respond to magnetic fields by developing a weakly opposing magnetic field (Bind ~ -Bapp x 10-5).
Bind = Induced Magnetic Field, Bapp = Applied Magnetic Field

22. Key Ideas All magnets have North and South Poles
Magnetic field lines originate in the North and end at the south pole.
Magnetic field lines do not cross.
Magnetism exists at the atomic level.
Magnetism is the result of moving charges.
Some magnets are temporary while others are permanent.
Types of Magnetism.
Ferromagnetism.
Paramagnetism.
Diamagnetism.

23. Magnetic Fields due to Current

24. Source of Magnetic Fields
Electrical Charge in motion.
Currents occur at the atomic level in atoms due to the orbits of electrons around the nucleus.
The intrinsic spin (+1/2, -1/2) is critical in the case of magnetism.

25. A Surprising Discovery
In 1820, Hans Christian Oersted discovered that moving charges create a magnetic field.

26. Magnetic Field of a Current Carrying Wire
Hans Christian Oersted discovered that a wire carrying current influenced the needles of nearby compasses.
By applying right-hand-rule #2, the direction of the magnetic field can be determined around the wire.
For an infinitely long straight wire:
B is proportional to I and inversely
proportional to r.
Magnetic Field due to a wire. I r
B a

27. Magnetic Field in a Loop of Wire
For the center of a circular loop, the magnetic field is:
Where:
N = number of turns of wire.
R = Radius of loop. NI R
B a

28. Magnetic Field of a Solenoid
For a solenoid, the magnetic field is given by:
B a NI L
B a nI
Where:
n = the number of turns per length of coil = N/L L

29. Magnetic Force on Current Carrying Wires
When two current carrying wires have current flowing in the same direction, they will be attracted to one another (a).
When two current carrying wires have current flowing in opposite directions, they will repel (b). F
(a) F
(b)

30. Magnetic Force on Current Carrying Wires(cont.)
-The influence of the magnetic field of wire (a) on wire (b).
-Using RHR #1, we see that the force by wire (a) on wire (b) is such that it is attracted to wire (b).
-The same is true for wire (b) on wire (a).
-However, even if the current is flowing in opposite directions, won’t the conductors be attracted to one another? x
(a)
(b) x x B

31. Magnetic Force on Current Carrying Wires(cont.)
                              
-No. Note that the magnetic fields cancel each other between the conductors while they add outside for two parallel conductors with current moving in the same direction.
-As a result the conductors are attracted to one another.
-In the case where the conductors have current flowing in opposite directions, the field lines add between them while they cancel outside. This results in a net repulsion between the two conductors.

32. Key Ideas
The strength of a magnetic field created by current in a wire is inversely proportional to the distance from the wire.
Two current carrying wires will attract each other if the current flows in the same direction
Two current carrying wires will repel each other if the current is in opposite directions.
The strength of the magnetic field of current in a loop is proportional the current in the loop and the number of loops.

33. Magnetic Forces

34. Forces in Magnetism
The existence of magnetic fields is known because of their affects on moving charges.
What is magnetic force (FB)?
How does it differ from electric force (FE)?
What is known about the forces acting on charged bodies in motion through a magnetic field?
Magnitude of the force is proportional to the component of the charge’s velocity that is perpendicular to the magnetic field.
Direction of the force is perpendicular to the component of the charge’s velocity perpendicular to the magnetic field(B).

35. Magnetic Force (Lorentz Force)
FB = |q|vB sinθ
Because the magnetic force is always perpendicular to the component of the charge’s velocity perpendicular to the magnetic field, it cannot change its speed.
Force is maximum when the charge is moving perpendicular to the magnetic field ( = 90).
The force is zero if the charge’s velocity is in the same direction as the magnetic field ( = 0).
Also, if the speed is not changing, KE will be constant as well.

36. What is the magnetic field (B)?
The magnetic field is a force field just like electric and gravitational fields.
It is a vector quantity.
Hence, it has both magnitude and direction.
Magnetic fields are similar to electric fields in that the field intensity is directly proportional to the force and inversely related to the charge.
E = FE/q
B = FB/(|q|v)
Units for B: N•s/C•m = 1 Tesla

37. Right Hand Rules
Right hand rule is used to determine the relationship between the magnetic field, the velocity of a positively charged particle and the resulting force it experiences.

38. Right Hand Rules #1 #2 #3
FB = |q|v x B

39. The Lorentz Force Equation & RHR
FB = qvB sinθ V +
Uniform B θ
vsinθ q
What is the direction of force on the particle by the magnetic field?
Right b. Left c. Up d. Down
Into the page f. Out of the Page

40. Lorentz Force
Two protons are launched into a magnetic field with the same speed as shown. What is the difference in magnitude of the magnetic force on each particle?
a. F1 < F2 b. F1 = F2 c. F1 > F2
x x x x v2 + v1
F = qv x B = qvBsinθ
Since the angle between B and the particles is 90o in both cases, F1 = F2.
How does the kinetic energy change once the particle is in the B field?
a. Increase b. Decrease c. Stays the Same
Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

41. Right Hand Rule – What is the Force?
x x x x x x + v
What is the direction of the magnetic force on the charge?
a) Down b) Up c) Right d)Left

42. Right Hand Rule – What is the Charge?
Particle 1:
Positive
Negative
Neutral
Particle 2:
Particle 3:

43. Right Hand Rule – What is the Direction of B
What is the direction of the magnetic field in each chamber? Up
Down
Left
Right
Into Page
Out of Page 1 4 2 3
What is the speed of the particle when it leaves chamber 4?
v/2 b. -v
v d. 2v
Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

44. Example 2: Lorentz Force
Two protons are launched into a magnetic field with the same speed as shown. What is the difference in magnitude of the magnetic force on each particle?
a. F1 < F2 b. F1 = F2 c. F1 > F2
x x x x v2 + v1
F = qv x B = qvBsinθ
Since the angle between B and the particles is 90o in both cases, F1 = F2.
How does the kinetic energy change once the particle is in the B field?
a. Increase b. Decrease c. Stays the Same
Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

45. Trajectory of a Charge in a Constant Magnetic Field
What path will a charge take when it enters a constant magnetic field with a velocity v as shown below?
x x x x x x + v
Since the force is always perpendicular to the v and B, the particle will travel in a circle
Hence, the force is a centripetal force.

46. Radius of Circular Orbit
What is the radius of the circular orbit?
x x x x x x
Lorentz Force: F = qv x B
Centripetal Acc: ac = v2/R
Newton’s Second Law: F = mac
qvB = mv2/R
R = mv/qB v + Fc R

47. Crossed Fields in the CRT
How do we make a charged particle go straight if the magnetic field is going to make it go in circles?
Use a velocity selector that incorporates the use of electric and magnetic fields.
Applications for a velocity selector:
Cathode ray tubes (TV, Computer monitor)

48. Crossed Fields - v + + + + + x x x x FE FB E - - - - - B into page E - v
Phosphor Coated Screen FB FE
E and B fields are balanced to control the trajectory of the charged particle.
FB = FE
Velocity Selector
qvB = qE
v = E/B

49. Earth’s Magnetosphere
Magnetic field of Earth’s atmosphere protects us from charged particles streaming from Sun (solar wind)

50. Aurora
Charged particles can enter atmosphere at magnetic poles, causing an aurora

51. The magnetic North Pole is responsible for more than just the direction a compass points. It's also the source of the aurora borealis, the dramatic lights that appear when solar radiation bounces off the Earth's magnetic field. 
This happens at the South Pole as well. In the southern hemisphere, the lights are called the aurora australas.

52. Force on a Current Carrying Wire
FB = |q|v x B = qvB sinθ (1)
Lets assume that the charge q travels through the wire in time t.
FB = (q)vBsinθ
When t is factored in, we obtain:
FB = (q/t)(vt) Bsinθ (2)
Where:
q/t = I (current)
vt = L (length of wire)
Equation (2) therefore reduces to:
FB = BIL sinθ

53. External Magnetic Field – Electromagnet or permanent magnet that provides an attractive and repulsive force to drive armature.
DC Motor
Split Ring Commutator – Brushes and split ring that provide the electrical connection to the armature from the external electrical source.
Armature – Part of the motor that spins that contains windings and an iron core.
DC Electric Motor

54. Key Ideas
Lorentz Force: A charge moving perpendicular to a magnetic field will experience a force.
Charged particles moving perpendicular to a magnetic field will travel in a circular orbit.
The magnetic force does not change the kinetic energy of a moving charged particle – only direction.
The magnetic field (B) is a vector quantity with the unit of Tesla
Use right hand rules to determine the relationship between the magnetic field, the velocity of a positively charged particle and the resulting force it experiences.

55. Optional Material

56. Torque on a Current Carrying Coil (Electric Motors/Galv.)
 = F•r

57. Torque on a Current Carrying Coil (cont.)B x • F -F
Zero Torque w
Direction of Rotation -F F • x I  • x -F F
Max Torque
Axis of Rotation

58. Torque on a Current Carrying Coil (cont.)
At zero torque, the magnetic field of the loop of current carrying wire is aligned with that of the magnet.
At maximum torque, the magnetic field of the loop of current carrying wire is at 90o.
The net force on the loop is the vector sum of all of the forces acting on all of the sides.
When a loop with current is placed in a magnetic field, the loop will rotate such that its normal becomes aligned with the externally applied magnetic field.

59. Torque on a Current Carrying Coil (cont.)
What is the contribution of forces from the two shorter sides (w)?
F = IwB sin (90o – )
Note 1:  is the angle that the normal to the wire makes with the direction of the magnetic field.
Note 2: Due to symmetry, the forces on the two shorter sides will cancel each other out (Use RHR #1). L w I
Axis of rotation
X X X X

60. Torque on a Current Carrying Coil (cont.)
What is the contribution of torque from the two longer sides (L)?
F = BIL for each side since L is always perpendicular to B.
The magnitude of the torque due to these forces is:
 = BIL (½w sin) + BIL (½w sin) = BILw sin (1)
Note: Since Lw = the area of the loop (A), (1) reduces to:
 = IAB sin
For a winding with N turns, this formula can be rewritten:
 = NIAB sin

61. Electromagnetic Induction

62. Faraday’s Hypothesis
If moving charges produced a magnetic field, could a moving or changing magnetic field produce a current?

63. Faraday’s Discovery
Faraday discovered that he could induce current by moving a wire loop through a magnetic field or moving the magnetic field through a wire loop.
Faraday’s Discovery is known as Electromagnetic Induction
Faraday's Discovery
Demo with large magnet and wire with galvanometer.
Demo with magnet and coil with galvanometer.

64. Electromotive Force FB = qvB sinθ We know that the Lorentz Force.
When a conductor moves through a magnetic field, a force is exerted on these charges causing them to separate, inducing an EMF. Which end of the wire is positive?
x x x x x x x x x v L

65. Electromotive Force
When a conductor moves through a magnetic field, a force is exerted on these charges causing them to separate, inducing an EMF
(Electro-motive force = voltage)
x x x x x x x x x v + - L

66. Electromotive Force + x x x x x x x x x -
The EMF results when the conductor has a velocity component perpendicular to the magnetic field.
Use RHR #1 where the thumb points in the direction of the velocity. The force on the bar is opposite the velocity.
x x x x x x x x x I v F - + I

67. Example 1: EM Induction
A segment of a wire loop is moving downward through the poles of a magnet, as shown. What is the direction of the induced current?
a. The current direction is out-of the page to the left.
b. There is no induced current.
c. The current direction is into the page to the right.

68. Example 2: EM Induction H Wed 4/3
The drawing shows three identical rods (A, B, and C) moving in different planes in a constant magnetic field directed along the +y axis. The length of each rod and the speeds are the same, vA = vB = vC. Which end (1 or 2) of each rod is positive?
Rod A:
1 b. 2 c. neither
Rod B:
Rod C:

69. Magnetic Flux What is magnetic flux? =BAcos Like electric flux
A measure of the strength of the magnetic field, B, passing through a surface perpendicular to the field.
For a bar magnet, the flux is maximum at the poles.
The more magnetic field lines, the higher the flux.
=BAcos

70. Magnetic Flux and EMF + x x x x x x - EMF = -ΔΦ/Δt Where:
 = BA cos and
= the angle the normal
to the surface makes
with B (in this drawing it
is 0o).
Note that the area enclosed by the circuit is increasing. I +
x x x x x x F I v -

71. Faraday’s Law of EM Induction
In the drawing on the previous slide, there is only one loop in the circuit.
When there is more than one loop in a circuit, as in the coil of a solenoid, the EMF induced by a changing magnetic field will increase by a factor equal to the number of loops in the coil.
EMF = -N ΔΦ/Δt
Where N = the number of loops in the coil.

72. Lenz’s Law
The induced EMF resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.
If the magnetic field is increasing, a current will develop to oppose the increasing magnetic field.
If the magnetic field is decreasing, a current will develop to create a magnetic field in the same direction as the one that is decreasing.
A current will form that attempts to keep the magnetic field constant.
Lenz’s Law abides by the laws of conservation of energy.
Lenz’s Law Demonstration.

73. Lenz’s Law
Lenz's Law

74. Note that the area inside the field is constant.
Lenz’s Law
No Current
Induced
Current
Current will be induced in the copper ring when it passes through a region where the magnetic field changes. When the magnetic field is constant or absent, their will be no induced current.
x x x x x x

75. Applications of Lenz’s Law (Eddy Currents)
Eddy current balances.
Eddy current dynamometer.
Metal detectors (Lenz's Law)
Braking systems on trains.
What are Eddy currents?
Eddy currents are currents created in conductors to oppose the changing magnetic fields they are exposed to.
Eddy currents respond to the changes in an external magnetic field.
Eddy currents can form in conductors even if they are not capable of being magnetized.

76. Key Ideas Moving charges create a magnetic field
Changing magnetic field produces a current (moving charges)
The current induced by a changing magnetic field produces a field that opposes the changing field!