Magnetic Materials. Ferromagnetic materials (ferrum iron) have strong magnetic properties. Loadstone contains magnetite which contains iron.

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2 Magnetic Materials Ferromagnetic materials (ferrum iron) have strong magnetic properties. Loadstone contains magnetite which contains iron. Magnetite is an oxide of iron and has the composition Fe 3 O 4.

3 Magnetizing Materials Magnetic Domains become aligned in External Magnetic Field. B

4 Magnetic Materials

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6 Moving Charges Produce Magnetic Fields

7 Atom Smallest Magnet: Electron Atomic Sources of Magnetic Fields

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9 B: The Magnetic Field Magnetic Field Lines point from North (+) to South (-)

10 Magnetic Compass North seeking compass points to Earth s Magnetic North which is really a South Pole. A compass arrow head is the north pole.

11 Magnets a magnet is electrically neutral a magnet has two poles: north & south like poles repel unlike poles attract No Magnetic Monopoles!

12 Use a compass to map out the field lines. How does a compass work?

13 A compass is a small magnet. Outside Field lines point from North to South.

14 A compass is a small magnet. Inside the Magnet, the Field points from South to North.

15 Which way will the magnet rotate? N N S S External B Field Like Poles repel, Unlike Poles Attract.

16 Which way will the magnet rotate? N S N S External B Field Magnets align themselves so that their internal field is aligned with the external B field.

17 Magnetic Force A charged particle moving in an EXTERNAL magnetic field experiences a force that is perpendicular to both the velocity and field. Only the perpendicular components give rise to a force. F qv B F qvb sin

18 F qv B

19 F qv B Review the Vector Product The magnitude of C is AB sin and is equal to the area of the parallelogram formed by A and B The direction of C is perpendicular to the plane formed by A and B The best way to determine this direction is to use the right-hand rule = r x F L r p A B ˆ i ˆ j k ˆ A B A B A B A B A B A B y z z y x z z x x y y x

20 Direction: Right-Hand Rule #1 The fingers point in the direction of v B comes out of your palm Curl your fingers in the direction of B The thumb points in the direction of v x B which is the direction of F B

21 Direction: Right-Hand Rule #2 Alternative to Rule #1 Thumb is in the direction of v Fingers are in the direction of B Palm is in the direction of F B On a positive particle You can think of this as your hand pushing the particle

22 Direction: Right Hand Rule #2 For Protons! Fingers Field, Thumb Beam, Palm Force

23 Direction of the Force? Into the Page. Same Greatest Same Rank the Force Magnitudes.

24 Direction: Left Hand Rule #1 For electrons! Fingers Field, Thumb Beam, Palm Force

25 Which way will a proton move? An electron?

26 Which way will a proton move? An electron?

27 All three charges have the same mass. Determine if each charge is positive, negative or neutral. F F

28 Magnetic Field Strength (Magnitude Only) F qvb sin B F qv sin B N Tesla C m / s The cgs unit is a gauss (G) 1 T = 10 4 G N Am

29 Some typical B fields: surface of the Earth small bar magnet MRI LHC Magnet lab surface of neutron star 10-4 T 10-2 T 2-3 T 10T 30 T 10 8 T

30 Magnetic Force A charged particle moving in an EXTERNAL magnetic field experiences a force that is perpendicular to both the velocity and field. Only the perpendicular components give rise to a force. F qvb sin 0 90 No Force Max Force

31 Example F qvb sin A proton in a particle accelerator has a speed of 6x10 6 m/s. The magnetic field is 0.40T and makes an 30 degree angle with the velocity of the proton as shown. What is the acceleration? F qvb sin x10 C(6x10 m / s)(.40 sin 30) 1.92x10 a 13 F / m N Ns Cm p: direction UP e: direction DOWN / x N x kg 1.2x10 m/ s 14 2

32 Circular Trajectory The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. 2 F C mv r F qvb sin Radius of Circular Path: r mv qb

33 Cyclotron Frequency The angular speed of a particle is referred to as the cyclotron frequency: v r qb m T 2 2m qb r mv qb The angular speed and period do not depend on the linear speed or on the radius of the orbit!

34 Example A proton with a speed of 2.2 x 10 6 m/s is shot into a region of constant B separated by a distance of 0.18m. What is B so that the proton misses the opposite plate?

35 Example A proton with a speed of 2.2 x 10 6 m/s is shot into a region of constant B separated by a distance of 0.18m. What is B so that the proton misses the opposite plate? r mv qb B mv qr B / x10 C.18m x kg x m s m/ s 0.13 kg C m s x s 0.13 N Am B 0.13T

36 Example The electric potential difference between the plates is 2100V. What is the speed of the proton when it exits the capacitor? KE 1 PE 2 2 mv qv v 2qV m

37 Mass Spectrometer An ion source in a spectrometer produces doubly ionized gold ions (Au 2+ ) each with a mass of 3.27 x10 25 kg. The ions are accelerated from rest through a potential difference of 1kV. Then, a 0.500T magnetic field causes the ions to follow a circular path. Determine the radius of curvature. v r 2qV m r Eliminate v to get: mv qb r x10 kg 10 J / C 2 1.6x10 C(.5 Ns / Cm) r = 0.09m mV 2 qb

38 Three ions with the same charge move through a constant Magnetic Field. Rank their masses. m 2 qr 2V B 2 1 > 3 > 2

39 Simple Motor feature=fvwp&nr=1

40 MHD Propulsion Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids Yamato 1

41 Last Time: Magnetic Force A charged particle moving in an EXTERNAL magnetic field experiences a force that is perpendicular to both the velocity and field. Only the perpendicular components give rise to a force. F qv B F qvb sin

42 Charged Particle in a Magnetic Field with velocity component parallel to the field moves in a Helical path. The pitch is the distance between loops. mv r qb v v v 2 2 y z

43 Radius of Gyration r mv qb

44 Particle in a Nonuniform The motion is complex For example, the particles can oscillate back and forth between two positions This configuration is known as a magnetic bottle Magnetic Field

45 Magnetic Bottles: Tokamaks Such a plasma-confinement scheme could fulfill a crucial role in the control of nuclear fusion, a process that could supply us with an almost endless source of energy Serway, page 838

46 Problems with Fusion? Tritium is RARE! Tritium is RARE! Breeding it: Cost: ~ $200 million/kg Need ~ 56kg/year for the ITER Breathing it:

47 Cost of Fusion? Average US Budget for Fusion Energy per year over past 50 years: $~250 Million x 50 years ~ $13 Billion so far 2008 Budget: Fusion Energy Science: $428 Million 2012 Budget: Fusion Energy Science: $398 Million

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49 Confined Fusion: The Energy of the Future and it ALWAYS will be! World Cost for ITER: $25 Billion

50 FREE: Solar Fusion: The Energy of the Present and it ALWAYS will be!

51 Solar Wind

52 The Earth s magnetic field shield us from the stream of charged particles from the Sun called the solar wind

53 Van Allen Radiation Belts The particles are trapped by the Earth s magnetic field and spiral from pole to pole, creating auroras The inner Van Allen Belt extends from an altitude of ,000 km (0.1 to 1.5 Earth radii) above the Earths surface, and contains high concentrations of energetic protons with energies exceeding 100 MeV and electrons in the range of 100's of kev, trapped by the strong (relative to the outer belts) magnetic fields in the region. The outer belt consists mainly of high energy ( MeV) electrons trapped by the Earth's magnetosphere.

54 Starfish Prime: Man Made Belts Starfish Prime was a high-altitude (400 km) nuclear bomb test conducted by the United States of America on July 9, It produced a yield of 1.4 megatons of TNT. While some of the energetic beta particles followed the earth's magnetic field and illuminated the sky, other high-energy electrons became trapped in manmade radiation belts around the earth. These man-made radiation belts eventually crippled one-third of all satellites in low orbit. Seven satellites were destroyed as radiation knocked out their solar arrays or electronics, including the first commercial communication satellite ever, Telstar. The flash created by the explosion as seen through heavy cloud cover from Honolulu 1,300 km away

55 Auroras The colors are caused by energetic electrons colliding with oxygen and nitrogen molecules in the atmosphere. This excites the molecules, and when they decay from the excited states they emit the light that we see in the aurora.

56 Aurora surrounding the north geomagnetic pole as seen from space

57 Aurora as seen from space

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60 Radius of Gyration r mv qb A charged particle from the solar wind traveling with a speed of 9.0x10 6 m/s encounters the Earth s Magnetic Field at an altitude where the field has a magnitude of 1.2x10-7 T. Assuming that the particle s velocity is perpendicular to the magnetic field, find the radius of curvature of the path if it is a) a proton and b) an electron.

61 Great Demo: Wire JUMP

62 Magnetic Force on a Current Carrying Wire F qv B F qv Bsin d x q Bsin t q xbsin t F ILB sin OR: F total F qv total d qv I nqv A d B(#charges) d B(nAL) L LLˆ F ILB

63 Magnetic Force on a Current Carrying Wire F ILB L LLˆ

64 Force on a Wire, Arbitrary Shape Consider a small segment of the wire, The force exerted on this segment is df The total force is b F B B I dsb I a dsb ds

65 Use Vector Notation! F ILB

66 Use Vector Notation! F ILB

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68 HW 37. A rod of mass m and radius R rests on two parallel rails that are a distance d apart and have a length L. The rod carries a current I (in the direction shown) and rolls along the rails without slipping. A uniform magnetic field B is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails? F I LB

69 Review! Review! Review!

70 Great Demo: Jumping Ring The magnetic force on each bit of ring is radially inward and upward, at angle above the radial line. The radially inward components tend to squeeze the ring but all cancel out as forces. The upward components add: F ILB df IdsB sin F IBsin ds F I2rB sin up

71 The Motor Effect: Torque An electric current in a magnetic field experiences a force that is perpendicular to both the direction of current and the direction of the field. If that current is bent into the shape of a loop, the magnetic force produces a torque that causes the loop to rotate. This is the basis of The Motor Effect.

72 F ILB Torque on a Current Loop The rectangular loop carries a current I in a uniform magnetic field No magnetic force acts on sides 1 & 3 The wires are parallel to the field and L x B = 0

73 F ILB Torque on a Current Loop There is a force on sides 2 & 4 perpendicular to the field The magnitude of the magnetic force on these sides will be: F 2 = F 4 = IaB The direction of F 2 is out of the page The direction of F 4 is into the page

74 F ILB Torque on a Current Loop The forces are equal and in opposite directions, but not along the same line of action The forces produce a torque around point O

75 F ILB Torque on a Current Loop The maximum torque is found by: b b b b τmax F2 F4 (I ab ) (I ab ) I abb The area enclosed by the loop is ab, so max = IAB This maximum value occurs only when the field is parallel to the plane of the loop

76 Torque on a Current Loop Assume the magnetic field makes an angle of < 90 o with a line perpendicular to the plane of the loop The net torque about point O will be = IAB sin τ IAB sin τ IAB

77 Problem τ IAB sin τ IAB A coil of wire has an area of 2.0x10-4 m 2 consists of 100 loops or turns, and contains a current of A. The coil is in a uniform magnetic field of 0.15 T. Find the maximum torque acting on the coil. This maximum value occurs only when the field is parallel to the plane of the loop NIABsin (0.045 A)2x10 m.015t sin x10 4 Nm

78 F ILB Magnetic Dipole Moment The product IA is defined as the magnetic dipole moment, m, of the loop Often called the magnetic moment SI units: A m 2 Torque in terms of magnetic moment: μ IAAˆ A AAˆ τ μb Potential Energy of a magnetic moment in an external mag field: U μb

79 Compare Dipoles p 2aq m IA τ pe τ μ E U -pe U -μb A AAˆ

80 Review! Review! Review! Torque is a Vector obeying the Right Hand Rule!!

81 23. A rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = m and b = m. The coil is hinged along the y axis, and its plane makes an angle θ = 30.0 with the x axis (Fig. P29.23). What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = T directed along the x axis when the current is I = 1.20 A in the direction shown? What is the expected direction of rotation of the coil? B τ μb μ IAAˆ The loop will rotate so as to align the magnetic moment with the B field. Looking down along the y-axis, the loop will rotate in a clockwise direction.

82 23. A rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = m and b = m. The coil is hinged along the y axis, and its plane makes an angle θ = 30.0 with the x axis (Fig. P29.23). What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = T directed along the x axis when the current is I = 1.20 A in the direction shown? What is the expected direction of rotation of the coil? NBAI sin T m 1.20 A sin N m Clockwise

83 The Motor Effect: Meters

84 The Motor Effect: Motors The loop will rotate so as to align the magnetic moment with the external magnetic field. A IABsin Fsin Loop Width: w, Length: l

85 The Motor Effect: Motors The loop will rotate so as to align the magnetic moment with the external magnetic field. A IAB sin Loop Width: w, Length: l

86 The Motor Effect: Motors The loop will rotate so as to align the magnetic moment with the external magnetic field. IABsin A Loop Width: w, Length: l

87 The Motor Effect: Motors The loop will rotate so as to align the magnetic moment with the external magnetic field. The loop with oscillate back and forth unless there are brushes. IABsin A Torque Reverses! KILL CURRENT! LET MOMENTUM CARRY LOOP! Loop Width: w, Length: l

88 Motors: Brushes The split-ring commutator keeps the current in the proper direction to yield a torque that produces a continuous rotation of the coil. Split-ring commutator

89 Motors: Brushes The split-ring commutator keeps the current in the proper direction to yield a torque that produces a continuous rotation of the coil.

90 Brushless DC Motors In a BLDC motor, the electromagnets do not move; instead, the permanent magnets rotate and the armature remains static. The brush-system/commutator assembly is replaced by an intelligent electronic solid-state circuit controller rather than a commutator/brush system. Spindle motor from a 3.5" floppy disk drive A BLDC motor powering a micro remote-controlled airplane. The motor is connected to a microprocessor-controlled BLDC controller. The poles on the stator of a twophase BLDC motor. This is part of a computer cooling fan; the rotor has been removed.

91 Fun Problems! Draw Vector Diagrams! Use Vector Notation!

92 The TOTAL FORCE Electric & Magnetic Fields The Electric Force acts parallel to the Electric Field. F qe qvb The Magnetic Force acts perpendicular to the Magnetic Field and the velocity.

93 Cathode Ray Tube Electric Force makes the Electron gun. Magnetic Force directs the beam. Cathode TV has 3 electron guns, one for each color RGB which scan 525 times in 1/30 of a second.

94 Velocity Selector Used when all the particles need to move with the same velocity A uniform electric field is perpendicular to a uniform magnetic field When the force due to the electric field is equal but opposite to the force due to the magnetic field, the particle moves in a straight line This occurs for velocities of value v = E / B Only those particles with the given speed will pass through the two fields undeflected The magnetic force exerted on particles moving at speed greater than this is stronger than the electric field and the particles will be deflected upward Those moving more slowly will be deflected downward

95 Bainbridge Mass Spectrometer A mass spectrometer separates ions according to their mass-to-charge ratio A beam of ions passes through a velocity selector and enters a second magnetic field In general, m/q can be determined by measuring the radius of curvature and knowing the magnitudes of the fields JJ Thomson s variation found e/m e by measuring the deflection of the beam and compared it to mass-to-charge ratio of protons, proving the existence of the electron as a subatomic particle! m q rbob E

96 Hall Voltage This shows an arrangement for observing the Hall effect The Hall voltage is measured between points a and c

97 Hall Voltage When the charge carriers are negative, the upper edge of the conductor becomes negatively charged c is at a lower potential than a When the charge carriers are positive, the upper edge becomes positively charged c is at a higher potential than a

98 Hall Voltage V H = E H d = v d B d d is the width of the conductor v d is the drift velocity If B and d are known, v d can be found IB RH IB VH nqt t R H = 1 / nq is called the Hall coefficient A properly calibrated conductor can be used to measure the magnitude of an unknown magnetic field

99 The Hall Effect When a current carrying conductor is placed in a magnetic field, the magnetic force causes a separation of charge in the conductor which produces a charge separation and voltage, V H, in a direction that is perpendicular to both the current and the magnetic field. V qe qv B H d This Hall voltage produces an E field that opposes the Hall Effect and tries to push the electrons back up. Eventually, balance is reached. By measuring the voltage you can use a hall probe to measure the magnetic field.

100 Earth s interior consists of a rocky mantle and an iron rich core

101 The Earth s magnetic field is caused by dynamo movements in Earth s core

102 Earth s magnetic field flips poles. Consecutive reversals are spaced 5 thousand years to 50 million years apart. The last reversal happened 740,000 years ago. Some researchers think our planet is overdue for another one, but nobody knows exactly when the next reversal might occur.

103 The Sun's north magnetic pole is pointing through the Sun's southern hemisphere, until the year 2012 when they will reverse. This transition happens, as far as we know, at the peak of every 11- year sunspot cycle -- like clockwork.

104 Babcock s magnetic dynamo is one possible explanation of the sunspot cycle where magnetic field lines become complexly entangled after many solar rotations

105 The Sun s magnetic fields create sunspots Zeeman effect - spectral lines split in regions of high magnetic fields

106 Magnetic field lines connect sunspots on the Sun s photosphere

107 Solar magnetic fields also create other atmospheric phenomena plages filaments

108 Solar magnetic fields also create other atmospheric phenomena plages filaments prominences

109 Solar magnetic fields also create other atmospheric phenomena plages filaments prominences solar flares

110 Solar magnetic fields also create other atmospheric phenomena plages filaments prominences solar flares coronal holes

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112 Solar magnetic fields also create other atmospheric phenomena plages filaments prominences solar flares coronal holes coronal mass ejections (CMEs)

113 NEXT: Currents Produce Magnetic Fields Too! Smallest Magnet: Electron

114 Magnetic Fields due to Currents Magnitude of the Field: B m 2 0 I r 7 m 4x10 T m/ A 0 mew not : The permeability of free space. Permeability is a measure of a materials ability to be permeated by magnetic fields ferromagnetic materials have a higher permeability.

115 This Week s Lab Using a Tangent Galvanometer to Measure the Earth s Magnetic Field Magnetic Field at the center of the loop: B m0i 2 r Horizontal Earth Field Total Field