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

This Week n n n Exam #2 Returned Today we begin magnetism – a This Week n n n 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 Web. Assignment Next week: Spring Break – Enjoy! Magnetism 2

SEE JBB Magnetism Average Grade = 54% 3 SEE JBB Magnetism Average Grade = 54% 3

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

Magnetism was known long ago. Magnetism 5 Magnetism was known long ago. Magnetism 5

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

New Concept The Magnetic Field – We give it the symbol B. – A 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 7

Magnetism • Refrigerators are attracted to magnets! Magnetism 8 Magnetism • Refrigerators are attracted to magnets! Magnetism 8

Where is Magnetism Used? ? • Motors • Navigation – Compass • Magnetic Tapes Where is Magnetism Used? ? • Motors • Navigation – Compass • Magnetic Tapes – Music, Data • Television – Beam deflection Coil • Magnetic Resonance Imaging • High Energy Physics Research Magnetism 9

Magnet Demo – Compare to Electrostatics N Magnet What Happens? ? S Pivot Magnetism Magnet Demo – Compare to Electrostatics N Magnet What Happens? ? S Pivot Magnetism 10

Results - Magnets S N Shaded End is NORTH Pole Shaded End of a 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. 11

Observations • Bring a magnet to an electrically charged object and the observed attraction 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 12

Magnets ld ie c. F ti gne Ma Cutting a bar magnet in half Magnets ld ie c. F ti gne Ma Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles. Magnetism 13

Consider a Permanent Magnet N S The magnetic Field B goes from North to Consider a Permanent Magnet N S The magnetic Field B goes from North to South. Magnetism 14

Introduce Another Permanent Magnet N N S pivot S The bar magnet (a magnetic Introduce Another Permanent Magnet N N S pivot S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 15

Field of a Permanent Magnet N N S S The south pole of the Field of a Permanent Magnet 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 16

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

Convention For Magnetic Fields X Field INTO Paper Magnetism B Field OUT of Paper Convention For Magnetic Fields X Field INTO Paper Magnetism B Field OUT of Paper 18

Typical Representation Magnetism 19 Typical Representation Magnetism 19

Experiments with Magnets Show • Current carrying wire produces a circular magnetic field around 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 20

Current Carrying Wire Current into the page. B Right hand Rule. Thumb in direction Current Carrying Wire Current into the page. B Right hand Rule. Thumb in direction of the current Fingers curl in the direction of B Magnetism 21

Current Carrying Wire • B field is created at ALL POINTS in space surrounding 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 22

Compass and B Field • Observations – North Pole of magnets tend to move 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 23

Planet Earth Magnetism 24 Planet Earth Magnetism 24

Inside it all. 8000 Miles Magnetism 25 Inside it all. 8000 Miles Magnetism 25

On the surface it looks like this. . Magnetism 26 On the surface it looks like this. . Magnetism 26

Inside: Warmer than Floriduh Magnetism 27 Inside: Warmer than Floriduh Magnetism 27

Much Warmer than Floriduh Magnetism 28 Much Warmer than Floriduh Magnetism 28

Finally Magnetism 29 Finally Magnetism 29

In Between n n n The molten iron core exists in a magnetic field In Between n n n 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 30

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

This planet is really screwed up! NORTH POLE Magnetism SOUTH POLE 32 This planet is really screwed up! NORTH POLE Magnetism SOUTH POLE 32

Repeat Navigation DIRECTION N S If N direction is pointed to by the NORTH 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 33

Rowland’s Experiment Field is created by any moving charge. Rotating INSULATING Disk which is Rowland’s Experiment Field is created by any moving charge. Rotating INSULATING Disk which is CHARGED + or – on exterior. ++ Magnetism + + ++ xxx B xxx Increases with charge on the disk. Increases with angular velocity of the disk. Electrical curent is a moving charge. 34

A Look at the Physics q There is NO force on a charge placed A Look at the Physics q 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. 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 35

WHAT THE HECK IS THAT? ? ? • A WHAT PRODUCT? • A CROSS WHAT THE HECK IS THAT? ? ? • A WHAT PRODUCT? • A CROSS PRODUCT – Like an angry one? ? • Alas, yes …. • F=qv X B Magnetism 36

The Lorentz Force This can be summarized as: F or: v B mq q The Lorentz Force This can be summarized as: F or: v B mq q is the angle between B and V Magnetism 37

Nicer Picture Magnetism 38 Nicer Picture Magnetism 38

Another Picture Magnetism 39 Another Picture Magnetism 39

VECTOR CALCULATIONS Magnetism 40 VECTOR CALCULATIONS Magnetism 40

Practice B and v are parallel. Crossproduct is zero. So is the force. Which Practice B and v are parallel. Crossproduct is zero. So is the force. Which way is the Force? ? ? Magnetism 41

Units Magnetism 42 Units Magnetism 42

teslas are Magnetism 43 teslas are Magnetism 43

The Magnetic Force is Different From the Electric Force. Whereas the electric force acts 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 44

Wires • A wire with a current contains moving charges. • A magnetic field 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 45

The Wire in More Detail Assume all electrons are moving with the same velocity The Wire in More Detail Assume all electrons are moving with the same velocity vd. L B out of plane of the paper Magnetism 46

Magnetic Levitation Magnetic Force mg Where does B point? ? Magnetism Current = i Magnetic Levitation Magnetic Force mg Where does B point? ? Magnetism Current = i Into the paper. 47

Mag. Lev Magnetism 48 Mag. Lev Magnetism 48

A conductor suspended by two flexible wires as shown in the diagram has a 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 49

There was a crooked man who lived in a crooked house that was wired There was a crooked man who lived in a crooked house that was wired with crooked wires Magnetism 50

Crooked Wire (in a plane) in a constant B field Magnetism 51 Crooked Wire (in a plane) in a constant B field Magnetism 51

Case 1 The magnetic force on a curved current carrying conductor in a uniform 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. Magnetism 52

Case 2 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! Magnetism 53

Current Loop What is force on the ends? ? Loop will tend to rotate Current Loop What is force on the ends? ? Loop will tend to rotate due to the torque the field applies to the loop. Magnetism 54

The Loop (From the top) OBSERVATION Force on Side 2 is out of the 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 55

An Application The Galvanometer Magnetism 56 An Application The Galvanometer Magnetism 56

The other sides t 1=F 1 (b/2)Sin(q) =(B i a) x (b/2)Sin(q) total torque The other sides t 1=F 1 (b/2)Sin(q) =(B i a) x (b/2)Sin(q) total torque on the loop is: 2 t 1 Total torque: t=(ia. B) b. Sin(q) =i. ABSin(q) (A=Area) Magnetism 57

A Coil Normal to the coil RIGHT HAND RULE TO FIND NORMAL TO THE 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. Magnetism 58

Dipole Moment Definition Define the magnetic dipole moment of the coil m as: m=Ni. Dipole Moment Definition Define the magnetic dipole moment of the coil m as: m=Ni. A 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. 59

A 40. 0 -cm length of wire carries a current of 20. 0 A. 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 60

Motion of a charged particle in a magnetic Field Magnetism 61 Motion of a charged particle in a magnetic Field Magnetism 61

Trajectory of Charged Particles in a Magnetic Field (B field points into plane of Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper. ) + +B + v+ + + + + F + + + + + + B + + + Magnetism v 62

Trajectory of Charged Particles in a Magnetic Field (B field points into plane of Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper. ) v+ + B + +B + v + + + F + + + + + + Magnetism Magnetic Force is a centripetal force 63

Review of Rotational Motion = s / r s = r ds/dt = d 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 = v 2 / 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 = v 2/r = 2 r KE = ½ mv 2 = ½ mw 2 r 2 F = mar = mv 2/r = m 2 r 64

Magnetism 65 Magnetism 65

Radius of a Charged Particle Orbit in a Magnetic Field +B + v+ + Radius of a Charged Particle Orbit in a Magnetic Field +B + v+ + + r + + + Centripetal Magnetic = Force Force + Magnetism F Note: as , the magnetic force does no work! 66

Cyclotron Frequency +B + v + + + r + + + The time Cyclotron Frequency +B + v + + + r + + + The time taken to complete one orbit is: + Magnetism F + 67

More Circular Type Motion in a Magnetic Field Magnetism 68 More Circular Type Motion in a Magnetic Field Magnetism 68

Review Problem. An electron moves in a circular path perpendicular to a constant magnetic Review Problem. An electron moves in a circular path perpendicular to a constant magnetic field of magnitude 1. 00 m. T. 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 69

Mass Spectrometer Smaller Mass Magnetism 70 Mass Spectrometer Smaller Mass Magnetism 70

Magnetism 71 Magnetism 71

An Example A beam of electrons whose kinetic energy is K emerges from a 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 Magnetism 72

Problem Continued r Magnetism 73 Problem Continued r Magnetism 73

Let’s Look at the effect of crossed E and B Fields: x x x Let’s Look at the effect of crossed E and B Fields: x x x B E x x x v q , m Magnetism • 74

What is the relation between the intensities of the electric and magnetic fields for 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 q. E=qv. B v=E/B FB FE • Magnetism 75