Magnetism A Whole New Topic October 23 2006

Magnetism A Whole New Topic October 23, 2006 Magnetism 1

This Week n n Today we begin magnetism – a topic that will occupy us for most of the remainder of the semester. Wednesday – Examination #2 • Potential, Capacitors, Resisters and DC Circuits. n n n There is a new, SHORT Web. Assign on board on RC. (2 problems) No quiz on Friday. We continue with Magnetism. Watch for new WA popping up after the exam. Magnetism 2

What did you think about the quiz on Friday? Both answers = 3 points. n n It was fair. It was unfair. Magnetism 3

Magnetism was known long ago. Magnetism 4

Lodestone (Mineral) • Lodestones attracted iron filings. • Lodestones seemed to attract each other. • Used as a compass. – One end always pointed north. – Called the “North Pole” • Lodestone is a natural magnet. Magnetism 5

Magnetism • Refrigerators are attracted to magnets! Magnetism 6

Where is Magnetism Used? ? • Motors • Navigation – Compass • Magnetic Tapes – Music, Data • Television – Beam deflection Coil • Magnetic Resonance Imaging • High Energy Physics Research Magnetism 7

Magnet Demo – Compare to Electrostatics N Magnet What Happens? ? S Pivot Magnetism 8

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. 9

Bring a magnet to a wooden rod • The wooden rod is attracted to the magnet. • The wooden rod is repelled by the magnet. • Nothing happens. Magnetism 10

Bring a magnet to an aluminum rod. • Nothing happens. • The magnet attracts the rod. • The magnet repels the rod. • It depends on whether the N or S pole is closest to the rod. • Nothing happens. Magnetism 11

Bring a neutral Teflon rod to a magnet… • The rod attracts the magnet. • The rod repels the magnet. • Nothing happens. Magnetism 12

Bring a charged Teflon rod to a magnet. . • It will attract the NORTH pole and repel the SOUTH pole. • It will repel the NORTH pole and will attract the SOUTH pole. • It will repel both poles. • It will attract both poles. • Nothing will happen. Magnetism 13

Observations • Bring a magnet to an electrically charged object and the observed attraction will be a result of charge induction. • 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 14

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 15

Consider a Permanent Magnet N Magnetism S 16

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

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 18

Field of a Permanent Magnet N N S S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 19

The Magnetic Field • Similar to Electric Field … exists in space. – Has Magnitude AND Direction. • The “stronger” this field, the greater is the ability of the field to interact with a magnet. Magnetism 20

Convention For Magnetic Fields X Field INTO Paper Magnetism B Field OUT of Paper 21

Experiments with Magnets Show • Current carrying wire produces a circular magnetic field around it. • Force on Compass Needle (or magnet) increases with current. Magnetism 22

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 23

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 24

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 25

Planet Earth Magnetism 26

Inside it all. 8000 Miles Magnetism 27

On the surface it looks like this. . Magnetism 28

Inside: Warmer than Floriduh Magnetism 29

Much Warmer than Floriduh Magnetism 30

Finally Magnetism 31

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 32

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 33

Ancient Navigation Magnetism 34

This planet is really screwed up! NORTH POLE Magnetism SOUTH POLE 35

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 36

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. 37

So much for the observations. Let’s do the physics! Magnetism 38

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 39

WHAT THE HECK IS THAT? ? ? • A WHAT PRODUCT? • A CROSS PRODUCT – Like an angry one? ? • Alas, yes …. • F=qv X B Magnetism 40

The Lorentz Force This can be summarized as: F or: v B mq q is the angle between B and V Magnetism 41

Nicer Picture Magnetism 42

VECTOR CALCULATIONS Magnetism 43

Note See proof of previous approach on the website. Magnetism 44

Practice B and v are parallel. Crossproduct is zero. So is the force. Which way is the Force? ? ? Magnetism 45

Units Magnetism 46

teslas are Magnetism 47

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 48

So… A moving charge can create a magnetic field. A moving charge is acted upon by a magnetic field. In Magnetism, things move. In the Electric Field, forces and the field can be created by stationary charges. Magnetism 49

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 50

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

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

Mag. Lev Magnetism 53

Motion of a charged particle in a magnetic Field Magnetism 54

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

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

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 57

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

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

The Loop 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 60

An Application The Galvanometer Magnetism 61

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 62

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 63

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. 64

Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper. ) + +B + v+ + + + + F + + + + + + B + + + Magnetism v 65

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 66

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 67

Magnetism 68

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! 69

Cyclotron Frequency +B + v + + + r + + + The time taken to complete one orbit is: + Magnetism F + 70

More Circular Type Motion in a Magnetic Field Magnetism 71

Mass Spectrometer Smaller Mass Magnetism 72

Magnetism 73

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 74

Problem Continued r Magnetism 75

Let’s Look at the effect of crossed E and B Fields: x x x B E x x x v q , m Magnetism • 76

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 77