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Transcript
Magnetism A Whole New Topic March 8, 2006 Magnetism 1 Introductory Material Magnetism 2 Dis Here Week Today we begin magnetism – a topic that will occupy us for most of the remainder of the semester. • I do not yet have the exam papers (Tuesday PM) but I will return them if I get them. Friday – Quiz on DC Circuits New material on the web New WebAssign on board – READ THE CHAPTER!! Magnetism 3 DEMO ON Magnetism Magnetism 4 Lodestone (Mineral) • Lodestones attracted iron filings. • Lodestones seemed to attract each other. • Used as a compass. – One end always pointed north. • Lodestone is a natural magnet. Magnetism 5 Magnetism • Refrigerators are attracted to magnets! Magnetism 6 Applications • Motors • Navigation – Compass • Magnetic Tapes – Music, Data • Television – Beam deflection Coil • Magnetic Resonance Imaging • High Energy Physics Research Magnetism 7 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. 8 Observations • Bring a magnet to an electrically charged object and nothing happens. No forces. • 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. – 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 9 Magnets Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles. Magnetism 10 Consider a Permanent Magnet B N Magnetism S 11 Introduce Another Permanent Magnet B N N S pivot S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 12 Field of a Permanent Magnet B N N S S The south pole of the small bar magnet is attracted towards the north pole of the big magnet. Also, the small bar magnet (a magnetic dipole) wants to align with the B-field. The field attracts and exerts a torque on the small magnet. Magnetism 13 Field of a Permanent Magnet B N N S S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 14 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 15 Convention For Magnetic Fields X Field INTO Paper Magnetism B Field OUT of Paper 16 Experiments with Magnets Show • Current carrying wire produces a circular magnetic field around it. • Force on Compass Needle (or magnet) increases with current. Magnetism 17 Current Carrying Wire Current into the page. B Right hand RuleThumb in direction of the current Fingers curl in the direction of B Magnetism 18 Current Carrying Wire • B field is created at ALL POINTS in space surrounding the wire. • The B field had magnitude and direction. • Force on a magnet increases with the current. • Force is found to vary as ~(1/d) from the wire. Magnetism 19 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 20 Planet Earth Magnetism 21 Inside it all. 8000 Miles Magnetism 22 On the surface it looks like this.. Magnetism 23 Inside: Warmer than Floriduh Magnetism 24 Much Warmer than Floriduh Magnetism 25 Finally Magnetism 26 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 27 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 28 Ancient Navigation Magnetism 29 This planet is really screwed up! NORTH POLE Magnetism SOUTH POLE 30 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 31 Rowland’s Experiment Field is created by any moving charge. Rotating INSULATING Disk which is CHARGED + or – on exterior. ++ Magnetism + + ++ xxx xxx B xxx Increases with charge on the disk. Increases with angular velocity of the disk. Electrical curent is a moving charge. 32 So much for the observations. Let’s do the physics! Magnetism 33 A Look at the Physics B q v q B 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. • If the charge is moving, there is a force on the charge, perpendicular to both v and B. F=qvxB Magnetism 34 WHAT THE HECK IS THAT??? • A WHAT PRODUCT? • A CROSS PRODUCT – Like an angry one?? • Alas, yes …. • F=qv X B Magnetism 35 The Lorentz Force This can be summarized as: F qv B F or: F qvBsin v B mq is the angle between B and V Magnetism 36 Nicer Picture Magnetism 37 VECTOR CALCULATIONS Magnetism i a b ax j ay k az bx by bz 38 Note See proof of previous approach on the website. Magnetism 39 Practice B and v are parallel. Crossproduct is zero. So is the force. Which way is the Force??? Magnetism 40 Units F Bqv Sin(θ ) Units : F N N B qv Cm / s Amp m Magnetism 1 tesla 1 T 1 N/(A - m) 41 teslas are Magnetism 42 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: F qE F qv B (Use “Right-Hand” Rule to determine direction of F) And --the charge must be moving !! Magnetism 43 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 44 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 vd. q it i L vd F qvd B i L vd B iLB vd vector : F iL B L in the direction of the motion of POSITIVE charge (i). B out of plane of the paper Magnetism 46 Magnetic Levitation Magnetic Force mg Current = i iLB mg Where does B point???? Into the paper. mg B iL Magnetism 47 MagLev Magnetism 48 WELCOME BACK! Magnetism 49 SCHEDULE 10 13-Mar BREAK BREAK BREAK 11 20-Mar Magnetic Field Sources of B Sources of B 12 27-Mar Ampere’s Law Faraday's Law Faraday’s Law 13 3-Apr Inductance Inductance EXAM #3 14 10-Apr Inductance - Finish AC Circuits AC Circuits 15 17-Apr AC Circuits EM FIELDS Light Topics 16 24-Apr Light Topics No Class FINAL EXAM 17 1-May No Class No Class No Class Magnetism 50 What’s are we doing?? This week • Finish B Fields and the motion of Particles • Sources of Magnetic Fields Friday • QUIZ – materials from the week before the break through this Wednesday Magnetism 51 What in the world were we doing before the binge??? F qv B Magnetism 52 AND ….. L q it i vd L F qvd B i vd B iLB vd vector : F iL B L in the direction of the motion of POSITIVE charge (i). Magnetism 53 Motion of a charged particle in a magnetic Field March 20, 2006 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 dFB Ids B b Fb I ds B I ds B a a b Magnetism 56 Case 1 dFB Ids B b Fb I ds B I ds B a a Fb IL'B b 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 dFB Ids B b Fb I ds B I ds B 0 a 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 t1=F1 (b/2)Sin() =(B i a) x (b/2)Sin() total torque on the loop is: 2t1 Total torque: t=(iaB) bSin() =iABSin() (A=Area) Magnetism 62 A Coil For a COIL of N turns, the net torque on the coil is therefore : Normal to the coil τ NiABSin(θ ) 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=NiA 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 Magnetism 65 Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper.) + +B + v+ + + + + + + + + F + + + + F + + + + + + + + + + + + + + + + + + + B + + + + + Magnetism v 66 Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper.) + +B + v+ + + + + + + + + F + + + + F + + + + + + + + + + + + + + + + + + + B + + + + + Magnetism v Magnetic Force is a centripetal force 67 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 = v2 / 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 = v2/r = 2 r KE = ½ mv2 = ½ mw2r2 F = mar = mv2/r = m2r 68 Magnetism 69 Radius of a Charged Particle Orbit in a Magnetic Field +B + + v+ + + + + + + + + + r + + + + + + F + Magnetism Centripetal Force = Magnetic Force mv 2 qvB r mv r qB Note: as Fv , the magnetic force does no work! 70 Cyclotron Frequency +B + + v+ + + + + + + + + + r + + + + + + F + Magnetism The time taken to complete one orbit is: 2r v 2 mv v qB T 1 qB f T 2 m qB c 2f m 71 More Circular Type Motion in a Magnetic Field Magnetism 72 Mass Spectrometer Smaller Mass Magnetism 73 Magnetism 74 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 2mK B 2 2 ed Magnetism 75 Problem Continued r From Before mv r qB 1 2 2K K mv so v 2 m m 2K 2mK r d 2 2 eB m e B Solve for B : 2mK B e2d 2 Magnetism 76 Let’s Look at the effect of crossed E and B Fields: x x x B E x x x v q , m Magnetism • 77 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 qE=qvB v=E/B FB FE • Magnetism 78