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Transcript
Magnetism A Whole New Topic Magnetism 1 Bad Week ….. Examination #2 on Friday Don’t miss the WebAssign on RC • RC will not be on the exam (you’re welcome!) Problem session on Wednesday Morning – 7:30 AM – Rm 306 – for BOTH sections. Spring Break Cancelled. Today we start on a new topic MAGNETISM. Check the two files on the website concerning vector products. • They may be helpful in this topic. Magnetism 2 Magnetism was known long ago. Magnetism 3 Lodestone (Mineral) • Lodestones attracted iron filings. • Lodestones seemed to attract each other. • Lodestone is a natural magnet. Magnetism 4 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 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 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 10 Magnets Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles. Magnetism 11 Consider a Permanent Magnet B N S The magnetic Field B goes from North to South. Magnetism 12 Introduce Another Permanent Magnet B N N S pivot S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 13 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. 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 14 Field of a Permanent Magnet B N N S S The bar magnet (a magnetic dipole) wants to align with the B-field. Magnetism 15 Convention For Magnetic Fields X Field INTO Paper Magnetism B Field OUT of Paper 16 Typical Representation Magnetism 17 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 18 Current Carrying Wire Current into the page. B Right hand RuleThumb in direction of the current Fingers curl in the direction of B Magnetism 19 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 20 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 21 Planet Earth Magnetism 22 Inside it all. 8000 Miles Magnetism 23 On the surface it looks like this.. Magnetism 24 Inside: Warmer than Floriduh Magnetism 25 Much Warmer than Floriduh Magnetism 26 Finally Magnetism 27 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 28 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 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 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 33 WHAT THE HECK IS THAT??? • A WHAT PRODUCT? • A CROSS PRODUCT – Like an angry one?? • Alas, yes …. • F=qv X B Magnetism 34 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 35 Nicer Picture Magnetism 36 Another Picture Magnetism 37 VECTOR CALCULATIONS Magnetism i a b ax j ay k az bx by bz 38 Practice B and v are parallel. Crossproduct is zero. So is the force. Which way is the Force??? Magnetism 39 Units F Bqv Sin(θ ) Units : F N N B qv Cm / s Amp m Magnetism 1 tesla 1 T 1 N/(A - m) 40 teslas are Magnetism 41 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 42 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 43 The Wire in More Detail Assume all electrons are moving with the same velocity vd. L L q it i vd F qvd B i L vd B iLB vd vector : F iL B B out of plane of the paper Magnetism Vector L in the direction of the motion of POSITIVE charge (i). 44 Magnetic Levitation Magnetic Force mg Current = i iLB mg Where does B point???? Into the paper. mg B iL Magnetism 45 MagLev Magnetism 46 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 47 There was a crooked man who lived in a crooked house that was wired with crooked wires Magnetism 48 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 49 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 50 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 51 Current Loop What is force on the ends?? Loop will tend to rotate due to the torque the field applies to the loop. Magnetism 52 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 53 An Application The Galvanometer Magnetism 54 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 55 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 56 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. 57 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 58 Motion of a charged particle in a magnetic Field Magnetism 59 Trajectory of Charged Particles in a Magnetic Field (B field points into plane of paper.) + +B + v+ + + + + + + + + F + + + + F + + + + + + + + + + + + + + + + + + + B + + + + + Magnetism v 60 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 61 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 62 Magnetism 63 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! 64 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 65 More Circular Type Motion in a Magnetic Field Magnetism 66 Review Problem. An electron moves in a circular path perpendicular to a constant magnetic field of magnitude 1.00 mT. 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 67 Mass Spectrometer Smaller Mass Magnetism 68 Magnetism 69 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 70 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 71 Let’s Look at the effect of crossed E and B Fields: x x x B E x x x v q , m Magnetism • 72 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 73