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Magnetism

Magnetism. B. B. B. x x x x x x x x x x x x x x x x x x. ® ® ® ® ® ® ® ® ® ®. ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ . v. v. v. ´. The Magnetic Force. q. q. q. F. F = 0. F. Introduction to Magnetic Phenomena Bar magnets & Magnetic Field Lines

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Magnetism

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  1. Magnetism B B B x x x x x x x x x x x x x x x x x x ® ® ® ® ® ® ® ® ® ® ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ v v v ´ The Magnetic Force q q q F F = 0 F

  2. Introduction to Magnetic Phenomena Bar magnets & Magnetic Field Lines Source of Fields: Monopoles? Currents? Zip disks and refrigerators Magnetic forces: The Lorentz Force equation Motion of charged particle in a Constant Magnetic Field. Today... Text Reference: Chapter 28.1, 28.2, 28.4, 29.5 Examples: 28.1 and 28.4 through 28.6

  3. Magnetic effects from natural magnets have been known for a long time. Recorded observations from the Greeks more than 2500 years ago. The word magnetism comes from the Greek word for acertain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece. Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched. Small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field. Magnetism

  4. Bar magnet ... two poles: N and S Like poles repel; Unlike poles attract. Magnetic Field lines: (defined in same way as electric field lines, direction and density) Bar Magnet You will map this field (and others) in lab !! • Does this remind you of a similar case in electrostatics?

  5. Electric Field Linesof an Electric Dipole Magnetic Field Lines of a bar magnet

  6. Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge). How can you isolate this magnetic charge? Try cutting a bar magnet in half: S N S N S N Magnetic Monopoles Even an individual electron has a magnetic “dipole”! • Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac) • No monopoles have ever been found:

  7. What is the source of magnetic fields, if not magnetic charge? Answer: electric charge in motion! e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet. Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter. Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) Source of Magnetic Fields?

  8. Magnetic Materials(a simple look at an advanced topic) • Materials can be classified by how they respond to an applied magnetic field, Bapp. • Paramagnetic (aluminum, tungsten, oxygen,…) • Atomic magnetic dipoles (~atomic bar magnets) tend to line up with the field, increasing it. But thermal motion randomizes their directions, so only a small effect persists: Bind ~ Bapp•10-5 • Diamagnetic (gold, copper, water,…) • The applied field induces an opposing field; again, this is usually very weak; Bind ~ -Bapp•10-5[Exception: Superconductors exhibit perfect diamagnetism  they exclude all magnetic fields] • Ferromagnetic (iron, cobalt, nickel,…) • Somewhat like paramagnetic, the dipoles prefer to line up with the applied field. But there is a complicated collective effect due to strong interactions between neighboring dipoles  they tend to all line up the same way. • Very strong enhancement.Bind ~ Bapp•10+5

  9. Magnetic Domains • Even in the absence of an applied B, the dipoles tend to strongly align over small patches – “domains”. Applying an external field, the domains align to produce a large net magnetization. • “Soft” ferromagnets • The domains re-randomize when the field is removed • “Hard” ferromagnets • The domains persist even when the field is removed • “Permanent” magnets • Domains may be aligned in a different direction by applying a new field • Domains may be re-randomized by sudden physical shock • If the temperature is raised above the “Curie point” (770˚ for iron), the domains will also randomize  paramagnet Ferromagnets, cont.

  10. 1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? Lecture 12, Act 1 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic

  11. Diamagnetism and paramagnetism are far too weak to be used for a video tape. Since we want the information to remain on the tape after recording it, we need a “hard” ferromagnet. These are the key to the information age—cassette tapes, hard drives, ZIP disks, credit card strips,… Lecture 12, Act 1 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic

  12. 1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? End of paper clip S N Lecture 12, Act 1 The materials are all “soft” ferromagnets. The external field temporarily aligns the domains so there is a net dipole, which is then attracted to the bar magnet. - The effect vanishes with no applied B field - It does not matter which pole is used.

  13. IBM introduced the first hard disk in 1957, when data usually was stored on tapes. It consisted of 50 platters, 24 inch diameter, and was twice the size of a refrigerator. A “bit” of history It cost $35,000 annually in leasing fees (IBM would not sell it outright). It’s total storage capacity was 5 MB, a huge number for its time!

  14. What is the "magnetic force"? How is it distinguished from the "electric" force? Let’s start with some experimental observations about the magnetic force: a) magnitude: µto velocity of q b) direction: ^ to direction of q’s velocity c) direction: ^ to direction of B q v B is the magnetic field vector F mag We know about the existence of magnetic fields by their effect on moving charges. The magnetic field exerts a force on the moving charge. Magnetic Fields

  15. • The forceF on a charge q moving with velocity vthrough a region of space with electric field E and magnetic field B is given by: What’s that?? = + ´ F q E q v B B B B x x x x x x x x x x x x x x x x x x ® ® ® ® ® ® ® ® ® ® ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ v v v ´ q q q F F = 0 F Lorentz Force r r r r

  16. Preflight 12: Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero 2) The positive charge moves from point A toward B. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero

  17. Preflight 12: 3) The positive charge moves from point A toward C. The direction of the magnetic force on the particle is: a) up and right b) up and left c) down and right d) down and left

  18. Magnetic Force: If v = 0 F = 0. If then F = qvB Ifvis up, andBis into the page, thenFis to the left.

  19. Two protons each move at speedv (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons. What is the relation between the magnitudes of the forces on the two protons? y v 1 2A B v 2 x z (a) F1 < F2 (c)F1 > F2 (b) F1 = F2 • Inside the B field, the speed of each proton: • What is F2x, the x-component of the force on the second proton? 2B 2C (c)F2x > 0 (b) F2x = 0 (a) F2x < 0 (c)stays the same (b) increases (a) decreases Lecture 12, Act 2

  20. Two independent protons each move at speedv(as shown in the diagram) in a region of space which contains aconstant B fieldin the-z-direction.Ignore the interaction between the two protons. What is the relation between the magnitudes of the forces on the two protons? y v 1 2A B v 2 x z (a) F1 < F2 (c)F1 > F2 (b) F1 = F2 • The magnetic force is given by: r r r = ´ Þ = F q v B F qvB sin θ • In both cases the angle betweenvandBis 90°!! • ThereforeF1= F2. Lecture 12, Act 2

  21. Two independent protons each move atspeedv(as shown in the diagram) in a region of space which contains a constant B field in the-z-direction. Ignore the interaction between the two protons. What isF2x,the x-component of the force on the second proton? y v 1 2B B v 2 x z • To determine the direction of the force, we use the • right-hand rule. (c)F2x > 0 (b) F2x = 0 (a) F2x < 0 • As shown in the diagram,F2x < 0. F1 F2 Lecture 12, Act 2

  22. Two protons each move atspeedv(as shown in the diagram) in a region of space which contains a constant B field in the-z-direction. Ignore the interaction between the two protons. Inside the B field, the speed of each proton: y v 1 B v 2 x z Although the proton does experience a force (which deflects it), this is always to . Therefore, there is no possibility to do work, so kinetic energy is constant and is constant. 2C (c)stays the same (b) increases (a) decreases Lecture 12, Act 2

  23. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x B v q v F F R • Force is always ^ to velocity and B. What is path? • Path will be circle.Fwill be the centripetal force needed to keep the charge in its circular orbit.Calculate R: Trajectory in Constant B Field • Suppose chargeqentersB-field with velocityvas shown below. What will be thepath qfollows?

  24. Lorentz force: x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x F qvB = B v • centripetal acc: 2 v q = v a F F R R • Newton's 2nd Law: 2 v Þ = F ma = qvB m R mv Þ This is an important result, with useful experimental consequences ! = R qB Radius of Circular Orbit

  25. e- 1) Turn on electron ‘gun’ R 1 = 2 mv qV 2 DV 2) Turn on magnetic fieldB ‘gun’ mv = R qB 4) Rearrange in terms of measured values, V,R and B q 2 = 2 æ ö q v 2 V and = 2 ç ÷ v RB m è m ø Þ q 2 V = 2 2 m R B Ratio of charge to mass for an electron 3) Calculate B … next week; for now consider it a measurement

  26. m 8 NI - = = ´ × 4 for our coils 0 B 7 . 8 10 I 5 5 r q 2 V ≈1.8 1011 C/kg = 2 2 m R B e ( = 1.761011 C/kg ) me Let’s Try It... 1) Do the expt. Adjust I and V to get a good circle 2) Measure R = .05 m 3) What was V?V = 230 V 4) How about B?B~10-3 T

  27. Preflight 12: The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. 5) What is the direction of the magnetic field in chamber 1? a) Up b) Down c) Left d) Right e) Into page f) Out of page

  28. Preflight 12: 6) What is the direction of the magnetic field in chamber 2? a) Up b) Down c) Left d) Right e) Into page f) Out of page

  29. In chamber 1, the velocity is initially up. Since the particle’s path curves to the right, the force is to the right as the particle enters the chamber. Three ways to figure out the direction of B from this: 1) Put your thumb in the direction of theF(right) and your fingers in the direction of v (up) The way that your fingers curl is the direction ofB. 2) Put your palm in the direction ofF(right), and your thumb in the direction ofv(up), your fingers (keep them straight) point in the direction ofB. 3) Keep your thumb, index and middle fingers at right angles from each other. Your thumb points in the direction ofv(up), middle finger points towards F(right), then the index finger gives the the direction ofB(out of page)

  30. Preflight 12: 8) Compare the magnitude of the magnetic field in chamber 1 to the magnitude of the magnetic field in chamber 2. a) B1 > B2 b) B1 = B2 c) B1 < B2

  31. The magnetic force is always perpendicular to v. The force doesn’t change the magnitude of v, it only changes the particle’s direction of motion. The force gives rise to a centripetal acceleration. The radius of curvature is given by:

  32. L v B v B v1 B v1 B (c) W1 > W (b) W1 = W (a)W1 < W • A proton, moving atspeed v, enters a region of space which contains aconstant B field in the-z-direction and is deflected as shown. Lecture 12, Act 3 • Another proton, moving atspeedv1 = 2v,enters the same region of space and is deflected as shown. • Compare the work done by the magnetic field (W for v, W1for v1) to deflect the protons.

  33. L v B v B v1 B v1 B (c) W1 > W (b) W1 = W (a)W1 < W • Remember that the work doneWis defined as: • Also remember that the magnetic force is always perpendicular to the velocity: • Therefore, the work done isZEROin each case: • A proton, moving atspeedv, enters a region of space which contains a constant B fieldin the-z-direction and is deflected as shown. Lecture 12, Act 3 • Another proton, moving atspeedv1 = 2v,enters the same region of space and is deflected as shown. • Compare the work done by the magnetic field (W for v, W1for v1) to deflect the protons.

  34. Lorentz force equation: Static B-field does no work Velocity-dependent force given by right hand rule formula Next time: magnetic forces and dipoles Summary Reading assignment: Chapter 28.1 and 28.3 Examples: 28.2, 28.3, and 28.6 through 28.10

  35. Which charges carry current? The Hall Effect • Positive charges moving counterclockwise experience upward force • Upper plate at higher potential • Negative charges moving clockwise experience upward force • Upper plate at lower potential Equilibrium between electrostatic & magnetic forces: • This type of experiment led to the discovery (E. Hall, 1879) that current in conductors is carried by negative charges (not always so in semiconductors). • Can be used as a B-sensor; used in some ABS to detect shaft rotation speed – ferromagnetic rotating blades interupt the magnetic field  oscillating voltage

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