General Physics (PHY 2140)

1. General Physics (PHY 2140) Lecture 7 • Electricity and Magnetism • Magnetism • Magnetic fields and force • Application of magnetic forces http://www.physics.wayne.edu/~alan/2140Website/Main.htm Chapter 19

2. Lightning Review • Last lecture: • DC circuits • Series and Parallel Resistors • Kirchoff’s rules • RC circuit Review Problem: The three light bulbs in the circuit all have the same resistance. Given that brightness is proportional to power dissipated, the brightness of bulbs B and C together, compared with the brightness of bulb A, is 1. twice as much. 2. the same. 3. half as much. P=I2R, I=V/2R P=2x(V2/4R2)R So P=1/2(V2/R)

3. Magnetism • 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.

4. 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

5. Magnetic Domains Ferromagnets, cont. • 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

6. 1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? Mini-quiz 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic

7. 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,… Mini-quiz 1A • Which kind of material would you use in a video tape? (a) diamagnetic (c) “soft”ferromagnetic (d) “hard”ferromagnetic (b) paramagnetic

8. 1B • How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”? End of paper clip S N Mini-quiz 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.

9. Applications: A “bit” of history 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. 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!

10. Magnetic Field Direction • The magnetic field direction (of a magnet bar) can studied with a small compass. S N

11. Magnetic Field Lines S N

12. Bar Magnet • 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) • Does this remind you of a similar case in electrostatics?

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

14. S N S N S N Magnetic Monopoles • 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: 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!

15. Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) Source of Magnetic Fields? • 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.

16. 19.2 Magnetic Field of the Earth • A small magnetic bar should be said to have north and south seeking poles. The north of the bar points towards the North of the Earth. • The geographic north corresponds to a south magnetic pole and the geographic south corresponds to a magnetic north. • The configuration of the Earth’s magnetic field resembles that of a (big) magnetic bar put in its center.

17. Magnetic Field of the Earth

18. Magnetic Field of the Earth • Near the ground, the field is NOT parallel to the surface of the Earth. • The angle between the direction of the magnetic field and the horizontal is called dip angle. • The north and south magnetic pole do not exactly correspond to the south and north geographic north. • South magnetic pole found (in 1832) to be just north of Hudson bay in Canada – 1300 miles from the north geographical pole.

20. More on the Magnetic Field of the Earth • The difference between the geographical north and the direction pointed at by a compass changes from point to point and is called the magnetic declination. • Source of the field : charge-carrying convection currents in the core of the earth. • In part related to the rotation of the earth • The orientation of the field “flips” and changes over time – every few million years… • Basalt rocks (iron content) • Other planets (e.g. Jupiter) are found to have a magnetic field. http://www.nasa.gov/vision/earth/lookingatearth/29dec_magneticfield.html

21. Magnetic Field of the Earth - normal G.A. Glatzmaier and P.H. Roberts

22. Magnetic Field of the Earth During a Field Reversal G.A. Glatzmaier and P.H. Roberts

23. Mini-quiz • You travel to Australia for a business trip and bring along your American-made compass. Does the compass work correctly in Australia??? • No problem using the compass in Australia. • North pole of the compass will be attracted to the South magnetic pole…i.e. the North geo. pole • The vertical component of the field is different (opposite) but that cannot be detected with normal operation of the compass.

24. 19.3 Magnetic Fields • Stationary charged particles do NOT interact with a magnetic field. • Charge moving through a magnetic field experience a magnetic force. • Value of the force is maximum when the charge moves perpendicularly to the field lines. • Value of the force is zero when the charge moves parallel to the field lines.

25. Magnetic Fields in analogy with Electric Fields Electric Field: • Distribution of charge creates an electric field E(r) in the surrounding space. • Field exerts a force F=q E(r) on a charge q at r Magnetic Field: • Moving charge or current creates a magnetic field B(r) in the surrounding space. • Field exerts a force Fon a charge movingq at r

26. Strength of the Magnetic Field • Define the magnetic field, B, at a given point in space in terms of the magnetic force imparted on a moving charge at that point. • Observations show that the force is proportional to • The field • The charge • The velocity of the particle • The sine of the angle between the field and the direction of the particle’s motion.

27. Strength and direction of the Magnetic Force on a charge in motion F B +q q v

28. Magnetic Field Magnitude

29. Magnetic Field Units • [F] = newton • [v] = m/s • [q] = C • [B] = tesla (T). • Also called weber (Wb) per square meter. • 1 T = 1 Wb/m2. • 1 T = 1 N s m-1 C-1. • 1 T = 1 N A-1 m-1. • CGS unit is the Gauss (G) • 1 T = 104 G. (Earth’s field ~ 0.5 G)

30. Right Hand Rule • Provides a convenient trick to remember the spatial relationship between F, v, and B. • Consider the motion of positive charge • Direction of force reversed if negative charge.

31. V = 1.0 x 105 m/s B = 55 mT Example: Proton traveling in Earth’s magnetic field. A proton moves with a speed of 1.0 x 105 m/s through the Earth’s magnetic field which has a value of 55 mT a particular location. When the proton moves eastward, the magnetic force acting on it is a maximum, and when it moves northward, no magnetic force acts on it. What is the strength of the magnetic force? And what is the direction of the magnetic field? N proton Northward or southward.

32. 19.4 Magnetic Force on Current-carrying conductor. • A magnetic force is exerted on a single charge in motion through a magnetic field. • That implies a force should also be exerted on a collection of charges in motion through a conductor i.e. a current. • And it does!!! • The force on a current is the sum of all elementary forces exerted on all charge carriers in motion.

33. 19.4 Magnetic Force on Current: some notation conventions x x x x x x x x x x x x x x x x x x x x x x x x • If B is directed into the page we use blue crosses representing the tail of arrows indicating the direction of the field, • If B is directed out of the page, we use dots. • If B is in the page, we use lines with arrow heads. . . . . . . . . . . . . . . . . . . . . . . . .

34. Force on a wire carrying current in a magnetic field. Bin 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 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 Bin Bin I I = 0 I

35. Force on a wire carrying current in a magnetic field. 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 x x x x x x vd q A Magnetic Field and Current at right angle from each other.

36. Force on a wire carrying current in a magnetic field. • General Case: field at angle q relative to current. B B sin q q I

37. Voice Coil

38. Reasoning: Negative charge flow down. Positive Current upward. B field direction Geo South to Geo North Answer: Force towards the west. I Mini-Quiz In a lightning strike, there is a rapid flow of negative charges from a cloud to the ground. In what direction is a lightning strike deflected by the Earth’s magnetic field?

40. Example: Wire in Earth’s B Field A wire carries a current of 22 A from east to west. Assume that at this location the magnetic field of the earth is horizontal and directed from south to north, and has a magnitude of 0.50 x 10-4 T. Find the magnetic force on a 36-m length of wire. What happens if the direction of the current is reversed? B=0.50 x 10-4 T. I = 22 A l = 36 m Fmax = BIl

41. I F B B F a/2 b F F a 19.5 Torque on a Current Loop • Imagine a current loop in a magnetic field as follows:

42. I F B B F a/2 b F F a

43. In a motor, one has “N” loops of current

44. 30.0o B Example: Torque on a circular loop in a magnetic field A circular loop of radius 50.0 cm is oriented at an angle of 30.0o to a magnetic field of 0.50 T. The current in the loop is 2.0 A. Find the magnitude of the torque. r = 0.500 m q= 30o B = 0.50 T I = 2.0 A N = 1

45. Galvanometer/Applications Device used in the construction of ammeters and voltmeters. Scale Current loop or coil Magnet Spring

46. Galvanometer used as Ammeter • Typical galvanometer have an internal resistance of the order of 60 W - that could significantly disturb (reduce) a current measurement. • Built to have full scale for small current ~ 1 mA or less. • Must therefore be mounted in parallel with a small resistor or shunt resistor. 60 W Galvanometer Rp

47. 60 W Galvanometer Rp • Let’s convert a 60 W, 1 mA full scale galvanometer to an ammeter that can measure up to 2 A current. • Rp must be selected such that when 2 A passes through the ammeter, only 0.001 A goes through the galvanometer. • Rp is rather small! • The equivalent resistance of the circuit is also small!

48. Galvanometer used as Voltmeter • Finite internal resistance of a galvanometer must also addressed if one wishes to use it as voltmeter. • Must mounted a large resistor in series to limit the current going though the voltmeter to 1 mA. • Must also have a large resistance to avoid disturbing circuit when measured in parallel. Rs 60 W Galvanometer

49. Rs 60 W Galvanometer Maximum voltage across galvanometer: Suppose one wish to have a voltmeter that can measure voltage difference up to 100 V: Large resistance

50. q v F 19.6 Motion of Charged Particle in magnetic field Bin • Consider positively charge particle moving in a uniform magnetic field. • Suppose the initial velocity of the particle is perpendicular to the direction of the field. • Then a magnetic force will be exerted on the particle and make follow a circular path. ´ ´´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ r