February 11, 2009

1. February 11, 2009 Warmup: A 2.5 ohm resistor is connected in parallel with 5 ohm resistor. They are both connected in series with a 4 ohm resistor. There is a 6 V power source. What is the power dissipated through the 2.5 ohm resistor?

2. Magnetic Fields and Moving Charges AP PHYSICS GIANCOLI CH.20 & 21

3. Objectives Discuss characteristics of magnets. Describe magnetic field lines Quantify magnetic fields. Calculate force on wires and charges.

4. Today’s Plan Turn in quiz corrections Discuss next unit and assignments, lab reports Intro magnetism Homework: Electricity practice, Lab report due Friday, Read for homework assignment

5. Magnetism Use the following website and any additional websites and resources to research your topic. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html Be ready to teach your subject to the class. You may use powerpoint or just draw on the board

6. Topics Ferromagnetic Paramagnetic Magnetic Fields Oersted and Right hand Rule Force on a single Chage (Lorentz Force) Induced EMF Gauss Tesla Magnetic Flux

7. Magnets • Knowledge of magnets has been around for thousands of years. • All magnets have a south and north pole. • No magnetic monopoles exist. • Like poles repel and unlike poles attract.

8. Magnets (some basics) 2 poles…always Ferromagnetic materials include iron, cobalt, nickel, and gadolinium Paramagnetic materials

9. Magnetic Fields Described with field lines Bar magnets Large poles Direction of field is tangent to line at any point Number of lines per unit area proportional to the magnitude of the field

10. Magnetic Field Lines • Magnets produce magnetic fields that come out of the north pole and into the south pole. • A compass (magnet free to move) will align itself with an external magnetic field. • North pole points in the direction of the magnetic field lines.

11. The Earth’s Magnetic Field

12. Quantifying Field Direction based on compass needle Magnitude of B defined as torque exerted on compass needle

13. Magnetic Fields and Forces on Electric Currents • Hans Christian Oersted found that when a compass needle is placed near an electric wire, the compass needle is deflected as soon as the wire carries a current. • He had discovered that an electric current produces a magnetic field. • The field lines are found to form concentric circles around the wire. I I

14. Magnetic Field around a Wire • The common method of determining the direction of the B-field is called the right hand rule. • Note: the rule is for conventional current, which means the flow of positive current.

15. Bin I P 30o Bout Example Problem 20-1 • Determine the direction of the unknown quantity in the following scenarios: • “X” = into the page, “•” = out of the page Direction of B, caused by I in the wire, at point P: Direction of I in the wire, which is causing B: x x x x x x x x • • •• • • ••

16. Forces on Current Carrying Wire • During the 19th century scientists found that a moving electric charge and a magnet have forces on each other. • Notice that the current and magnetic field are always both perpendicular to the force exerted on the wire. Units: Tesla (T), 1T =1N/A*m FB I B

17. Force on I in B Force is perpendicular to current in wire and magnetic field (B ) Right hand rule F = IlBsin() Strongest when current and B are perpendicular

18. Units for B Tesla (use this for calculations!) 1T = 1 N/A-m Gauss 1G = 1 x 10-4 T

19. Example Problem 20-2 • Determine the direction of the unknown quantity in the following scenarios: • “X” = into the page, “•” = out of the page Direction of I in a wire, if B causes Fmagto act on the wire: x x x x x Bin x x x x x Fmag x x x x x x x x x x

20. Railguns • Use high currents (millions of amps) to generate a strong magnetic force to accelerate and launch a projectile.

21. Rail Guns http://images.google.com/imgres?imgurl=http://static.howstuffworks.com/gif/railgun-8.gif&imgrefurl=http://science.howstuffworks.com/rail-gun1.htm&h=400&w=401&sz=23&hl=en&start=3&um=1&tbnid=2MwyfPiwGIwLjM:&tbnh=124&tbnw=124&prev=/images%3Fq%3Drail%2Bgun%2Bdiagram%26um%3D1%26hl%3Den%26rls%3Dcom.microsoft:*

22. Example Problem 20-4 • A current of 15A is directed along the positive x-axis and is perpendicular to a magnetic field. The conductor experiences a magnetic force per unit length of 0.12N/m in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes. B = 0.008T in the + z-direction

23. Magnetic Forces on Moving Charges • The force experienced by a current in a B-field is really just the combination of all of the individual forces on the charges that make up the current.

24. Cosmic Rays • Cosmic rays are electronsand protons streaming infrom the Sun.Most of these particlesare deflected by theEarth's magnetic field.

25. Example Problem 20-5 • Determine the magnitude and direction of the magnetic force that acts on an electron traveling upward at 3m/s in a horizontally-oriented B-field of strength 0.08T directed to the north. FB = 3.84x10-20 N West

26. Example Problem 20-6 • A proton is accelerated through a potential difference of 900V before it enters into a magnetic field of strength 0.04T. Calculate the magnitude of force exerted by the B-field on the proton if the field is perpendicular to its velocity. FB = 2.66x10-15 N

27. Motion of a Moving Charge in a B-Field • When a charge particle enters a B-field, moving perpendicular to the field, the magnetic force will always be directed perpendicular to the velocity and therefore will cause circular motion.

28. RHR for moving charges

29. Example Problem 20-7 • An alpha particle (m = 4mp, Q = +2e) enters into a B-field perpendicular to its velocity which has a strength of 1.52T. What is the radius of the path taken by the particle if its velocity is 7.6x106 m/s? r = 10.4cm

30. Mass Spectrometer • This fact is used in a device called a mass spectrometer to find the mass of a charged particle.

31. Strength of B-Field caused by Current • The strength of the magnetic field caused by the current (I) in a wire is proportional to the size of the current and inversely proportional to the distance from the wire. x x x x x x x x x x x x x x x I ••••• ••••• uo = vacuum permeability = 4πx10-7 T•m/A •••• •

32. 2 Long Wires 2 current carrying wires will exert forces on each other. Right hand rules to determine field direction and force direction on wire. Currents same direction—attractive. Currents opposite directions—repulsive.

33. Example Problem 20-8 and 20-9 • Wire 1 and wire 2 are separated by a distance of 18cm, and carry current of 9A upward and 20 downward. Find the magnitude and direction of the net magnetic field at point P, 12cm to the left of wire. Btotal = 2x10-4T • Find the magnitude and direction of the force that wire 1 is exerting on wire 2. 9A 20A P 12cm 18cm F = 2x10-4 N/m Wire 1 Wire 2

34. Magnetic Fields by Circular Wires • A single loop of a current carrying wire can produce a magnetic field similar to a permanent magnet. N S

35. Solenoids • A solenoid is a long coil of wire consisting of many loops (or turns). The magnetic field inside a solenoid can be very large because: the total field will be the sum of the fields due to each current loop. N= # of current loops

36. Electromagnets • If a piece of iron is placed inside a solenoid, the magnetic field increases greatly, because the iron becomes magnetized. We call this kind of iron-core solenoid an electromagnet.

37. Uses for Electromagnets • Electrical Relays, doorbell, speakers, etc…

38. Electric Motors • Converts electrical potential energy into kinetic energy • A magnetic force acts on a current carrying wire placed in a magnetic field between two permanent magnets. • Changing the direction of the current in the wire loop allows the motor to continually spin.

39. Current Measuring Device • The electromagnet tends to align its north face withthe iron magnet's southface. • A spring (not shown)resists this tendency to twist; the greater the current, the greaterthe deflection of theneedle.

40. Inducing a Current • What can you do to change the size or direction of the current induced in the coil?

41. Electromagnetic Induction • Michael Faraday found that a magnetic field can be used to produce an electric current. • Only a changing B-field induces an emf (voltage).

42. Electromagnetic Induction • Through further experimentation he found that an induced emf in a coil can be created by changing the… • Magnetic field strength • Area of the wire loop • The angle or orientation of the loop with the magnetic field Iinduced ϴ A

43. Magnetic Flux • Instead of talking about each independent quantity that could change and induce an emf or current, Faraday grouped all three together and called it flux. • Example: A 23cm-diameter wire coil is initially oriented so that its plane is perpendicular to a 0.8T magnetic field. The coil is then rotated by 90°. Find the initial and final flux through the loop. Iinduced ϴ Unit: Weber, 1T•m2 = 1Wb ɸm (initial) = 0.1328Wb ɸm (final) = 0Wb

44. Faraday’s Law • The induced emf is equal to the changing flux though the coil. • Note: This gives the emf induced in 1 turn of a wire loop. If there are multiple turns, just multiply the emf by the number of wire loops.

45. Changing Flux (Δɸ) • For an emf to be induced, one of the following must be changing: • Magnetic Field (B) • Increasing or decreasing the strength of the magnetic field • Moving the loop toward or away from the source of a magnetic field • Area of the loop (A) • Increasing or reducing the surface area of the loop • Angle of Orientation (ϴ) • Rotating the source of the magnetic field or the wire loop **See the PhET simulation: Faraday’s Electromagnetic Lab**

46. Direction of Induced Current? • Example: For each of the following examples, use Lenz’s law to find the direction of the induced current in the wire loop. x x x x x x x I 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 Loop is pulled to the right out of the B-field I in a straight wire is increasing B is decreasing

47. Transformers (…not the robots in disguise) • Device used for increasing or decreasing an AC voltage. • Used in powersupplies for laptops, iPods and cell phones to reduce 120V AC to a lower voltage. • Made with 2 coils of wire called the primary and the secondary. Primary Coil Secondary Coil VP (input) VS (output) N= # of turns or loops

48. ADD MORE!! • Pictures of actual transformers • Picture of series of transformers from power company to home.

49. Conceptual Question: • On a whiteboard, draw a device that you could use to steal power from an AC transmission line? …Or calculate the amount of power that you could steal from the Power company every day. 240,000V for high voltage transmission lines 2400V for normal power lines. Make assumption that the magnetic field Strength is constant through the loop. Calculate for 1/120th of a second, Then extrapolate.

50. Motional emf • When a conductor moves (in the way pictured in the diagram) through a B-field, the charges in the conductor are also moving. These charges experience a magnetic field force, and will start flowing as a current. Therefore we can say that the motion induced an emf, and this type of emf is called “motional emf”.