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1. Chapter 19 Magnetism

2. Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract.

3. If you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

4. Types of Magnetic Materials • Soft magnetic materials, such as iron, are easily magnetized • They also tend to lose their magnetism easily • Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize • They tend to retain their magnetism

5. Sources of Magnetic Fields • The region of space surrounding a moving charge includes a magnetic field • The charge will also be surrounded by an electric field • A magnetic field surrounds a properly magnetized magnetic material

6. Magnetic Fields • A vector quantity • Symbolized by • Direction is given by the direction a north pole of a compass needle points in that location • Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look

7. Magnetic Field Lines, sketch • A compass can be used to show the direction of the magnetic field lines (a) • A sketch of the magnetic field lines (b)

8. Magnetic Field Lines, Bar Magnet • Iron filings are used to show the pattern of the magnetic field lines • The direction of the field is the direction a north pole would point

9. Magnetic Field Lines, Unlike Poles • Iron filings are used to show the pattern of the magnetic field lines • The direction of the field is the direction a north pole would point • Compare to the magnetic field produced by an electric dipole

10. Magnetic Field Lines, Like Poles • Iron filings are used to show the pattern of the electric field lines • The direction of the field is the direction a north pole would point • Compare to the electric field produced by like charges

11. Earth’s Magnetic Field • The Earth’s geographic north pole corresponds to a magnetic south pole • The Earth’s geographic south pole corresponds to a magnetic north pole • Strictly speaking, a north pole should be a “north-seeking” pole and a south pole a “south-seeking” pole

12. Earth’s Magnetic Field • The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior

13. More About the Earth’s Magnetic Poles • The magnetic and geographic poles are not in the same exact location • The difference between true north, at the geographic north pole, and magnetic north is called the magnetic declination • The amount of declination varies by location on the earth’s surface

14. Earth’s Magnetic Declination

15. Source of the Earth’s Magnetic Field • There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization • The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core

16. Reversals of the Earth’s Magnetic Field • The direction of the Earth’s magnetic field reverses every few million years • Evidence of these reversals are found in basalts resulting from volcanic activity • The origin of the reversals is not understood

17. Magnetic Fields • When moving through a magnetic field, a charged particle experiences a magnetic force • This force has a maximum value when the charge moves perpendicularly to the magnetic field lines • This force is zero when the charge moves along the field lines

18. Magnetic Fields, cont • One can define a magnetic field in terms of the magnetic force exerted on a test charge moving in the field with velocity • Similar to the way electric fields are defined

19. Units of Magnetic Field • The SI unit of magnetic field is the Tesla (T) • Wb is a Weber • The cgs unit is a Gauss (G) • 1 T = 104 G

20. A Few Typical B Values • Conventional laboratory magnets • 25000 G or 2.5 T • Superconducting magnets • 300000 G or 30 T • Earth’s magnetic field • 0.5 G or 5 x 10-5 T

21. Finding the Direction of Magnetic Force • Experiments show that the direction of the magnetic force is always perpendicular to both and • Fmax occurs when is perpendicular to • F = 0 when is parallel to

22. Right Hand Rule #1 • Place your fingers in the direction of • Curl the fingers in the direction of the magnetic field, • Your thumb points in the direction of the force, , on a positive charge • If the charge is negative, the force is opposite that determined by the right hand rule

23. x x x x x x x x x x x x x x x x x x v q 1) out of the page 2) into the page 3) downwards 4) to the right 5) to the left A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

24. A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? x x x x x x x x x x x x x x x x x x v q F 1) out of the page 2) into the page 3) downwards 4) to the right 5) to the left Using the right-hand rule, you can see that the magnetic force is directed to the left. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

25. x x x x x x x x x x x x x x x x x x v q 1) out of the page 2) into the page 3) downwards 4) upwards 5) to the left A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

26. x x x x x x x x x x x x x x x x x x F v q A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? 1) out of the page 2) into the page 3) downwards 4) upwards 5) to the left Using the right-hand rule, you can see that the magnetic force is directed upwards. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

27. ® ® ® ® ® ® ® ® ® ® v ® ® ® ® ® ® ® ® ® ® q 1) out of the page 2) into the page 3) zero 4) to the right 5) to the left A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

28. ® ® ® ® ® ® ® ® ® ® v ® ® ® ® ® ® ® ® ® ® ´ q F A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? 1) out of the page 2) into the page 3) zero 4) to the right 5) to the left Using the right-hand rule, you can see that the magnetic force is directed into the page. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

29. ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ v ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ q 1) out of the page 2) into the page 3) zero 4) to the right 5) to the left A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force?

30. ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ v ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ q F = 0 A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? 1) out of the page 2) into the page 3) zero 4) to the right 5) to the left The charge is moving parallel to the magnetic field, so it does not experience any magnetic force. Remember that the magnetic force is given by: F = v B sin(q) .

31. Quick Quiz A charged particle moves in a straight line through a region of space. Which of the following answers must be true? (Assume any other fields are negligible.) The magnetic field (a) has a magnitude of zero (b) has a zero component perpendicular to the particle’s velocity (c) has a zero component parallel to the particle’s velocity in that region.

32. Answer (b). The force that a magnetic field exerts on a charged particle moving through it is given by , where is the component of the field perpendicular to the particle’s velocity. Since the particle moves in a straight line, the magnetic force (and hence , since ) must be zero.

33. Quick Quiz The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?

34. Answer (c). The magnetic force exerted by a magnetic field on a charge is proportional to the charge’s velocity relative to the field. If the charge is stationary, as in this situation, there is no magnetic force.

35. 1 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 2 3 4 A beam of atoms enters a magnetic field region. What path will the atoms follow?

36. 1 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 2 3 4 A beam of atoms enters a magnetic field region. What path will the atoms follow? Atoms are neutral objects whose net charge is zero. Thus they do not experience a magnetic force.

37. Example 1 An electron gun fires electrons into a magneticfield directed straight downward. Find the direction of theforce exerted by the field on an electron for each of the followingdirections of the electron’s velocity: (a) horizontaland due north; (b) horizontal and 30° west of north; (c) duenorth, but at 30° below the horizontal; (d) straight upward.(Remember that an electron has a negative charge.)

38. Example 2 (a) Find the direction of the force on a proton (a positivelycharged particle) moving through the magnetic fieldsin Figure P19.2, as shown. (b) Repeat part (a),assuming the moving particle is an electron.

39. Example 3 An electron is accelerated through 2 400 V from rest andthen enters a region where there is a uniform 1.70-T magneticfield. What are (a) the maximum and (b) the minimummagnitudes of the magnetic force acting on thiselectron?

40. Practice 1 A proton moves perpendicularly to a uniform magneticfield at 1.0 × 107 m/s and exhibits an acceleration of2.0 × 1013 m/s2 in the +x-direction when its velocity is inthe +z-direction. Determine the magnitude and directionof the field.

41. Magnetic Force on a Current Carrying Conductor • A force is exerted on a current-carrying wire placed in a magnetic field • The current is a collection of many charged particles in motion • The direction of the force is given by right hand rule #1

42. Force on a Wire • The blue x’s indicate the magnetic field is directed into the page • The x represents the tail of the arrow • Blue dots would be used to represent the field directed out of the page • The • represents the head of the arrow • In this case, there is no current, so there is no force

43. Force on a Wire,cont • B is into the page • The current is up the page • The force is to the left

44. Force on a Wire,final • B is into the page • The current is down the page • The force is to the right

45. Force on a Wire, equation • The magnetic force is exerted on each moving charge in the wire • The total force is the sum of all the magnetic forces on all the individual charges producing the current • F = B I ℓ sin θ • θ is the angle between and the direction of I • The direction is found by the right hand rule, placing your fingers in the direction of I instead of

46. I B 1) left 2) right 3) zero 4) into the page 5) out of the page A horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?

47. I B 1) left 2) right 3) zero 4) into the page 5) out of the page A horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? Using the right-hand rule, we see that the magnetic force must point out of the page. Since F must be perpendicular to both I and B, you should realize that F cannot be in the plane of the page at all.

48. Torque on a Current Loop • Applies to any shape loop • N is the number of turns in the coil • Torque has a maximum value of NBIA • When q = 90° • Torque is zero when the field is parallel to the plane of the loop

49. Magnetic Moment • The vector is called the magnetic moment of the coil • Its magnitude is given by m = IAN • The vector always points perpendicular to the plane of the loop(s) • The angle is between the moment and the field • The equation for the magnetic torque can be written as t = mB sinq

50. Electric Motor • An electric motor converts electrical energy to mechanical energy • The mechanical energy is in the form of rotational kinetic energy • An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field