# Ch. 22: Magnetism. (Dr. Andrei Galiautdinov, UGA) 2014FALL - PHYS1112

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1 Ch. 22: Magnetism (Dr. Andrei Galiautdinov, UGA) 2014FALL - PHYS1112

2 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 1

3 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge 2

4 3

5 4

6 5

7 So, in a magnetic field B, the moving charge q is pushed sideways Weird 6

8 Examples: 7

9 8

10 9

11 (Velocity, v) (B-field, B) (Force, F m ) This is the Right-Hand-Rule for a POSITIVE charge q > 0: Fix index and thumb at 90 Then adjust the middle accordingly (notice that middle and thumb should 10 also be at 90 )

12 Stop! Electron beam in a magnetic field 11

13 Don t forget to use the Left-Hand-Rule in this case! 12

14 13

15 The strength of the magnetic force F m on charge q depends on the angle α between v and B: Let s start increasing α from 0 to 180 keeping the values of v and B fixed: F m starts at 0 (since sin 0 = 0), then reaches maximum at α = 90 (since sin 90 = 1), then decreases back to 0 when α = 180 (since sin 180 = 0). Notice: Once α exceeds 180 (α > 180 ), F m will point downward (check this for yourself using 14 the R.H.R.)

16 15

17 = tesla (the unit of magnetic field) 16

18 17

19 Problem 1. 1) A proton is projected with a velocity of m/s into a magnetic field of 0.60 T perpendicular to the motion of the proton. What is the force that acts on the proton? A) N B) 0 N C) N D) N E) N 18

20 Problem 1. 1) A proton is projected with a velocity of m/s into a magnetic field of 0.60 T perpendicular to the motion of the proton. What is the force that acts on the proton? A) N B) 0 N C) N D) N E) N 19

21 Problem 2. 2) A proton moving with a velocity of m/s enters a magnetic field of 0.20 T. If the angle between the velocity of the proton and the direction of the magnetic field is 60, what is the magnitude of the force on the proton? A) N B) N C) N D) N E) N 20

22 Problem 2. 2) A proton moving with a velocity of m/s enters a magnetic field of 0.20 T. If the angle between the velocity of the proton and the direction of the magnetic field is 60, what is the magnitude of the force on the proton? A) N B) N C) N D) N E) N 21

23 Problem 3. 3) An electron moving with a speed of 9.1 x 10 5 m/s in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.0 x N that points in the negative z direction. What is the direction and magnitude of the magnetic field? 22

24 Problem 3. 3) An electron moving with a speed of 9.1 x 10 5 m/s in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.0 x N that points in the negative z direction. What is the direction and magnitude of the magnetic field? negative x-direction, 1.4 T 23

25 24

26 Problem 4. 4) A 6.6 μc particle moves through a region of space where an electric field of magnitude 1250 N/C points in the positive x direction, and a magnetic field of magnitude 1.02 T points in the positive z direction. If the net force acting on the particle is 6.23 x 10-3 N in the positive x direction, find the magnitude and direction of the particle s velocity. Assume the particle s velocity is in the x-y plane. 25

27 Problem 4. 4) A 6.6 μc particle moves through a region of space where an electric field of magnitude 1250 N/C points in the positive x direction, and a magnetic field of magnitude 1.02 T points in the positive z direction. If the net force acting on the particle is 6.23 x 10-3 N in the positive x direction, find the magnitude and direction of the particle s velocity. Assume the particle s velocity is in the x-y plane. negative y-direction, 300 m/s 26

28 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 27

29 28

30 Part 3: Motion of charged particles in a magnetic field 29

31 Let s make a guess as to how R depends on m, v, B, q: 30

32 Derivation: 31

33 Another example of discovering a formula using dimensional analysis: Period of oscillation of a pendulum. 32

34 Back to our example: 33

35 34

36 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 35

37 Part 4(a): Magnetic force acting on current-carrying wire 36

38 37

39 38

40 39

41 40

42 41

43 Switch open No force on wire (magnet underneath) 42

44 Switch closed Wire pushed sideways (magnet underneath) 43

45 Switch closed B N S F m v (electrons) Wire pushed sideways (magnet underneath) Different view 44

46 45

47 wire electron Overall, the wire is neutral: positively charged ions of the crystal lattice are delicately balanced by negatively charged electrons. You, watching When an electron leaves the wire, the wire immediately becomes positively charged (it lost the electron!) The electrostatic attraction then pulls 46 the electron back.

48 47

49 Part 4(b): Magnetic torque acting on a loop/coil with current 48

50 49

51 50

52 51

53 52

54 53

55 Application: electric motors (demo) 54

56 55

57 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 56

58 Part 5: Magnetic fields produced by currents; Ampere s Law 57

59 Oersted s experiment (1820 ): moving charges produce magnetic 58 field

60 Oersted s ghost Switch closed needle rotates Oersted s experiment (1820 ): moving charges produce magnetic 59 field

61 Oersted s dog Switch closed needle rotates Oersted s experiment (1820): moving charges produce magnetic 60 field

62 Magnetic field around a current-carrying wire (I points into the page) 61

63 62

64 Problem 8. 8) Consider the long, straight, current-carrying wires shown in the Figure. One wire carries a current of 6.2 A in the positive y direction; the other wire carries a current of 4.5 A in the positive x direction. (a) At which of the two points, A or B, do you expect the magnitude of the net magnetic field to be greater? Explain. (b) Calculate the magnitude of the net magnetic field at points A and B. 63

65 Problem 8. 8) Consider the long, straight, current-carrying wires shown in the Figure. One wire carries a current of 6.2 A in the positive y direction; the other wire carries a current of 4.5 A in the positive x direction. (a) At which of the two points, A or B, do you expect the magnitude of the net magnetic field to be greater? Explain. (b) Calculate the magnitude of the net magnetic field at points A and B. (a) According to the RHR, the magnetic field due to each current is out of the page at A, whereas at B, the field due to the 6.2 A current is into the page and the field due to the 4.5 A current is out of the page. So, since the magnitudes of the fields due to each wire are the same at each point but their directions are opposite at B, the magnitude of the net magnetic field is greatest at A. (b) 1.34 x 10-5 T 2.12 x 10-6 T 64

66 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 65

67 Part 6: Forces between current-carrying wires 66

68 67

69 68

70 An old slide 69

71 An old slide 70

72 Part 1: Magnetic field Part 2: Magnetic force acting on a moving charge Part 3: Motion of charged particles in a magnetic field Part 4: Magnetic force acting on current-carrying wire; magnetic torque acting on loop of current Part 5: Magnetic fields produced by currents; Ampere s Law Part 6: Forces between current-carrying wires Part 7: Magnetic fields produced by current loops and solenoids 71

73 Part 7: Magnetic fields produced by current loops and solenoids 72

74 Switch is open After closing, the compass needle rotates perpendicular to the loop 73

75 74

76 Magnetic field around a current-carrying loop (In our experiment, we use a coil consisting of hundreds of turns to make the B-field stronger and easily detectable) 75

77 Compass needle is not exactly normal to the plane of the loop b/c magnetic field of Earth is acting too. Here s how we can estimate the number of turns in the coil if we are given the following data: (from my side): 76

78 Magnetic field inside a long solenoid 77

79 Problem 9. 9) A solenoid that is 75 cm long produces a magnetic field of 1.3 T within its core when it carries a current of 8.4 A. How many turns of wire are contained in this solenoid? 78

80 Problem 9. 9) A solenoid that is 75 cm long produces a magnetic field of 1.3 T within its core when it carries a current of 8.4 A. How many turns of wire are contained in this solenoid? 9.2 x

81 Problem )To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12 cm in diameter and 55 cm in length. You would like a 2.0-A current to produce a 2.5-kG magnetic field inside your solenoid. What is the total length of wire you will need to meet these specifications? 80

82 Problem )To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12 cm in diameter and 55 cm in length. You would like a 2.0-A current to produce a 2.5-kG magnetic field inside your solenoid. What is the total length of wire you will need to meet these specifications? 21 km 81

83 The End 82

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