Chapter 27. Gauss s Law

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1 Chapter 27 Gauss s Law

36 Electric Flux Field lines penetrating an area A perpendicular to the field The product of EA is the flux, Φ In general: Φ E = E A sin θ

37 Electric Field of a Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge Q E = = 2 4πr ε o The electric field inside the shell is zero k e Q 2 r

38 Electric Field of a Nonconducting Plane Sheet of Charge Use a cylindrical Gaussian surface The flux through the ends is EA, there is no field through the curved part of the surface The total charge is Q = σa E = 2 σ ε Note, the field is uniform o

40 Solutions of Problems EOC: 54 Part a) F = ma = qe a = 2 1 ( ) 2 x( ) ( ) ( 0.04 m) 8 ( t t ) = = s x = x + v t t + a t t 0.04 m = 0 m + v cos45 t t + 0 m 1 0 0x ( ) m/s cos45 qe m t1 t0 qe t1 t0 v1y = v0y + ay 0 m/s = v0sin m 2 2 m v sin 45 ( t ) 31 6 ( )( ) 19 8 ( C)( s) 0 = = = E q t kg m/s sin N/C

41 Solutions of Problems EOC: 54 Part b) ( 6 ) v 0 = m/s sin 45 y ( ) ( ) v = v + 2a y y 0 m /s = v sin a y y y 0y y y v0sin 45 v0 ( y1 y0) = = 2a 4a y y a y ( C)( 3550 N/C) qe = = = m/s m kg ( m/s) ( ) y1 y0 = = m = 1.0 cm m/s

42 0y qe F = ma = qe a = m ( C)( N/C) = = m/s a y Solutions of Problems EOC: kg v cos45 0x = v0 v0y = v0sin 45 ( ) ( ) y 0y 2 y m/s 0y 2 y ( )( ) 15 2 v = v + a y y = v + a Δy v = a Δ y = = y m/s 0.02 m m/s v m/s = = sin m/s

43 Chapter 6 EOC: 55 a) Bottom is positive charge a = aj ˆ b) K = = mv J ( ) 1/2 6 K m v0 = 2 = m/s Final point (x 1, y 1 ) = (1 cm, 0 cm) 1 2 x1 = x0 + vx0t1 + 2 axt1 = vx0t1 = 0.01 m y1 = y0 + vy0t1 + 2ayt1 = vy0t1 + 2at1 = 0 m v = v cos45 = m/s v = v sin45 = m/s 6 6 x0 0 y0 0 a t x v x 9 1 = 1 0 = s 2 v t = = m/s t y

44 Chapter 6 EOC: 55 a (c) d min is height y max of the electron s above the bottom plate. Maximum height occurs at t x v x F q E ee ma m m m e 9 1 = 1 0 = s ( kg)( m/s 2 ) elec elec = = = E = = = 19 t = t = y v t at s C 1 2 max = y0 + 2 = m = 2.5 mm 37,500 N/C Thus, d min = 2.5 mm.

45 The figure shows two parallel plates that are 2.0 cm apart. The electric field between them is 6.7x10 4 N/C. An electron is launched at a 45 0 angle and with initial speed v o from the positive plate. What is the maximum v o such that the electron won't hit the negative plate? v o =3.1x10 7 m/s

46 At the position of the dot, the electric field points 1. Left. 2. Down. 3. Right. 4. Up. 5. The electric field is zero.

47 At the position of the dot, the electric field points 1. Left. 2. Down. 3. Right. 4. Up. 5. The electric field is zero.

48 A piece of plastic is uniformly charged with surface charge density 1. The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3. Rank in order, from largest to smallest, the surface charge densities 1 to 3. 1P > η 2 > η 3 2. η 1 > η 2 = η 3 3. η 1 = η 2 = η 3 4. η 2 = η 3 > η 1 5. η 3 > η 2 > η 1

49 A piece of plastic is uniformly charged with surface charge density 1. The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3. Rank in order, from largest to smallest, the surface charge densities 1 to η 1 > η 2 > η 3 2. η 1 > η 2 = η 3 3. η 1 = η 2 = η 3 4. η 2 = η 3 > η 1 5. η 3 > η 2 > η 1

50 Which of the following actions will increase the electric field strength at the position of the dot? 1. Make the rod longer without changing the charge. 2. Make the rod shorter without changing the charge. 3. Make the rod fatter without changing the charge. 4. Make the rod narrower without changing the charge. 5. Remove charge from the rod.

51 Which of the following actions will increase the electric field strength at the position of the dot? 1. Make the rod longer without changing the charge. 2. Make the rod shorter without changing the charge. 3. Make the rod fatter without changing the charge. 4. Make the rod narrower without changing the charge. 5. Remove charge from the rod.

52 Rank in order, from largest to smallest, the electric field strengths E a to E e at these five points near a plane of charge. 1. E a = E b = E c = E d = E e 2. E a > E c > E b > E e > E d 3. E b = E c = E d = E e > E a 4. E a > E b = E c > E d = E e 5. E e > E d > E c > E b > E a

53 Rank in order, from largest to smallest, the electric field strengths E a to E e at these five points near a plane of charge. 1. E a = E b = E c = E d = E e 2. E a > E c > E b > E e > E d 3. E b = E c = E d = E e > E a 4. E a > E b = E c > E d = E e 5. E e > E d > E c > E b > E a

54 Rank in order, from largest to smallest, the forces F a to F e a proton would experience if placed at points a e in this parallelplate capacitor. 1. F a = F b = F c = F d = F e 2. F a = F b > F c > F d = F e 3. F a = F b = F d = F e > F c 4. F e > F d > F c > F b > F a 5. F e = F d > F c > F a = F b

55 Rank in order, from largest to smallest, the forces F a to F e a proton would experience if placed at points a e in this parallelplate capacitor. 1. F a = F b = F c = F d = F e 2. F a = F b > F c > F d = F e 3. F a = F b = F d = F e > F c 4. F e > F d > F c > F b > F a 5. F e = F d > F c > F a = F b

56 Which electric field is responsible for the trajectory of the proton? (1) (2) (3) (4) (5)

57 Which electric field is responsible for the trajectory of the proton? (1) (2) (3) (4) (5)

58 Chapter 26 Reading Quiz

59 What device provides a practical way to produce a uniform electric field? 1. A long thin resistor 2. A Faraday cage 3. A parallel plate capacitor 4. A toroidal inductor 5. An electric field uniformizer

60 What device provides a practical way to produce a uniform electric field? 1. A long thin resistor 2. A Faraday cage 3. A parallel plate capacitor 4. A toroidal inductor 5. An electric field uniformizer

61 For charged particles, what is the quantity q/m called? 1. Linear charge density 2. Charge-to-mass ratio 3. Charged mass density 4. Massive electric dipole 5. Quadrupole moment

62 For charged particles, what is the quantity q/m called? 1. Linear charge density 2. Charge-to-mass ratio 3. Charged mass density 4. Massive electric dipole 5. Quadrupole moment

63 Which of these charge distributions did not have its electric field calculated in Chapter 26? 1. A line of charge 2. A parallel-plate capacitor 3. A ring of charge 4. A plane of charge 5. They were all calculated

64 Which of these charge distributions did not have its electric field calculated in Chapter 26? 1. A line of charge 2. A parallel-plate capacitor 3. A ring of charge 4. A plane of charge 5. They were all calculated

65 The worked examples of charged-particle motion are relevant to 1. a transistor. 2. a cathode ray tube. 3. magnetic resonance imaging. 4. cosmic rays. 5. lasers.

66 The worked examples of charged-particle motion are relevant to 1. a transistor. 2. a cathode ray tube. 3. magnetic resonance imaging. 4. cosmic rays. 5. lasers.

67 Chapter 27

68 A uniformly charged rod has a finite length L. The rod is symmetric under rotations about the axis and under reflection in any plane containing the axis. It is not symmetric under translations or under reflections in a plane perpendicular to the axis other than the plane that bisects the rod. Which field shape or shapes match the symmetry of the rod? A. a and d B. c and e C. b only D. e only E. none of the above

69 A uniformly charged rod has a finite length L. The rod is symmetric under rotations about the axis and under reflection in any plane containing the axis. It is not symmetric under translations or under reflections in a plane perpendicular to the axis other than the plane that bisects the rod. Which field shape or shapes match the symmetry of the rod? A. a and d B. c and e C. b only D. e only E. none of the above

70 This box contains A. a net positive charge. B. no net charge. C. a net negative charge. D. a positive charge. E. a negative charge.

71 This box contains A. a net positive charge. B. no net charge. C. a net negative charge. D. a positive charge. E. a negative charge.

72 The total electric flux through this box is A. 0 Nm 2 /C. B. 1 Nm 2 /C. C. 2 Nm 2 /C. D. 4 Nm 2 /C. E. 6 Nm 2 /C.

73 The total electric flux through this box is A. 0 Nm 2 /C. B. 1 Nm 2 /C. C. 2 Nm 2 /C. D. 4 Nm 2 /C. E. 6 Nm 2 /C.

74 These are two-dimensional cross sections through threedimensional closed spheres and a cube. Rank order, from largest to smallest, the electric fluxes a to e through surfaces a to e. A. Φ a > Φ c > Φ b > Φ d > Φ e B. Φ b = Φ e > Φ a = Φ c = Φ d C. Φ e > Φ d > Φ b > Φ c > Φ a D. Φ b > Φ a > Φ c > Φ e > Φ d E. Φ d = Φ e > Φ c > Φ a = Φ b

75 These are two-dimensional cross sections through threedimensional closed spheres and a cube. Rank order, from largest to smallest, the electric fluxes a to e through surfaces a to e.

76 Which Gaussian surface would allow you to use Gauss s law to determine the electric field outside a uniformly charged cube? A. A sphere whose center coincides with the center of the charged cube. B. A cube whose center coincides with the center of the charged cube and which has parallel faces. C. Either A or B. D. Neither A nor B.

77 Which Gaussian surface would allow you to use Gauss s law to determine the electric field outside a uniformly charged cube? A. A sphere whose center coincides with the center of the charged cube. B. A cube whose center coincides with the center of the charged cube and which has parallel faces. C. Either A or B. D. Neither A nor B.

78 Chapter 27 Reading Quiz

79 The amount of electric field passing through a surface is called A. Electric flux. B. Gauss s Law. C. Electricity. D. Charge surface density. E. None of the above.

80 The amount of electric field passing through a surface is called A. Electric flux. B. Gauss s Law. C. Electricity. D. Charge surface density. E. None of the above.

81 Gauss s law is useful for calculating electric fields that are A. due to point charges. B. uniform. C. symmetric. D. due to continuous charges.

82 Gauss s law is useful for calculating electric fields that are A. due to point charges. B. uniform. C. symmetric. D. due to continuous charges.

83 Gauss s law applies to A. lines. B. flat surfaces. C. spheres only. D. closed surfaces.

84 Gauss s law applies to A. lines. B. flat surfaces. C. spheres only. D. closed surfaces.

85 The electric field inside a conductor in electrostatic equilibrium is A. uniform. B. zero. C. radial. D. symmetric.

86 The electric field inside a conductor in electrostatic equilibrium is A. uniform. B. zero. C. radial. D. symmetric.

Chapter 22. Dr. Armen Kocharian. Gauss s Law Lecture 4

Chapter 22. Dr. Armen Kocharian. Gauss s Law Lecture 4 Chapter 22 Dr. Armen Kocharian Gauss s Law Lecture 4 Field Due to a Plane of Charge E must be perpendicular to the plane and must have the same magnitude at all points equidistant from the plane Choose