Introductory Physics Volume Two

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32 Electric Field 1.8 With the assumptions above, symmetry tells us that the electric field will point in a direction perpendicular to the surface; for a positive charge it will point away from the plate: E A σ E In the figure a Gaussian surface is indicated. Take it to be a small cylinder with cross-sectional area A. The electric flux in non-zero only through the endcaps: ∮ ∫ ∫ ∫ ⃗E · dA ⃗ = E · dA ⃗ + E · dA ⃗ + E · dA ⃗ upper cap sides = EA + 0 + EA = 2EA Using Gauss’s law: 2EA = σA ɛ 0 −→ E = σ 2ɛ 0 . lower cap § 1.8 Homework ⊲ Problem 1.13 y 7.0 µC x 0.50 m 0.50 m 2.0 µC 0.50 m −4.0 µC Three point charges are located at the corners of an equilateral triangle as shown. Calculate the net electric force on the 7.0µC charge.
1.8 Homework 33 ⊲ Problem 1.14 Richard Feynman said that if two people were at arm’s length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be about equal to the “weight” of the entire Earth. Was Feynman exaggerating? ⊲ Problem 1.15 A point charge q is at the position (x 0 , y 0 ). Find the electric field at an arbitrary point (x, y) due to the charge q. ⊲ Problem 1.16 <strong>Two</strong> 2.0 µC charges are located on the x axis at x = 1.0m and at x = −1.0m. (a) Determine the electric field on the y axis at y = 0.5.m. (b) Calculate the electric force on a −3.0µC charged place at this point. ⊲ Problem 1.17 A uniformly charged insulating rod of length 14 cm is bent into the shape of a semicircle. If the rod has a total charge of −7.5µC, find the magnitude and direction of the electric field at the center of the semicircle. ⊲ Problem 1.18 An electron moves at a speed of 3 × 10 6 m s into a uniform electric field of magnitude 1000 N/C. The field is parallel to the electron’s velocity and acts to decelerate the electron. How far does the electron travel before it is brought to rest? ⊲ Problem 1.19 A proton moves at 4.5 × 10 5 m s in the horizontal direction. It enters a uniform electric field of 9.6 × 10 3 N/C directed downward. Ignore any gravitational effects and find the time it takes the proton to travel 5.0 cm horizontally, its vertical displacement after it has traveled 5.0 cm horizontally, and the horizontal and vertical components of its velocity after it has traveled 5.0 cm horizontally. ⊲ Problem 1.20 y x θ E
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Page 3 and 4: 1.1 Electric Charge 3 Demo 1 Electr
Page 5 and 6: 1.1 Electric Charge 5 Then charge a
Page 7 and 8: - - - - - 1.2 Coulomb’s Law 7 How
Page 9 and 10: 1.2 Coulomb’s Law 9 Example Consi
Page 11 and 12: 1.3 Electric Field 11 + - Compute t
Page 13 and 14: 1.3 Electric Field 13 points a well
Page 15 and 16: 1.3 Electric Field 15 Look back now
Page 17 and 18: 1.5 Continuous Charge Distributions
Page 19 and 20: 1.6 Gauss’s Law 19 § 1.6 Gauss
Page 21 and 22: 1.6 Gauss’s Law 21 Suppose that y
Page 23 and 24: 1.7 More Examples 23 ⊲ Problem 1.
Page 25 and 26: 1.7 More Examples 25 The net force
Page 27 and 28: 1.7 More Examples 27 out the net fo
Page 29 and 30: 1.7 More Examples 29 -4q +2q -q E -
Page 31: 1.7 More Examples 31 The area vecto
Page 35 and 36: 1.9 Summary 35 § 1.9 Summary Defin
Page 37 and 38: 2.1 Electric Potential 37 2 Electri
Page 39 and 40: 2.1 Electric Potential 39 Example S
Page 41 and 42: 2.2 Equipotentials 41 ⊲ Problem 2
Page 43 and 44: 2.3 Conductors in Equilibrium 43
Page 45 and 46: 2.4 Capacitors 45 § 2.4 Capacitors
Page 47 and 48: 2.5 Energy in an Electric Field 47
Page 49 and 50: 2.7 More Examples 49 ⊲ Problem 2.
Page 51 and 52: 2.7 More Examples 51 The resulting
Page 53 and 54: 2.8 Homework 53 add up potential du
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Page 57 and 58: 3.2 Electric Current 57 3 Circuits
Page 59 and 60: 3.3 Ohm’s Law 59 Some materials,
Page 61 and 62: 3.5 Kirchhoff’s Rules 61 ⊲ Prob
Page 63 and 64: 3.6 Resistors in Combination 63 par
Page 65 and 66: 3.8 Capacitor Circuits 65 Theorem:
Page 67 and 68: 3.9 More Examples 67 Note that the
Page 69 and 70: 3.9 More Examples 69 This mean that
Page 71 and 72: 3.9 More Examples 71 15Ω 5Ω 10Ω
Page 73 and 74: 3.9 More Examples 73 First combine
Page 75 and 76: 3.10 Homework 75 ⊲ Problem 3.16 B
Page 77 and 78: 3.10 Homework 77 4 µF + - 2 µF +
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Page 81 and 82: 4.2 Magnetic Force on a Current 81
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4.3 Trajectories Under Magnetic For
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4.4 Lorentz Force 85 with a charge
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4.5 Hall Effect 87 But this charge
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4.6 More Examples 89 -e F E v F B =
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4.6 More Examples 91 The force on t
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4.7 Homework 93 Imagine the closed
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4.7 Homework 95 circular orbits. Wr
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5.1 Sources of Magnetic Field 97 5
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5.1 Sources of Magnetic Field 99
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5.2 Ampere’s Law 101 and ⃗ dr s
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5.2 Ampere’s Law 103 This satisfi
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5.4 More Examples 105 distance r fr
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5.4 More Examples 107 up the integr
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5.4 More Examples 109 Use the Biot-
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5.5 Homework 111 The magnetic force
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5.5 Homework 113 3.00 A 1.00 A 1 mm
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6.2 Faraday’s Law 115 6 Time Vary
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6.2 Faraday’s Law 117 Definition:
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6.3 Maxwell’s Extension of Ampere
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6.4 Inductance 121 Example Suppose
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6.7 AC Circuit Elements 123 + V S-
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6.8 Phasor Diagrams 125 Theorem: Im
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6.8 Phasor Diagrams 127 What we wan
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6.9 Homework 129 ⊲ Problem 6.6 Sh
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6.9 Homework 131 (b) A small circul
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6.9 Homework 133 maximum current in
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6.10 Summary 135 § 6.10 Summary De
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7.1 Maxwell Equations 137 7 Wave Op
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7.2 Describing Oscillations 139 tio
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7.3 Describing Waves 141 For a harm
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7.3 Describing Waves 143 Definition
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7.4 Electromagnetic Waves 145 § 7.
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7.5 Interference of Waves 147 I I A
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7.7 Interference of Two Sources 149
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7.8 Far Field Approximation 151 §
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7.9 Thin Film Interference 153 pass
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7.11 Homework 155 Second Min First
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7.11 Homework 157 θ 2 d θ 1 θ 2
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7.12 Summary 159 § 7.12 Summary De
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8.2 Reflection 161 8 Geometric Opti
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8.4 Snell’s Law 163 We see then t
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8.5 Virtual Image Caused by Refract
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8.6 Thin Lens Equation 167 back in
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8.7 Virtual Image in a Converging L
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8.8 Diverging Lenses 171 (b) virtua
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8.10 Multi-Lens Optical Systems 173
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8.11 Homework 175 We can also compu
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@ Summary 177 § 8.12 Summary Facts
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A Hints 179 1.14 Since this is only
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A Hints 181 2.27 Imagine that you b
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A Hints 183 4.12 Consider the vecto
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A Hints 185 7.26 The distance from
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B Index 187 † Ohm’s Law: Resist
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B Index 189
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C Power Series Expansions 191 The F
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D Unit Prefixes 193 § D.3 Fundamen
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