Introductory Physics Volume Two

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96 Magnetic Fields 4.8 § 4.8 Summary Definitions Facts Force on a moving charge: ⃗F = q⃗v × ⃗ B Force on a piece of wire carrying a current I: ⃗ dF = I ⃗ dl × ⃗ B Theorems
5.1 Sources of Magnetic Field 97 5 Sources of Magnetic Field § 5.1 Sources of Magnetic Field So far we have not considered how magnetic fields are created. As you may know it is possible to create an electromagnet by wrapping a wire around a nail and running a current through the wire. The precise way in which a current produces a magnetic field is captured in the following law. Fact: Biot-Savart Law If you have a wire carrying a current I, a small section of the wire ⃗dl will produce a magnetic field dB ⃗ = µ 0I ⃗dl × ˆr 4π r 2 where ⃗r is the vector that points from the location of the element ⃗dl to the field point. The total field is the sum of the contributions of each element of the wire. This may look complicated but it represents the simple fact that the magnetic field wraps around the wire, and decreases in strength as you move away. In the figure below is depicted two magnetic field lines that are due to the current element ⃗ dl indicated. Note that the field warps around the extension of the current element in circles. This figure does not depict how the field strength changes with position. The direction the field wraps around the current is the same direction the fingers of your right hand will wrap around the wire if you grasp the wire with your thumb pointing in the direction of the current.
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1 Introductory Physics Volume Two S
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1.1 Electric Charge 3 Demo 1 Electr
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1.1 Electric Charge 5 Then charge a
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- - - - - 1.2 Coulomb’s Law 7 How
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1.2 Coulomb’s Law 9 Example Consi
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1.3 Electric Field 11 + - Compute t
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1.3 Electric Field 13 points a well
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1.3 Electric Field 15 Look back now
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1.5 Continuous Charge Distributions
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1.6 Gauss’s Law 19 § 1.6 Gauss
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1.6 Gauss’s Law 21 Suppose that y
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1.7 More Examples 23 ⊲ Problem 1.
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1.7 More Examples 25 The net force
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1.7 More Examples 27 out the net fo
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1.7 More Examples 29 -4q +2q -q E -
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1.7 More Examples 31 The area vecto
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1.8 Homework 33 ⊲ Problem 1.14 Ri
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1.9 Summary 35 § 1.9 Summary Defin
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2.1 Electric Potential 37 2 Electri
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2.1 Electric Potential 39 Example S
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2.2 Equipotentials 41 ⊲ Problem 2
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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
Page 55 and 56: 2.8 Homework 55 ⊲ Problem 2.27 Ho
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 +
Page 79 and 80: 3.11 Summary 79 § 3.11 Summary Def
Page 81 and 82: 4.2 Magnetic Force on a Current 81
Page 83 and 84: 4.3 Trajectories Under Magnetic For
Page 85 and 86: 4.4 Lorentz Force 85 with a charge
Page 87 and 88: 4.5 Hall Effect 87 But this charge
Page 89 and 90: 4.6 More Examples 89 -e F E v F B =
Page 91 and 92: 4.6 More Examples 91 The force on t
Page 93 and 94: 4.7 Homework 93 Imagine the closed
Page 95: 4.7 Homework 95 circular orbits. Wr
Page 99 and 100: 5.1 Sources of Magnetic Field 99
Page 101 and 102: 5.2 Ampere’s Law 101 and ⃗ dr s
Page 103 and 104: 5.2 Ampere’s Law 103 This satisfi
Page 105 and 106: 5.4 More Examples 105 distance r fr
Page 107 and 108: 5.4 More Examples 107 up the integr
Page 109 and 110: 5.4 More Examples 109 Use the Biot-
Page 111 and 112: 5.5 Homework 111 The magnetic force
Page 113 and 114: 5.5 Homework 113 3.00 A 1.00 A 1 mm
Page 115 and 116: 6.2 Faraday’s Law 115 6 Time Vary
Page 117 and 118: 6.2 Faraday’s Law 117 Definition:
Page 119 and 120: 6.3 Maxwell’s Extension of Ampere
Page 121 and 122: 6.4 Inductance 121 Example Suppose
Page 123 and 124: 6.7 AC Circuit Elements 123 + V S-
Page 125 and 126: 6.8 Phasor Diagrams 125 Theorem: Im
Page 127 and 128: 6.8 Phasor Diagrams 127 What we wan
Page 129 and 130: 6.9 Homework 129 ⊲ Problem 6.6 Sh
Page 131 and 132: 6.9 Homework 131 (b) A small circul
Page 133 and 134: 6.9 Homework 133 maximum current in
Page 135 and 136: 6.10 Summary 135 § 6.10 Summary De
Page 137 and 138: 7.1 Maxwell Equations 137 7 Wave Op
Page 139 and 140: 7.2 Describing Oscillations 139 tio
Page 141 and 142: 7.3 Describing Waves 141 For a harm
Page 143 and 144: 7.3 Describing Waves 143 Definition
Page 145 and 146: 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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Introductory Physics Volume Two

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