Introductory Physics Volume Two

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14 Electric Field 1.3 +2 -3 The second style has curved field lines that follow the direction of the electric field. Check to see that the arrows are parallel to the field lines at the base of the arrow. This type of graph clearly shows the direction of the field. You can get an idea of the magnitude of the field by how close the field lines are to each other: the field is strong where the field lines are close together. Here is a graph showing just the field lines.
1.3 Electric Field 15 Look back now to the middle of the example, where we observed that in the calculation of the electric field the test charge q a had dropped out of the equation. We observed, at that time, that the electric field at any location ⃗r in space could be written out as ⃗E(⃗r) = q b ⃗r − ⃗r b 4πɛ 0 |⃗r − ⃗r b | 3 + q c ⃗r − ⃗r c 4πɛ 0 |⃗r − ⃗r c | 3 ⃗r−⃗r s |⃗r−⃗r s| 3 We see the contribution of each source charge is of the form qs 4πɛ 0 and that the net field is the sum of the contributions of each source charge. This is so because the net force is the vector sum of the individual force. Following this idea we would arrive at these two theorems. Theorem: Electric Field due to a Point Charge The electric field at the location ⃗r due to a point charge q s at the location ⃗r s is given by the following expression. ⃗E(⃗r) = q s ⃗r − ⃗r s 4πɛ 0 |⃗r − ⃗r s | 3 The magnitude of the electric field due to a point charge at a distance r from the point charge is E(r) = q 1 4πɛ 0 r 2 Theorem: Superposition Theorem The electric field due to a collection of point charges is the sum of the fields of the individual charges. ⃗E(⃗r) = ∑ q n ⃗r − ⃗r n 4πɛ n 0 |⃗r − ⃗r n | 3 ⊲ Problem 1.3 A charge q 1 = +q is placed at the location ⃗r 1 = 0î + aĵ and a second charge q 2 = −q is placed at ⃗r 2 = 0î − aĵ. (a) Write out the electric field at an arbitrary location on the x-axis: ⃗r = xî + 0ĵ. (b) Sketch a map of the electric field lines, in the first quadrant. Here is a table that gives the angle ( from the positive x-axis) of the electric field at different locations in the first quadrant.
Page 1 and 2: 1 Introductory Physics Volume Two S
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: 1.3 Electric Field 13 points a well
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 and 32: 1.7 More Examples 31 The area vecto
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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
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
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3.8 Capacitor Circuits 65 Theorem:
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3.9 More Examples 67 Note that the
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3.9 More Examples 69 This mean that
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3.9 More Examples 71 15Ω 5Ω 10Ω
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3.9 More Examples 73 First combine
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3.10 Homework 75 ⊲ Problem 3.16 B
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3.10 Homework 77 4 µF + - 2 µF +
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3.11 Summary 79 § 3.11 Summary Def
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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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Introductory Physics Volume Two

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