Introductory Physics Volume Two

More documents

Recommendations

Info

18 Electric Field 1.5 that we “sum” over all the pieces. Let us evaluate this integral for the case of the string that we introduced earlier. First we need to relate dq to dx. The entire length L of the string has a charge Q so that the charge per length is λ = Q/L. If the charge is uniformly spread over the string we expect the charge per length to be the same everywhere so that dq dx = Q = λ −→ dq = λdx L With this, and the fact that ⃗r s = x s î, we can write ∫ dq ⃗r − ⃗r s ⃗E(⃗r) = 4πɛ 0 |⃗r − ⃗r s | 3 ∫ L/2 λdx s ⃗r − x s î = −L/2 4πɛ 0 |⃗r − x s î| 3 If we write the field point as ⃗r = xî + yĵ, and then do the integration, we find that ⎡ ⎤ ⃗E(x, y) = λ ⎣ 1 1 − √ ⎦ î 4πɛ 0 √y 2 + (x − L 2 )2 y 2 + (x + L 2 )2 ⎡ ⎤ + λ 1 x − ⎣− L 2 x + L 2 + √ ⎦ ĵ 4πɛ 0 y √y 2 + (x − L 2 )2 y 2 + (x + L 2 )2 ⊲ Problem 1.4 Suppose that you have a circular hoop of radius R with a net charge Q spread uniform around the hoop. Compute the electric field at a distance z along the axis of the hoop?
1.6 Gauss’s Law 19 § 1.6 Gauss’s Law We have seen that the electric field due to any charge distribution can be computed. From this relationship between the electric field and the charge distribution, another one can be derived. First we will define a new quantity, the electric flux through a surface. To get an idea of what the flux represents first consider the following story. You wish to catch some butterflies but you don’t have time to chase them around, so you just set up your butterfly net on a pole. The butterflies are migrating south for the winter. They are flying by your house heading in a southerly direction, so you orient the net so that it faces north. The number of butterflies you catch should be proportional to both the density of butterflies in the air and the area of the mouth of the net. The number of butterflies caught will also depend on the orientation of the net relative to the direction the butterflies are moving. For example, if the butterflies end up flying to the south-west instead of directly south, you will not catch as many since the net was not facing the optimal direction. The electric flux is similar, it is the amount of electric field that “passes through” a surface. There are three things that determine the quantity of electric flux: the area of the surface, the magnitude of the electric field and the orientation of the field relative to the surface. To write this out clearly, we need to have a way to mathematically represent the orientation of a surface. We will define a vector area ⃗ A as the vector that has a magnitude equal to the area of the surface and has a direction that is normal to the surface. A good picture to keep in mind is a thumbtack, A A the nail part of the tack is the vector area and the flat part of the tack is the surface. This ends up being the best way to use a vector to represent a surface. Now we can define the electric flux.
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 and 14: 1.3 Electric Field 13 points a well
Page 15 and 16: 1.3 Electric Field 15 Look back now
Page 17: 1.5 Continuous Charge Distributions
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
Page 33 and 34: 1.8 Homework 33 ⊲ Problem 1.14 Ri
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
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 and 96:
4.7 Homework 95 circular orbits. Wr
Page 97 and 98:
5.1 Sources of Magnetic Field 97 5
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.
Page 147 and 148:
7.5 Interference of Waves 147 I I A
Page 149 and 150:
7.7 Interference of Two Sources 149
Page 151 and 152:
7.8 Far Field Approximation 151 §
Page 153 and 154:
7.9 Thin Film Interference 153 pass
Page 155 and 156:
7.11 Homework 155 Second Min First
Page 157 and 158:
7.11 Homework 157 θ 2 d θ 1 θ 2
Page 159 and 160:
7.12 Summary 159 § 7.12 Summary De
Page 161 and 162:
8.2 Reflection 161 8 Geometric Opti
Page 163 and 164:
8.4 Snell’s Law 163 We see then t
Page 165 and 166:
8.5 Virtual Image Caused by Refract
Page 167 and 168:
8.6 Thin Lens Equation 167 back in
Page 169 and 170:
8.7 Virtual Image in a Converging L
Page 171 and 172:
8.8 Diverging Lenses 171 (b) virtua
Page 173 and 174:
8.10 Multi-Lens Optical Systems 173
Page 175 and 176:
8.11 Homework 175 We can also compu
Page 177 and 178:
@ Summary 177 § 8.12 Summary Facts
Page 179 and 180:
A Hints 179 1.14 Since this is only
Page 181 and 182:
A Hints 181 2.27 Imagine that you b
Page 183 and 184:
A Hints 183 4.12 Consider the vecto
Page 185 and 186:
A Hints 185 7.26 The distance from
Page 187 and 188:
B Index 187 † Ohm’s Law: Resist
Page 189 and 190:
B Index 189
Page 191 and 192:
C Power Series Expansions 191 The F
Page 193:
D Unit Prefixes 193 § D.3 Fundamen
show all

Introductory Physics Volume Two

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?