Introductory Physics Volume Two

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128 Time Varying Fields 6.8 effective impedance of the system depends on ω. This can be a useful property, since sometimes we wish to treat different frequencies differently. For example in an audio system, there are big speakers for low frequencies and small speakers for high frequencies, but the signal coming from the amplifier to the speakers contains both high and low frequencies. Let us see how we can use a capacitor and resistor is series to split the signal so that the appropriate signal goes to each speaker. Example For the circuit in the previous example, let us find the voltage on the capacitor and resistor relative to the voltage from the source. G R (ω) ≡ V R 0 = V R 0 /I 0 R = √ V S0 V S0 /I 0 R2 + 1/(ωC) = 1 √ 2 1 + 1/(ωRC) 2 G C (ω) ≡ V C 0 = V C 0 /I 0 1/ωC = √ V S0 V S0 /I 0 R2 + 1/(ωC) = 1 √ 2 (ωRC)2 + 1 These ratios are called the gain. So we see that the voltage on the capacitor is equal the the source voltage at low frequencies and drops to zero at high frequencies, while the voltage on the resistor does just the reverse. So we see that the signal from the source is sorted by this circuit, high frequencies to the capacitor and low frequencies to the resistor. Thus we can send the voltage from the capacitor to the large speakers and the voltage from the resistor to the small speakers. ⊲ Problem 6.5 Suppose that you build a RL circuit instead of the RC, that is you replace the capacitor with an inductor in the previous example. (a) Find the gain for the resistor and inductor. (b) Graph the gain for the resistor and inductor. (c) Which will pass low frequencies better than high frequencies.
6.9 Homework 129 ⊲ Problem 6.6 Show that this LRC circuit √ has a maximum current when ω = 1 LC . This is called the resonance frequency. L + V S – R C § 6.9 Homework ⊲ Problem 6.7 Consider the hemispherical closed surface of radius R as shown . If the hemisphere is in a uniform magnetic field that makes an angle θ with the vertical, calculate the magnetic flux through the flat surface S 1 . Calculate the flux through the hemisphical surface S 2 . S 1 S 2 θ B ⊲ Problem 6.8 A powerful electromagnet has a field of 1.6T and a cross-sectional area of 0.20m 2 . If we place a coil having 200 turns and a total resistance of 20Ω around the electromagnet and then turn off the power to the electromagnet in 20ms, what is the current induced in the coil? ⊲ Problem 6.9 A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B = B o e −t/τ . What is the induced emf as a function of time? ⊲ Problem 6.10 A long, straight wire carries a current I = I o sin(ωt+δ) and lies in the plane of a rectangular loop of N turns as shown. Determine the emf induced in the loop by the magnetic field of the wire. I a b c ⊲ Problem 6.11
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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
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2.4 Capacitors 45 § 2.4 Capacitors
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2.5 Energy in an Electric Field 47
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2.7 More Examples 49 ⊲ Problem 2.
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2.7 More Examples 51 The resulting
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2.8 Homework 53 add up potential du
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2.8 Homework 55 ⊲ Problem 2.27 Ho
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3.2 Electric Current 57 3 Circuits
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3.3 Ohm’s Law 59 Some materials,
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3.5 Kirchhoff’s Rules 61 ⊲ Prob
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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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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
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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
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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
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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
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Page 147 and 148: 7.5 Interference of Waves 147 I I A
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Page 153 and 154: 7.9 Thin Film Interference 153 pass
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Page 157 and 158: 7.11 Homework 157 θ 2 d θ 1 θ 2
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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
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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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