Introductory Physics Volume Two

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140 Wave Optics 7.2 -A 0 A φ = 0 φ = π/4 φ = 2π/4 φ = 3π/4 φ = 4π/4 φ = 5π/4 φ = 6π/4 φ = 7π/4 φ = 8π/4 The actual value of the displacement (x) is the amplitude of the oscillation times the cosine of the phase angle. Displacement = Amplitude × cos φ x = A cos φ
7.3 Describing Waves 141 For a harmonic oscillator the phase increases at a constant rate: dφ dt = ω −→ φ = ωt + φ 0 and so the displacement is x = A cos(ωt + φ 0 ) ⊲ Problem 7.2 An oscillator has an amplitude of 3.2. At this instant the displacement of the oscillator is 1.4. What are the two possible phases of the oscillator at this instant? ⊲ Problem 7.3 You have a mass connected to a spring. 0 x You start the mass oscillating in the following ways. What is the initial phase φ 0 in each case. (a) Stretch the spring to the right, at t = 0 release the mass. (b) Compress the spring to the left, at t = 0 release the mass. (c) At t = 0 strike the mass so that it begins moving to the left. (d) At t = 0 strike the mass so that it begins moving to the right. (e) At t = 0 the mass is at the position x 0 = 2.0m and has a velocity of v 0 = 3.0 m rad s (assume that ω = 5.0 s ). ⊲ Problem 7.4 It takes a time of T = 0.025s in order for an oscillator to complete one cycle. What is the angular frequency (ω) of the oscillator? § 7.3 Describing Waves Consider dropping a rock into a pool of still water. Ripples spread out from the point at which the rock enters the water. If you examine the motion of the water at one fixed point, the surface of the water moves up and down as successive waves move past. The height of the water at our fixed point is an oscillation. This is true at other points a well, at each location the height of the water oscillates. Since an oscillation is so simple, the only thing that can differ between one point and another is the amplitude of the oscillation and the initial phase φ 0 . Let us write the height of the water, at position ⃗r and time t, as y(⃗r, t). Since the oscillation at each point is a harmonic oscillation we can write: y(r, t) = A(⃗r) cos [ωt + φ 0 (⃗r)]
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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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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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Page 91 and 92: 4.6 More Examples 91 The force on t
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Page 95 and 96: 4.7 Homework 95 circular orbits. Wr
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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
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Page 161 and 162: 8.2 Reflection 161 8 Geometric Opti
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Page 187 and 188: B Index 187 † Ohm’s Law: Resist
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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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