Introductory Physics Volume Two

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184 Hints A 6.6 Use a phasor diagram to draw Kirchhoff’s loop rule, then find the frequency that minimizes the effective impedance of the RLC combination. 6.8 Use Faraday’s law. Assume that the magnetic field decreases at a constant rate over the 20 ms that it goes from 1.6 T to zero, that is dB/dt = (−1.6T)/(20ms). 6.10 Since the field strength decreases as you move further from the wire you will need to do an integral in order to compute the magnetic flux. 6.11 Use Ampere’s Law. 6.13 Consider that Q = ∫ Idt and I = V/R = E/R. 7.2 Start from x = A cos φ. 7.3 Take a look at the diagram of the oscillator that shows the phase angle at different points in the cycle. For the last part remember that v = dx/dt and consider the quantity v/x. 7.4 Recall that the phase is φ = ωt + φ 0 so that ∆φ = ω∆t. Then consider by how much the phase must change in order for the oscillator to complete one cycle. 7.8 First compute the phase difference. Remember that φ 1 = −kr 1 and φ 2 = −kr 2 . Next use the addition of two waves theorem. 7.9 The collection of points with the same ∆r will form a continuous line, just like the collection of points that are all 5cm from a single point makes a circle or radius 5 cm. 7.10 Treat the two holes as two sources. 7.11 The phase of each path is now −kr plus the reflection phase shift. 7.12 Find the distance from the lower speaker to the point P as a function of the distance d. 7.15 The path difference occurs in air. 7.16 Use the far field approximation to find the path difference. 7.18 Use the trig identities in the appendix. 7.19 There is a path difference, d sin θ, on both sides of the screen. 7.22 The air gap between the plates will be wedge shaped, because the thickness of the air gap increases as you move toward the wire, there will be an increasing phase difference between the two reflected beams. This leads to the fringes. 7.24 As the slit gets narrower the angle of the first minima increases. There is a limit to the increase.
A Hints 185 7.26 The distance from the central maximum to the first order maximum is the same as it would be for a double slit with the same distance between the two slits as there is between successive lines in the diffraction grating. 8.1 Use geometry to show that α α/2 β α/2 Then use Snells law. 8.2 Each straight line segment that crosses the optical axis, creates two similar triangles, one above the axis and one below the axis. Use the properties of similar triangles to get an equation for each of these pairs. 8.5 Use the thin lens equation to find under what conditions the image distance is negative. 8.7 Use the thin lens equation. 8.8 Start with the magnification equation.
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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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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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Page 137 and 138: 7.1 Maxwell Equations 137 7 Wave Op
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Page 147 and 148: 7.5 Interference of Waves 147 I I A
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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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Page 191 and 192: C Power Series Expansions 191 The F
Page 193: D Unit Prefixes 193 § D.3 Fundamen
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Introductory Physics Volume Two

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