Introductory Physics Volume Two

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114 Sources of Magnetic Field 5.6 § 5.6 Summary Definitions Facts Field due to a section of current: dB ⃗ = µ 0I ⃗dl × ˆr 4π r 2 Theorems Ampere’s Law: ∮ ⃗B · ⃗dl = µ 0 ∫ ⃗J · ⃗ dA
6.2 Faraday’s Law 115 6 Time Varying Fields § 6.1 Introduction Let us take a moment to review what we know about the means of producing electric and magnetic fields. We have found two means to produce fields. • Electric fields are produced when there are regions in space with a net electric charge. This is encapsulated in Gauss’s law. ∮ ⃗E · dA ⃗ = 1 ∫ ρ dV ɛ 0 • Magnetic fields are produced when there is a flow of charge. This is encapsulated in Ampere’s law. ∮ ∫ ⃗B · ⃗dl = µ 0 ⃗J · dA ⃗ So far, we have investigated only steady state fields (fields that don’t change in time). A net electric charge and a steady flow of charge are the only means to produce steady state electric and magnetic fields. But these are not the only means of producing time varying fields. In this chapter we will investigate time varying electromagnetic systems. § 6.2 Faraday’s Law Let us start by considering what will happen if we have some source of time varying magnetic field. It could for example be a wire that is carrying a current and the current is changing rapidly in time. Since the current is changing in time, the magnetic field that the current creates will also change with time. If we place a loop of wire into this time varying magnetic field, the time varying field will produce a current in the wire. This is called an induced current. Nikola Tesla was able to produce such strong induced currents that he was able to make a light bulb glow with the current. In the photo to the right Tesla is holding a light bulb which has no wires connected to it. The current driving the bulb is entirely an induced current, which is caused by the time varying magnetic field.
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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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Page 67 and 68: 3.9 More Examples 67 Note that the
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Page 77 and 78: 3.10 Homework 77 4 µF + - 2 µF +
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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
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Page 91 and 92: 4.6 More Examples 91 The force on t
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Page 111 and 112: 5.5 Homework 111 The magnetic force
Page 113: 5.5 Homework 113 3.00 A 1.00 A 1 mm
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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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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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