Chapter 1 Fields 1.1 Action at a Distance versus Field Theory 1-2 1.2 Scalar Fields 1-3 Example 1.1:Half-Frozen/Half-Baked Planet... 1-5 1.2.1 Representations of a Scalar Field...... 1-5 1.3 Vector Fields. .1-7 1.4 Fluid Flow.… 1-8 Animation 1.1:Sources and Sinks.............. .1-8 Animation 1.2:Circulations........ .1-10 1.4.1 Relationship Between Fluid Fields and Electromagnetic Fields ...1-12 1.5 Gravitational Field................... .1-13 1.6 Electric Fields....... .1-14 1.7 Magnetic Field .1-15 1.8 Representations of a Vector Field.... 1-16 1.8.1 Vector Field Representation.......... .1-16 1.8.2 Field Line Representation....... .1-17 1.8.3 Grass Seeds and Iron Filings Representations .1-18 1.8.4 Motion of Electric and Magnetic Field Lines. .1-19 1.9 Summary.… 1-20 1.10 Solved Problems.............. .1-20 l.10.1 Vector Fields.… .1-20 1.l0.2 Scalar Fields… .1-22 1.11 Additional Problems. 1-23 1.11.1 Plotting Vector Fields.... .1-23 1.11.2 Position Vector in Spherical Coordinates.............................1-23 1.11.3 Electric Field.......... .1-24 1.11.4 An Object Moving in a Circle 1-24 l.1l.5 Vector Fields… 1-24 1.11.6 Object Moving in Two Dimensions 1-25 1.11.7 Law of Cosines.............. 1-25 1.11.8 Field Lines............. 1-26 1-1Chapter 1 Fields 1.1 Action at a Distance versus Field Theory.............................................................1-2 1.2 Scalar Fields..........................................................................................................1-3 Example 1.1: Half-Frozen /Half-Baked Planet.......................................................1-5 1.2.1 Representations of a Scalar Field...................................................................1-5 1.3 Vector Fields.........................................................................................................1-7 1.4 Fluid Flow.............................................................................................................1-8 Animation 1.1: Sources and Sinks.........................................................................1-8 Animation 1.2: Circulations ................................................................................1-10 1.4.1 Relationship Between Fluid Fields and Electromagnetic Fields.................1-12 1.5 Gravitational Field ..............................................................................................1-13 1.6 Electric Fields.....................................................................................................1-14 1.7 Magnetic Field ....................................................................................................1-15 1.8 Representations of a Vector Field.......................................................................1-16 1.8.1 Vector Field Representation ........................................................................1-16 1.8.2 Field Line Representation............................................................................1-17 1.8.3 Grass Seeds and Iron Filings Representations.............................................1-18 1.8.4 Motion of Electric and Magnetic Field Lines..............................................1-19 1.9 Summary.............................................................................................................1-20 1.10 Solved Problems ...............................................................................................1-20 1.10.1 Vector Fields..............................................................................................1-20 1.10.2 Scalar Fields...............................................................................................1-22 1.11 Additional Problems.........................................................................................1-23 1.11.1 Plotting Vector Fields................................................................................1-23 1.11.2 Position Vector in Spherical Coordinates..................................................1-23 1.11.3 Electric Field..............................................................................................1-24 1.11.4 An Object Moving in a Circle....................................................................1-24 1.11.5 Vector Fields..............................................................................................1-24 1.11.6 Object Moving in Two Dimensions...........................................................1-25 1.11.7 Law of Cosines ..........................................................................................1-25 1.11.8 Field Lines .................................................................................................1-26 1-1