Electricity and Magnetism

Mathematical Tools and Fields

01Series Approximations: Keeping One or Two Terms 02Integrals as Sums: Along a Line and a Curved Path 03Line Integrals: Work as the Integral of F · ds 04Closed Line Integrals: Work Around a Loop 05Double Integrals: Area, Charge and Volume 06Closed Surface Integrals: The Sphere and Its Charge 07Electric Flux Through Surfaces and Volume Integrals Problem set0/10 Problem set 20/10 MIT problem set0/4

01Field Theory Versus Action at a Distance 02Scalar Fields: Contour, Color and Relief Maps 03Vector Fields, Sources, Sinks and Divergence 04Curl: Measuring the Circulation of a Field 05Gravitational, Electric and Magnetic Fields 06Drawing Vector Fields: Arrows, Lines and Grass Seeds Problem set0/10 Problem set 20/10 MIT problem set0/1

Drawing Vector Fields: Arrows, Lines and Grass Seeds

Why can field lines never cross, and what do grass-seed patterns show that arrow grids hide?

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←Previous Gravitational, Electric and Magnetic Fields

Your summary note

1. The arrow-grid representation
  Draw the arrow grid for the two-charge field, positive charge three times the negative, and list the options for showing magnitude: arrow length, arrow color, or nothing at all.
2. Field lines and their two rules
  Describe the step-by-step construction of a field line, state the tangency and no-crossing rules, and record that more undrawn lines lie between the drawn ones.
3. Grass seeds and iron filings textures
  State how seeds in an electric field or filings in a magnetic field align with the local field, and record that this texture gives the densest picture of the field's structure.
4. Animating field patterns along $\vec{E}\times\vec{B}$
  State that animated patterns move along $\vec{E}\times\vec{B}$ , the energy-flow direction perpendicular to both fields, and contrast this with fluid animations that move along the velocity field itself.
Attempt 1 of 2