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

Curl: Measuring the Circulation of a Field

Why do magnetic fields swirl while electric fields spread, and what does curl measure that divergence misses?

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Your summary note

1. Circulating flows versus source and sink flows
  Record that circulating flows have non-zero curl and zero divergence while source and sink flows have zero curl and non-zero divergence, with a sketch of each pattern.
2. Splitting a field into curl-free and divergence-free parts
  State the decomposition of any vector field, then record that electrostatic fields are curl-free, magnetic fields are always divergence-free, and only time-varying electric fields have both.
3. Flux and circulation as borrowed fluid terms
  Define the flux of a fluid through a surface, then state that electric flux and magnetic circulation reuse these words although nothing flows along $\vec{E}$ or $\vec{B}$ .
Attempt 1 of 2