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

Field Theory Versus Action at a Distance

Why does physics replace action at a distance with a field, and what do Faraday's rubber bands and strings reveal about the force?

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Your summary note

1. Action at a distance versus action by continuous contact
  Define each worldview: what action at a distance requires besides the two objects, and how field theory passes the force element to element through intervening space at a finite speed.
2. Parallel current-carrying wires attracting and repelling
  Sketch both wire pairs, record which relative current directions attract and which repel, and name the measurable magnetic field filling the apparently empty space between them as the agent.
3. The total field and Faraday's rubber bands and strings
  Define the total field as the combined field of every object present, and record Faraday's analogy that the stresses it shows act like rubber bands and strings, with the parallel wires as the example.
Attempt 1 of 2