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Static Vector Fields
Course Overview
The Static Vector Field Paradigm continues the discussion of E&M from the Symmetries & Idealizations Paradigm, focusing on electric fields, magnetic fields, and the magnetic vector potential. This course uses a variety of pedagogical techniques (small group activities, computer visualization, kinesthetic activities, and lecture/discussion) to help students build a multifaceted understanding of these ideas. This course emphasizes extending the integral versions of Maxwell's equations (learned in introductory physics) to the local, differential versions; visualizing vector-valued functions in three dimensions using the computer algebra software Maple; and extending the techniques of vector calculus from rectangular to cylindrical and spherical coordinates. (Catalog Description)
Course Goals
- For students to build conceptual and geometric understanding of current density, magnetic field, and magnetic vector potential and a formal understanding of the relationships between them (using vector calculus)
- For students to understand divergence and curl - formally and geometrically - and the Divergence Theorem and Stoke's Theorem formally and geometrically
- To derive the differential form of Maxwell's equations from the integral form and for students to have link their conceptual understanding with the formalism of Maxwell's equations
- For students to understand Gauss' Law and Ampere's Law and how to make explicit symmetry arguments.
- For students to understand the continuity of electric and magnetic fields across charge/current boundaries.
- For students to understand how energy is stored in electric and magnetic fields, and be able to calculate the energy from sources, fields and potentials.
- For students to come to understand that sources, fields, and potentials are different constructs that address the same phenomena, but are useful in different ways.
