Module 2 — Electrostatics#
Electrostatics
Charges at rest, and the vector calculus that describes their fields.
Lessons 17–26 · Intro to Electromagnetics · Maj Ellis · Dr. Neil Rogers
Where This Module Goes
The vector calculus the rest of the course runs on, then the electric field of charges at rest: Coulomb’s law, Gauss’s law, potential, boundary value problems, boundary conditions, and capacitance.
Chapter 4: Vector Analysis
- I can recognize and apply common vector calculus operations, such as: gradient, divergence, curl, and Laplacian in the three major coordinate systems.
- I can calculate surface and volume integrals in rectangular, cylindrical, and spherical coordinate systems.
- I can differentiate between Stokes' Theorem and the Divergence Theorem and apply them to various problems to simplify integrals.
Chapter 5: Electrostatics
- I can apply Coulomb's Law to use direct integration to calculate the electric field due to charge density in various geometries, including rectangular, cylindrical, and spherical coordinate systems.
- I can apply the integral and differential forms of Gauss's Law to calculate the electric field due to charge density in various geometries, including rectangular, cylindrical, and spherical coordinate systems.
- I can calculate the electric field from the scalar electric potential in a variety of geometries.
- I can apply the electric field boundary conditions to calculate electric fields on both sides of a material boundary.
Lessons 17-19
Vector and Coordinate System Review
Gradient, divergence, curl, and the Laplacian in three coordinate systems; surface and volume integrals; Stokes' and the divergence theorem. Objectives 4.1, 4.2, 4.3.
Lesson · L18Coulomb's Law
The electric field of point charges, by superposition. Objective 5.1.
Lesson · L19Surface and Volume Charge
The field of a charge distribution, by direct integration. Objective 5.1.
Lessons 20-22
Gauss's Law (Integral Form)
Using symmetry and a Gaussian surface to find the field without integrating Coulomb's law. Objective 5.2.
Lesson · L21Gauss's Law (Differential Form)
The point form of Gauss's law, and charge density from a known field. Objective 5.2.
Lesson · L22Electric Potential
Work, potential, and the electric field as the gradient of the potential. Objective 5.3.
Lessons 23-25
Boundary Value Problems and Electric Potential
Laplace's equation for the parallel-plate capacitor and the coaxial line. Objective 5.3.
Lesson · L24Electric Boundary Conditions
Conductors, dielectrics, and the field on both sides of a material boundary. Objective 5.4.
Lesson · L25Boundary Conditions and Capacitance
Capacitance from the field, and boundary conditions put to work. Objective 5.4.