Calculating the flux through a sphere around a point charge, leading to the statement of Gauss's Law that flux through a closed surface is proportional to the net charge enclosed by the surface.

Need symmetric situations to find electric field using Gauss's Law. Example of finding the electric field inside and outside a hollow sphere with uniformly distributed charge. Comparison to gravitational field.

Finding the electric field around a plane with uniformly distributed charge. Result is stated, but some of the work is left to students as an exercise.

Finding the magnitude and direction of the electric field created by a long cylinder with uniform charge density.

Electric flux through a closed surface is proportional to the total charge enclosed by the surface. Electric flux and closed surface are defined. Diagrams of flux through open and closed surfaces. Example of calculating electric flux through a sphere.

Step-by-step methods for applying Gauss's Law and for choosing Gaussian surfaces. Table of Gaussian surfaces used for sources with spherical, symmetrical, and planar symmetry. Includes a worked example with diagrams for each type of symmetry.

Brief statement of the equation for Gauss's Law and a list of symmetry types (spherical, cylindrical, planar).

Finding the electric field, electric potential, magnetic field, and field energy between the plates of a charging capacitor.

Definition of flux through a surface. Statement of Gauss's Law with descriptions of the types of symmetry used in Gauss's Law and a step-by-step method for applying it.

Definition; flux through cylinder and closed surfaces; flux with contained charge; Gauss's Law.

Restatement; application to sphere of charge, shell of charge, plane of charge.

Theoretical and experimental verification of Gauss's Law.

Application of divergence to Gauss's Law; divergence theorem; definition with limits and derivatives; finding E from V.

Electric flux defined; Gauss's Law and Gaussian surfaces; symmetry concerns.

Use of Gauss's Law for infinite rod, infinite plane, spherical shell, uniformly charged sphere.

Strategies and solved Gauss's Law problems: Parallel planes; flux through flat surface; gravity; potential of sphere.

Two questions about electric flux through a plane and a sphere, with answers and explanations.

Questions about Gauss's Law and its applications, with answers and explanation.

5-part E-field problem; calculating and plotting E-field along z-axis; limiting cases; connection to Coulomb's law.

Solution (PDF)

4-part Gauss's law problem; finding E-field in 3 cases; plotting along z-axis.

Solution (PDF)

3-part Gauss's law problem; determining qualitative charge distributions for different locations of the charge.

Solution (PDF)

3-part Gauss's law problem; finding radial E-field and potential.

Solution (PDF)

Drawing and explaining electric field near sheet of charge.

Solution (PDF)

4-part problem; finding charge distribution, electric field, and potential for charged cylinder, then again with a dielectric.

Solution (PDF)

Finding charge distribution, E-field, and field lines of positive sphere inside negative spherical shell.

Solution (PDF)^#