8.6.A—Describe the properties of a charge distribution by applying Gauss’s law

Describe the properties of a charge distribution by applying Gauss’s law.

• Gauss’s law relates electric flux through a Gaussian surface to the charge enclosed by that surface. Relevant equations:
• A Gaussian surface is a three-dimensional, closed surface.
• The total electric flux through a Gaussian surface is independent of the size of the Gaussian surface if the amount of enclosed charge remains constant.
• Gaussian surfaces are typically constructed such that the electric field generated by the enclosed charge is either perpendicular or parallel to different regions of the Gaussian surface, resulting in a simplified surface integral.
• If a function of charge density is given for a charge distribution, the total charge can be determined by integrating the charge density over the length (one dimension), area (two dimensions), or volume (three dimensions) of the charge distribution. For example:
• Maxwell’s equations are the collection of equations that fully describe electromagnetism. Gauss’s law is Maxwell’s first equation. BOUNDARY STATEMENT AP Physics C: Electricity & Magnetism only expects students to quantitatively apply Gauss’s law to point charges and charge distributions that have spherical, cylindrical, or planar symmetry.