AP Physics C — Gauss's Law Examples

Gauss’s Law used for multiple different charged objects. For each, we construct gaussian surfaces with different radiuses or other properties.

For conductors, all the charge is at the surface. When our gaussian surface is within the object, .

We also employ the use of different charge densities:

• linear charge density
• surface charge density
• volume charge density

Conductive Spherical Symmetry

Construct a spherical gaussian surface with radius for a charged sphere with radius .

When :

Conductive Cylindrical Symmetry

We construct a cylindrical gaussian surface with radius and length to enclose our charged cylinder.

When :

Conductive Planar Symmetry

We construct a box gaussian surface of height , where the top and bottom sides of the box are away from the charged plane.

When

Nonconductive Spherical Symmetry

Since there is also charge within the object, not just on its surface, when our gaussian surface will still enclose charge.

We need to use volume charge density . In this case,

When

Nonconductive Cylindrical Symmetry

Just like before, since there is also charge within the object, not just on its surface, when our gaussian surface will still enclose charge.

We still need to use volume charge density . In this case, .

When :