These are two-dimensional cross sections through three-dimensional closed spheres and a cube. Rank order, from largest to smallest, the electric fluxes a to e through surfaces a to e.

A. Φa > Φc > Φb > Φd > Φe

B. Φb = Φe > Φa = Φc = Φd

C. Φe > Φd > Φb > Φc > Φa

D. Φb > Φa > Φc > Φe > Φd

E. Φd = Φe > Φc > Φa = Φb

4/15/15 1Oregon State University PH 213, Class #8

An electrically neutral cylindrical piece of material is placed in an external electric field, as shown. The net electric flux passing through the surface of the cylinder is…

1.positive.

2. negative.

3. zero.

4/15/15 2Oregon State University PH 213, Class #8

Speculate: Which Gaussian surface would allow you to use Gauss’s law to easily determine the electric field outside a uniformly charged cube?

A. A cube whose center coincides with the  center of the charged cube and which has  parallel faces.

A. A sphere whose center coincides with the  center of the charged cube.

B. Neither A nor B.

A. Both A and B.

4/15/15 3Oregon State University PH 213, Class #8

So, when is Gauss’s Law useful? When we already know the shape/form of the E-field (but not necessarily its magnitude)—and that form is symmetric and/or uniform, so that we can avoid nasty surface integrals by selecting certain simple Gaussian surfaces:

A spherical surface (for spherically symmetric charge distributions).

A cylindrical surface (for very long lines/cylinders of cylindrically symmetric charge distributions).

A rectangular “box” surface (for very large planes of rectangular symmetric charge distributions).

4/15/15 4Oregon State University PH 213, Class #8

Example (spherically symmetric charge distribution):Suppose we want to determine the E-field at any point either inside or outside a solid sphere (centered at the origin) of known radius R, with the following known volumetric charge distribution:

= dq/dV = cr (c is a positive known constant)

This is spherically symmetric (depends only on r, not on or ).

4/15/15 5Oregon State University PH 213, Class #8

Example (infinitely long cylindrically symmetric charge distribution): Suppose we want to determine the E-field at any point either inside or outside a long cylinder (parallel to, and centered on, the z-axis) of known radius R and with the following known volumetric charge distribution:

= dq/dV = cr (c is a known positive constant)

This is cylindrically symmetric (depends only on r, not on or z).

4/15/15 6Oregon State University PH 213, Class #8

Example (infinitely long rectangularly symmetric charge distribution): Suppose we want to determine the E-field at any point either inside or outside a long slab of known thickness W (parallel to and centered on the x-z plane), with the following volumetric charge distribution:

= dq/dV = cy (where c is a positive constant)

This is rectangularly symmetric (depends only on y, not on x or z).

4/15/15 7Oregon State University PH 213, Class #8