Ch – 27 Gauss’s Law

Symmetry

A charge distribution is said to be Symmetric if the following geometric transformations cause no physical change:

• Translation parallel to an axis• Rotation about an axis• Reflection in a plane containing or perpendicular

to an axis

3 Fundamental Symmetries

Stop to Think 27.1 p. 853

Answer

Both A and D. Why?

Electric Flux

The amount of electric field passing through a surface

A Gaussian surface is 3-dimensional closed surface surrounding a charge or charge distribution.

The electric field pattern through the surface is easy to draw if the closed surface matches the symmetry of the charge distribution inside

Electric Flux

• There is a outward flux through a closed surface around a net positive charge

• There is an inward flux through a closed surface around a net negative charge

• There is no net flux through a closed surface around a region of space with no net charge

• The flux in or out of an enclosed surface is is proportional to the number of field lines inside the surface

This box contains…

1. Only positive charge

2. Only negative charge

3. No charge

4. A net positive charge

5. A net negative charge

6. No net charge

Answer

5 – more field lines going in than going out

Area Vector

• A vector with the magnitude of the surface area and the direction normal to the surface

• The area vector is always directed outward from a closed surface

Electric flux of a constant electric field

Ф = E cosθ

Electric Flux of a nonuniform field

The 2 cases we will be evaluating

1.If the electric field is everywhere tangent to a surface, the electric flux through the surface is 0.

2. If the electric field is everywhere perpendicular to a surface and has the same magnitude E at every point, the electric flux through the surface is EA.