#### Transcript of Chapter 22 - Gauss' Law

**Gauss's Law**

Apply to 3 problems

Sphere - Ex 22-3 (hollow), 22-4 (solid)

Sphere, nonuniform charge 22-5

Cylinder - Ex 22-6

Sheet - Ex 22-8

E = sigma/epsilon - Field of a large, infinite sheet, very important

Gaussian Surface should follow symmetry of problem

Electric field is zero in a conductor

Flux

Enclosed Source

Gaussian Surfaces

Electric Flux

Important Results

E outside of sphere is the same as point charge (inside sphere is different, depends on if it's a conductor or insulator)

Nonuniform Concept 22-9

Applying Gauss' Law

Which surface has more flux through it?

Flux: Simple Examples

Assume each charge is q. What is the flux through surfaces 1, 2, and 3?

1

2

3

A Gaussian surface is a 3-dimensional, closed surface. It is an imaginary, mathematical construct. It does not really exist. But we use it as a tool to help us determine electric fields.

Light bulb analogy, if there is no light on INSIDE the bulb, how much flux is there through the surface?

Flux is a measure of a flow of a physical property through a surface

More flow = greater flux

If angle between flow and surface changes, flux changes

If area increases, flux increases (assuming uniform flux density

Φ = = q/ε0

We measure electric flux through a Gaussian surface

This means the area MUST be a closed surface

1

2

What is the direction of an area vector?

Area vector for a CLOSED surface always points out of surface

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