Gauss' Law

C& S Chap 10

S&F Section 15.9

S&J Sections 24.1 & 24.2

 

What is an electric field?  What does it look like ?

As a matter of fact, all you can see is electric fields !  Your eyes are detectors of changing electric fields ! 

 

Electric Flux - An effort to quantify electric field (light) coming through a window.  The amount of light  coming through a window depends upon :

           How strong the light is (magnitude of E), and

           What direction it is pointing. 

                       So one must resolve E into 2 components, one perpendicular to the window, E, and one parallel to the window, E||. 

 

The only thing you can see is E.  Demonstrate with a flashlight.

 

Maybe use the paint sprayer idea

 

Definition of  Electric Flux F = strength of E x Area, or, F = E A cos q = EA.

or, in the  case E varies over A, F = _E¥dA

Then along comes Gauss who "discovers" Fc the electric flux through a closed surface is equal to the charge inside the surface divided by the permitivity of free space, (denoted Fc = ºEdA = Q/eo).  Amazing !, or is it ?  Recall the electric field at a distance r from a point charge Q was defined was originally as E = kQ/r2.  But wait a minute.  It turns out k = 1/4¹eo, so E = Q/(4¹eor2).  But 4¹r2 is just the area of a sphere of radius r, so E was originally defined to be

E = Q/Aeo, so EA = Q/eo. But this is only for a sphere, and Gauss proved it true for any closed surface, so he does get some credit for cleverness.

GaussÕs Law:

The other big deal in this chapter is the rules for conductors, on page

 

1.  The electric field is zero everywhere inside a conductor.

2.  Any excess charge on an isolated conductor must reside entirely on its surface.

3.  The electric field just outside a charged conductor is s/eo , where s is the charge per unit area at that point.

4.  On an irregularly shaped conductor, charge tends to accumulate at locations where the radius of curvature of the surface is the smallest, that is, at sharp points.

 

Properties 1 and 2 are what tells us that the safest place to be during a lightening storm is inside any metal box, i.e. cars, even wire cages.  The wire mesh in the door of microwave ovens is what prevents the microwaves from escaping and cooking you as well as your food.