Gauss’s Law W4D2

What’s Happening Dude? Today Gauss’s Law is happening. Big time. There is a new WebAssign, don’t cha know? There is one of those Quiz thingys on Friday. You have to download the next unit for Friday and you should look at the website.

Electric Field Lines Which charge is bigger? A The (+) charge B The (-) charge C They are the same D You can’t tell

Where is the Electric Field The Strongest? B A D C

Field Lines flux The number of lines leaving (or entering) a charge is propositional to the charge The electric field at a place in space is proportional to the density of the lines. You can use a small area oriented perpendicular to the electric field to probe the strength of the field by counting the lines that pass through the area. We will define the FLUX (F) passing through the area as proportional to the number of lines passing through this area multiplied by the area.

Last time We can use a vector to represent a small flat area: It’s length is proportional to the area. Its direction is perpendicular to the area The area need not be square, round or anything else. It must be small. Very small. Teeny Tiny small. There is an ambiguity in which of two ways the vector can point for a particular small area.

Small Area Small Area

Ambiguity Which One??

The ambiguity is lost if We change the definition to include up and down. We apply the definition to a closed surface. We only use the vector that is un- obscured by the surface as we look at it. We really can’t deal with this in an undergraduate course.

The ins and outs of it ….. Closed Negative Entering the Volume Positive Leaving the Volume Closed Volume

We represent a surface as the area surrounded by a perimeter that we will call a “loop”. The loop defines the boundary of the area. The boundary of the shaded area below is the loop defined above.

Complete Pages 6-8 in the Unit Copy your chart to a whiteboard when you are finished. Then continue through page 9.

F=Normal Component of E X A The electric flux through a surface is defined as the magnitude of the electric field times the area of the surface times the cosine of the angle between the direction of the electric field and the area vector of surface The units of flux are Nm2/C. Qualitatively; flux is the number of field lines passing through a surface. When the angle between the area vector of the surface and the direction of the electric field is greater than 90, the flux is negative. F=Normal Component of E X A

NEW CONCEPT FLUX How Much Stuff Is There?

What is so important about FLUX?? OUTWARD Pointing Normal CLOSED Surface DF

Gauss’s Law Gaussian Surface

Gauss’s Law His Law!

May the flux be with you.