Transcript Gauss - UCF Physics

W4D2
 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
A. We change the definition to include up
and down.
B. We apply the definition to a closed
surface.
C. We only use the vector that is unobscured by the surface as we look at it.
D. We really can’t deal with this in an
undergraduate course.
The ins and outs of it …..
Negative
Entering the Volume
Closed
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.
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
  EAcos
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.
=Normal Component of E X A
NEW CONCEPT
What is so important about FLUX??
OUTWARD Pointing
Normal
CLOSED Surface
Gauss’s Law
    E ( A )
  E  A  EA  E (4 R )

i
i
2
i

q
4 0 R 2
4 R 2 
q
0
Gauss’s Law
 TOTAL FLUX 


LEAVING
ANY

  Total 
CLOSED VOLUME 

i 
Enclosed Charge
0
His Law!
May the flux be with you.