1 CHAPTER 22 GAUSS’S LAW TWO BASIC CONCEPTS ELECTRIC FLUX AND GAUSS’S LAW
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
CHAPTER 22
GAUSS’S LAW
TWO BASIC CONCEPTS
ELECTRIC FLUX
AND
GAUSS’S LAW
2
ELECTRIC FLUX
Consider a number of guns at the left
shooting to the right.
Bullets
Sheet
Flux of bullets is number of bullets times
area of sheet perpendicular to bullets.
3
Turn sheet on edge.
Bullets
Sheet
Flux now near zero since area of sheet is
parallel to bullets.
4
Turn sheet to angle.
Bullets
Sheet
Flux somewhere between previous two
values.
5
Assign area vector to sheet.
Bullets
φ
Sheet A
Flux will be
6
OR THINK ABOUT FLUX THE WAY YOUR
BOOK DOES.
7
8
FOR ELECTRIC FLUX
ELECTRIC
FIELD φ
Sheet A
9
WHAT WE HAVE DISCUSSED IS FOR A
UNIFORM ELECTRIC FIELD.
If the field varies we must use differential
calculus.
Small increment of flux d
Then integrate
10
GAUSS’S LAW
We will state the law then work some
examples. After that we will do an example
to justify the law.
Statement of Gauss’s law:
The flux through a closed surface is equal to
the net charge enclosed by the surface
divided by ε0.
Equation:
11
Consider a conducting sphere of radius R
with charge q on the surface.
12
Draw a Gaussian surface around this sphere
with radius r.
Apply Gauss’s Law
13
The same equation we had for a point
charge.
14
Example 22.9
Positive electric charge Q is distributed
uniformly throughout the volume of an
insulating sphere with radius R.
a. Find the electric field at point p where
r < R.
b. Find the electric field at point p where
r > R.
15
16
a. Radius of Gaussian Surface = r
Gauss’s Law
Need charge enclosed by surface.
Charge density
Charge enclosed by Gaussian Surface
17
18
For r < R
19
Part b.
Draw Gaussian Surface outside sphere.
20
Integral same as before
21
JUSTIFY GAUSS’S LAW
Coulomb’s Law Gauss’s Law
Consider point charge Q
P E
Q r
At P
Visualize a sphere centered on Q and with
radius r passing through P.
22
Integrate over surface.
23
Other Geometries
Line of charge
Charge on wire? Charge per unit length λ
Choose Gaussian surface – cylinder
24
Cylinder made up of two ends and
cylindrical surface.
· · ·
90
0
90
25
Charge enclosed
/
26
2
12
27
Infinite sheet of charge.
Remember in Chapter 21 we got
2
where σ was the charge per unit area.
Choose cylinder for Gaussian surface.
28
Cylinder made up of two ends and
cylindrical surface.
29
· · ·
Cylinder made up of two ends and
cylindrical surface.
0
90
0
30
0
0
Charge enclosed
31
0
2
Related Documents
