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Electric Field Lines
Consider the four field patterns below:
Assuming that there are no charges in the region of space depicted,
which field pattern(s) could represent electrostatic field(s)?
Electric Field Lines
Which
This
thin
of disk
the two
has surfaces
charge on(top
theand
top bottom)
and on the
hasbottom.
more charge
Whaton
type?
it?
A) Top
Positive
has more
charge on both
B) Bottom
Negativehas
charge
moreon both
C) They
Positive
arecharge
roughly
onequal
top, negative on bottom
D) Can’t
Negative
tell charge
from the
ongiven
top, positive
information
on bottom
E-Field from continuous charges
ke qi
E   2 rˆi
ri
ke dq
E   2 rˆ
r
•Volume charge density : dq =  dV
•Surface charge density : dq =  dA
•Linear charge density : dq =  dl
E-Field from continuous charges
Length L
Distance R
Linear charge density 
E-field here?
R L
ke  dr
R r 2
R L
ke  L
ke  
ke 
 ke 
ˆ

r
  rˆ 

 rˆ

R

L
R
r R

 R  R  L
ke dq
ke  dr
E   2 rˆ   2 rˆ  rˆ
r
r
Electric Fields and Forces
E  F /q
F  qE
F  ma
a  qE / m
A region of space has an electric field of 104 N/C, pointing in the plus
x direction. At t = 0, an object of mass 1 g carrying a charge of
1C is placed at rest at x = 0. Where is the object at t = 4 sec?
A) x = 0.2 m
C) x = 20 m
B) x = 0.8 m
D) x = 80 m
Electric Flux
•Electric Flux is the amount of electric field flowing through a
surface
•When electric field is at an angle, only the part perpendicular
E
to the surface counts
En

•Multiply by cos 
E = EnA= EA cos 
•For a non-constant electric field,
or a curvy surface, you have to
integrate over the surface
 E   E  dA   E cos dA
•Usually you can pick your surface so that the integration doesn’t
need to be done given a constant field.
Electric Flux
•What is electric flux
E
through surface
surrounding a charge q?
R
charge q
ke q
 4 R E  4 R 2  4 ke q
R
 E  4 ke q
2
2
 E  2 ke q  2 ke q
 4 ke q
Answer is
always 4keq
Gauss’s Law
•Flux out of an enclosed region
depends only on total charge inside
E 
qin
0
charge q
A positive charge q is set down outside a sphere. Qualitatively, what
is the total electric flux out of the sphere as a consequence?
A) Positive
B) Negative
C) Zero
D) It is impossible to tell from the given information
Gauss’ Law and Coulumb’s
•Suppose we had
measured the flux as:
 E  4 ke q
•From Gauss’ law:
 E  4 R E  4 ke q
2
E
R
charge q
Keq
R2
So Gauss’ law
implies
Coulomb’s law
•What if we lived in a
Universe with a different
number of physical
dimensions?
Gauss’s Law
charge q’’
charge q’
charge q
E 
 E  dA  4 k q  4 k q '  4 k  q  q '
e
e
 4 ke q ''
 E   E  dA  4 ke qin 
e
qin
0
Gauss’s Law
charge q
charge 2q
charge -q
charge -2q
How do we draw surfaces to contain the +2q charge and have flux?:
Zero ?
+3q/e0?
-2q/e0 ?
IMPOSSIBLE
Quizzes 1
A) q/o
B) -q/o
C) 0
Figure 24-29.
•What is the flux through the first surface?
•What is the flux through the second surface?
•What is the flux through the third surface?
•What is the flux through the fourth surface?
•What is the flux through the fifth surface?
D) 2q/o
Quizzes 2
A cube with 1.40 m edges is oriented as shown in the figure
Suppose there is a charge situated in the middle of
the cube.
• What is the magnitude of the flux through the
whole cube?
• What is the magnitude of the flux through any
one side?
A) q/o
B) q/4o
C) 0
D) q/6o
Quizzes 3
A cube with 1.40 m edges is oriented as shown in the figure
Suppose the cube sits in a uniform electric field of 10i ?
• What is the magnitude of the flux through the whole
cube?
• What is the magnitude of the flux through the top
side?
• How many sides have nonzero flux?
A) q/o
B) q/4o
C) 0
D) q/6o
A) 2 D) 1
B) 4
C) 0