E x
= 
0
R
1
4 
O
=
 x
2 
O





(
(
2  r dr x 2 + R 2
3 )
) x
2
=
 x
2 
O

0
R
( r dr
)
( x 2 + R 2
) 3
2
( x 2
1
+ R 2
)
+
1 x 



=

2 
O




1 
(
R 2
=
1 x 2 + 1
) 




Figure 22.20

Figure 22.19

What happens if the sheet is an insulator?, a conductor?
y
P x d d +Q
+

Clicker Question
A point charge +Q is a distance d above an insulating sheet with fixed charge density σ .
What is the best concept to use to find the Electric Field at point P ?
P d d +Q
+ σ
A. Conservation of energy
B. Second Law of Thermodynamics
C. Newton’s Laws
D. Superposition
E. Maxwell’s Equations

Clicker Question
A point charge +Q is a distance d above an insulating sheet with fixed charge density σ .
What is the best concept to use to find the Electric Field at point P ?
P d d +Q
+ σ
A. Conservation of energy
B. Second Law of Thermodynamics
C. Newton’s Laws
D. Superposition
E. Maxwell’s Equations

Clicker Question
A point charge +Q is a distance d above an insulating sheet with fixed charge density σ .
y x
What is the Electric Field at point P ?
A.
B.


1
4

O
1
4

O
Q d 2
Q d 2 i
ˆ
ˆ i
+

2

O
ˆ j
C.

2

O i
ˆ
D. Cannot determine
E. 0
P d d +Q
+ σ

Clicker Question
A point charge +Q is a distance d above an insulating sheet with fixed charge density σ .
y x
What is the Electric Field at point P ?
A.
B.


1
4

O
1
4

O
Q d 2
Q d 2 i
ˆ
ˆ i
+

2

O
ˆ j
C.

2

O i
ˆ
D. Cannot determine
E. 0
P d d +Q
+ σ

Clicker Question

Figure 23.35

Clicker Question
Two equal + charges are initially stationary and separated by r
0
.
If they are allowed to fly apart (to infinity), what will be the kinetic energy of each?
A.
B.
C.
D.
1
4

0
1
4

0
1
8

0
1
4

0 q r
0 q 2 r q
0
2
2 r q
0
2 r
0
E. 0

Clicker Question
Two equal + charges are initially stationary and separated by r
0
.
If they are allowed to fly apart (to infinity), what will be the kinetic energy of each?
A.
B.
C.
D.
1
4

0
1
4

0
1
8

0
1
4

0 q r
0 q 2 r q
0
2
2 r q
0
2 r
0
E. 0
Text

Clicker Question
Where an electric field line crosses an equipotential surface, the angle between the field line and the equipotential is
A. zero.
B. between zero and 90°.
C. 90°.
D. not enough information given to decide

Clicker Question
Where an electric field line crosses an equipotential surface, the angle between the field line and the equipotential is
A. zero.
B. between zero and 90°.
C. 90°.
D. not enough information given to decide