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From Last Time…
Magnitude of the
electric force
+
Direction of
the electric
force
+
1
Induced dipoles (charge redistribution)
charged rubber rod
Bring negative charge close.
Electrons on sphere
move away from rod.
2
Exam 1
Tue. Sep. 29, 5:30-7 pm, 145 Birge
Covers Chap. 21.5-7, 22, 23.1-4, 23.7,
24.1-5, 26 + lecture, lab, discussion, HW
8 1/2 x 11 handwritten note sheet (both sides) allowed
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Study ideas:
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Exam 1 Practice problems at Mastering Physics
Sample exams on website (blank & solutions)
Group/Quiz (blank & solutions).
Review lab question sheets.
3
Unusual dipoles:
Electrogenic fish
• Dipole +
nearby conducting object
Some fish generate charge
separation - electric dipole.
Dipole is induced in nearby
(conducting) fish
Small changes detected by
fish.
4
The idea of electric fields
• EM wave made up of
oscillating electric and magnetic fields.
• But what is an electric field?
• Electric field is a way to describe the force on
a charged particle due to other charges
around it.
• Force = charge  electric field
• The direction of the force is the direction of
the electric field.
5
Electric field of a point charge
Force on this charge…
Q2
+
+
+
Q1Q2
F  k 2 rˆ
r
Q1
…due to this charge

E  F r /Q2
+
= Force/charge
Units? N/C

6
+
Calculating the electric field
E 
+
r = 10 cm
Q1=1µC
kQ1

2
r
9
2
2
6
9
10
N

m
/C
10

 C
0.1m
2
 9 105 N /C

7
Electric field
• Electric field vector defined at every point in
space.
• Gives magnitude and direction of force on
test particle
e.g. wind velocity
(speed and
direction) in
different parts of
the country.
8
Superposition with Electric Fields
• At any point P, the total electric field due to a group of
source charges equals the vector sum of electric fields of
all the charges
Find the electric field due to q1, E1
Find the electric field due to q2, E2
E = E1 + E2

Remember, the fields add as vectors
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9
Question
Which vector best represents the electric
field at the red dot?
A
B
E
C
-
D
10
Electric Field Direction
• a) q is positive, F is
•
•
•
directed away from q
b) The direction of E is
also away from the
positive source charge
c) q is negative, F is
directed toward q
d) E is also toward the
negative source charge
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Relationship Between F and E
• Fe = qE
 Valid for a test charge
that does not disturb the
source charge distribution
• If q is positive, F and E are in the same direction
Qp=1.6x10-19 C
+
Electric field 1Å away
from proton
E
r=
9
2
19
9
10
N

M
/C
1.6
10
C


10
10
m
2
1x10-10
m
E
 2.9 1011 N /C
(to the right)
12
Quick Quiz
Which is the direction of the electric field at dot?
A. Left
B. Right
C. Up
Away from positive charge (right)
D. Down
E. Zero
y
+
-
x
Net E field is to right.
13
Quick Quiz
In this electric dipole, what is the direction of the
electric field at point A?
A) Up
A
B) Down
C) Left
D) Right
x=-a
+Q
x=+a
-Q
E) Zero
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Electric field: summary
• Electric field ->
will be a force on a charged particle.
• This force ( and electric field) can arise from
electric charges (via Coulomb’s law)
• But once electric field is known, don’t need
to know the charges that produce it.
15
The electric dipole
• Can all be approximated
•
by electric dipole.
Two opposite charges
magnitude q
separated by distance s
Dipole moment
Vector
p
Points from - charge to + charge
Has magnitude qs
16
Calculating dipole electric field
y
On the y-axis E  E y yˆ
E y  E   E
 kq
1
1

kq


2
2
y  s /2
y  s /2
q

s/2
2ys
 kq
2
2
y

s
/2
y

s
/2




 k 2qs

1
y3
For y  s
s

-q
x
s/2
Since p points from - charge to + charge

Ek
2p
r3
 y-axis of dipole only
on

17
Question: electric dipole
A and B are the same (large) distance from dipole.
How do the magnitude of the electric fields at A
and B compare?
A) E A  E B
A
B) E A  E B


C) E A  E B
B
D) E B  0


18
Pictorial representation of E: Electric Field Lines
19
Electric field lines
• Local electric field tangent to
•
•
•
•
field line
Density of lines proportional to
electric field strength
Fields lines can only start on +
charge
Can only end on - charge.
Electric field lines can never
cross
20
Electric field of a dipole
+
-
21
Electric field of two + charges
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Question
How are the charges A and B related?
A) A+, B-, A  B
B) A-, B+, A  B
C) A+, B-, A  B

D) A-, B+, A  B
A
B

E) A+, B-, A  B



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