From Last Time…
Forces between
charges
Electric dipole
1
Exam 1
Wed. Feb. 20, 5:30-7 pm
Covers Chap. 21.5-7, 22-23,25-26
+ lecture, lab, discussion, HW
8 1/2 x 11 handwritten note sheet (both sides) allowed
Students with schedule class conflicts:
stay after lecture today to arrange time
Review Group/Quiz (solutions on website).
Review lab question sheets.
Review sample exams on website.
HW4 (due Fri. next week)
covers exam material.
2
From Last Time…
Forces between
charges
Electric dipole
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/unit charge
Units? N/C

6
+
Question
Which vector best represents the electric
field at the red dot?
A
B
E
C
-
D
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
Relationship Between F and E
• Fe = qE
 This is valid for a test charge small
enough that it does not disturb the
source charge distribution
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
• 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)
9
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
10
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

11
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.
12
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
13
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.
14
Calculating dipole electric field
y
On the y-axis
E  E y yˆ
E y  E   E
 kq
 kq

1
1

kq


2
2
y

s
/2
y

s
/2




+ s/2
2ys
2
2
y  s /2 y  s /2
1
 k 2qs 3
y
For y  s

x
- s/2
Since p points from - charge to + charge

Ek
2p
r3
on y-axis of dipole only

15
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


16
Pictorial representation of E: Electric Field Lines
17
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
18
Point particles
19
Electric field of a dipole
+
-
20
Electric field of two + charges
21
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



22
Hydrogen Atom Example
• The magnitude of the electric force between the electron and
•
proton:
 Fe = ke|e| |-e| / r2 = 8.2 x 10-8 N, r ~ 0.53 x 10-10 m
The gravitational force between the electron and the proton
 Fg = Gmemp / r2 = 3.6 x 10-47 N
me = 9.11 x 10-31 kg, mp = 1.67 x 10-27 kg
G = 6.67 x 10-11 N m2/kg2
Fe/Fg ~ 2 x 1039
Mp=1.67x10-27 kg
Me = 9.11 x10-31 kg
+
r = 0.53x10-10 m
23