Last Week

1
Last Week
This Week
Electric Force (allowed equations)

• Capacitors in Circuits (allowed Equations)

F qE E not energy
Chapter 19 (sections 1-4, 5 up to eqn 19.10 but
skip eqn 19.7, 6 and 7)
Review Chapters 2, 3, 4
2
Introduction to ElectroStatics

• Like charges repel
• two negative charges repel
• two positive charges repel

After experiments it was found that there are two
types of charge

• Positive (example protons)
• Negative (example is electrons)

F2_on_1
q1

F1_on_2
q2

• Unlike charges attract
• A positive and negative charge attract

F2_on_1
q1
_
q1

F1_on_2
q2
Notice 3rd Law Pairs
q2

3

• Like charges repel
• two negative charges repel
• two positive charges repel

• The force required no direct contact between the
  two charges
• The force got weaker as the charges got further
  apart
• The force, as shown, was directed along the
  imaginary lines connecting the two charges

F2_on_1
q1

F1_on_2
q2

All of these are summarized in Coulombs Law
F2_on_1
F2_on_1
q1
r
q1
r distance between charges
F1_on_2
F1_on_2
q2
q2
k constant
4

• The force required no direct contact between the
  two charges
• The force got weaker as the charges got further
  apart
• The force, as shown, was directed along the
  imaginary lines connecting the two charges

Correctly describes force between charged objects
that are not too big in size - Big compared to
what? Big compared to the separation distance,
r
All of these are summarized in Coulombs Law
F2_on_1
q1
r
r distance between charges
F1_on_2
q2
k constant
5
The force between two equal charges is F.
F
F
What is the force on q1 from q2 if q2 triples?
q2
3q

• F
• 3F
• F/3
• 9F

6
The force between two equal charges is F.
F
F
What is the force on q2 from q1 if q2 triples?
q2
3q

• F
• 3F
• F/3
• 9F

7
Measure electric force on an object free to swing
How could we test that this equation is correct?
Or more importantly, how could we discover
Coulombs Law ourself? Devise an experiment
q
Which is the free body diagram of the object when
it comes to rest?
c
b
d
a
g
h
f
e
i
j
8
Which is the free body diagram of the object when
it comes to rest?
c
b
d
a

• a
• b
• c
• d
• e
• f
• g
• h
• i
• j

f
e
g
h
T
Fe
i
j
W
9
Hold the rod at different distances from the
object of known weight and record the angle of
the string.
q
Solve for the electric force as a function the
angle of the string when the everything else is
keep constant.
Sum of forces in x direction
T sin q Fe 0
Sum of forces in y direction

• Everything else is?
• Weight of the object
• Charge of the object
• Charge of the other object

T cos q W 0
Target Fe as a function of q with W known
Approach
Need to eliminate T from the equations
Choose a horizontal and vertical coordinate system
T cos q W 0
T cos q W
T W/ cos q
Put into the other equation
ay 0
ax 0
10
W sin q / cos q Fe 0
W sin q / cos q Fe
W tan q Fe
Fe measured for different distance between the
charged objects.
Sum of forces in x direction
T sin q Fe 0
Sum of forces in y direction
T cos q W 0
Target Fe as a function of q with W known
Need to eliminate T from the equations
T cos q W 0
T cos q W
T W/ cos q
Put into the other equation
Fe k (1/r2)
11
You are working in a research laboratory
investigating the solubility of polymers that can
deliver drugs to specific cancer sites in the
body. Although the polymers are neutral, they
can have a charge separation such that one end is
more positive and the other is more negative. To
check the computer model used to predict the
behavior of the polymer near a cell membrane, you
have been asked to calculate the force on a
sodium ion that approaches the polymer on a line
perpendicular to its axis and midway between its
ends. Your result should be a function of the
properties of the polymer, the properties of the
sodium ion, and the distance of the sodium ion
from the center of the molecule.
L/2
L/2
Relevant properties of the polymer Length
L Charge q
Relevant properties of the sodium ion Charge
Q Mass m
Question Calculate the force on the ion as a
function of the length of the polymer, the charge
of the end of the polymer, the charge of the ion,
and the mass of the ion.
12
Approach Calculate the electric force on the ion
from each end of the polymer.
Since force is a vector, need components.
L/2
L/2
Q
?
Relevant properties of the polymer Length
L Charge q

?
?
r
d
qA
qB
?
?
-

L/2
L/2
B
A
Relevant properties of the sodium ion Charge
Q Mass m
y
?
x
?
Question Calculate the force on the ion as a
function of the length of the polymer, the charge
of the end of the polymer, the charge of the ion,
and the mass of the ion.
Fx FAx FBx
13
Approach Calculate the electric force on the ion
from each end of the polymer.
Fy FAy - FBy
Fy 0
Since force is a vector, need components.
Net Result
?
?
?
No done yet. r and q are not known.
r
From the triangle
?
?
B
A
?
r2 d2 (L/2)2
?
r (d2 (L/2)2)1/2
Fx FAx FBx
14
Fy FAy - FBy
Evaluate
Check units
This is the correct units for force since
Fy 0
Net Result
It is reasonable that the net force is horizontal
since the vertical components caused by the ends
of the dipole are in opposite directions and
cancel.
No done yet. r and q are not known.
From the triangle
The force increases as either the charge at the
end of the polymer increases or the ion charge
increases. This is not unreasonable since the
strength of the electric force depends on the
charge.
r2 d2 (L/2)2
r (d2 (L/2)2)1/2
As the distance of the ion from the molecule gets
larger than the molecule length, the force goes
to zero more rapidly than 1/r2. This is not
unreasonable since in that case, the charge
separation is small and the electric force of a
neutral object is 0.
15
Four positive charges q sit in a plane at the
corners of a square whose sides have a length d.
A negative charge, -q, is placed in the middle of
the square. What is the magnitude of the force
on the negative charge?
q
q
q
q
16
Four positive charges q sit in a plane at the
corners of a square whose sides have a length d.
A negative charge, -q, is placed in the middle of
the square. What is the magnitude of the force
on the negative charge?

• a
• b
• c
• d
• e

17
Notice something interesting going on here in the
force equations
It is not a coincidence. And it means that
whatever Q I put in the position near the polymer
say for example, qs, then qA and qB are going to
create a force on that charge. That force is the
charge qs multiplied by that stuff in
paranthesis. Interesting. So, we give that
stuff in paranthesis a special name. We call it
a field. We call it, to be more precise, the
electric field created by qA and qB
In each case, a Q can be factored out so we
have
So, it can be written
F qE
If we know the electric field, E, and we put a
charge in that field, q, then it will get a force
F qE on it
What does that mean? Is it a coincidence?
Well discuss this more later
18
Another Example
It is not a coincidence. And it means that
whatever Q I put in the position near the polymer
say for example, qs, then qA and qB are going to
create a force on that charge. That force is the
charge qs multiplied by that stuff in
paranthesis. Interesting. So, we give that
stuff in paranthesis a special name. We call it
a field. We call it, to be more precise, the
electric field created by qA and qB
An electron is injected into a electron
microscope such that its path crosses directly
between two spherical electrodes of radius 1.0
cm. At the point that the electron crosses
directly between the two electrodes, it is 1.0 m
from one of the electrodes. What is the
acceleration of that electron at that point? The
electrodes each have a charge of 100
microcoulombs and are 1.5 m apart. The mass of
the electron is 9.1x10-31 kg and its charge is
1.6x10-19C. The constant for the electric force,
k, is 9 x 10 9 N m2/C 2
So, it can be written
F qE
If we know the electric field, E, and we put a
charge in that field, q, then it will get a force
F qE on it
Well discuss this more later
19
A and B are conductors, initially uncharged, and
touching.
20
What is the charge of B?
A
B
A
B



2
1
A
B
3

• -
• 0

21
A and B are conductors, initially uncharged, and
touching.
22
What is the charge of B?
A
B
A
B






2
1
A
B
3

• -
• 0