My
Chapter 16
Lecture
Outline
1
Chapter 16: Electric Forces and
Fields
•Electric Charge
•Conductors & Insulators
•Coulomb’s Law
•Electric Field
•Motion of a Point Charge in a Uniform E-field
•Conductors in Electrostatic Equilibrium
•Gauss’s Law (not taught !!)
2
§16.1 Electric Charge
There are two kinds of electric charge: positive and negative.
A body is electrically neutral if the sum of all the charges in a
body is zero.
Charge is a conserved quantity.
3
The elementary unit of charge is e = 1.60210-19 C.
The charge on the electron is 1e.
The charge on the proton is +1e.
The charge on the neutron is 0e.
Experiments show that likes charges will repel each other
and unlike charges will attract each other and that the force
decreases with increasing distance between charges.
4
This body is electrically neutral.
  +
+ +
+

+ 

An object can become polarized if the charges within it can
be separated. When grounded, the sphere will be charged
by induction.
By holding a
charged rod near
the body, it can
be polarized.

+ + + + +



+
+
+
+

+
5
Example (text problem 16.4): A metallic sphere has a charge
of +4.0 nC. A negatively charged rod has a charge of 6.0
nC. When the rod touches the sphere, 8.2109 electrons are
transferred. What are the charges of the sphere and the rod
now?
Each electron has a charge 1.60210-19 C so the total
charge transferred is 1.3 nC.
The rod is left with 6.0 nC + 1.3 nC = 4.7 nC of charge
and the sphere now has +4.0 nC  1.3 nC = +2.7 nC of
charge.
6
§16.2 Conductors and Insulators
A conductor is made of material that allows electric charge to
move through it easily.
An insulator is made of material that does not allow electric
charge to move through it easily.
7
§16.3 Coulomb’s Law
The magnitude of the force
between two point charges is:
F
k q1 q2
r2
where q1 and q2 are the charges, r is the separation between
the two charges and k = 8.99109 Nm2/C2.
where k 
1
4 0
and  0  8.851012 C2 /Nm2
and 0 is called the permittivity of free space.
8
The electric force is directed between the centers of the two
point charges.
q1
F21
F12
q2
r
Repulsive force
between q1 and q2.
F21
Attractive force
between q1 and q2.
q1
q2
F12
r
The electric force is an example of a long-range or field
force, just like the force of gravity.
9
Example: What is the net force on the charge q1 due to the
other two charges? q1 = +1.2 C, q2 = 0.60 C, and q3 =
+0.20 C.
F21

F31
The net force on q1 is Fnet = F21 + F31
10
Example continued:
The magnitudes of the forces are:
F21 
k q1 q2
r212

9 10


9
Nm2 /C2 (1.2 106 C)(0.60106 C)
(1.2 m)2  (0.5 m)2
9
Nm2 /C2 (1.2 106 C)(0.20106 C)
(1.2 m)2
 3.8 103 N
F31 
k q1 q3
r312

9 10


 1.5 103 N
11
Example continued:
The components of the net force are:
Fnet, x  F31, x  F21, x  F31  F21 cos  2.0 103 N
Fnet, y  F31, y  F21, y  0  F21 sin   1.4 103 N
1.2 m
 0.92
1.3 m
0 .5 m
sin  
 0.38
1.3 m
cos 
Where from the figure
12
Example continued:
The magnitude of the net force is:
2
2
3
Fnet  Fnet
N
, x  Fnet , y  2.4 10
The direction of the net force is:
tan 
Fnet , y
Fnet , x
 0.70
  35
13
§16.4 The Electric Field
Recall :
Fg  mg
Where g is the strength of
the gravitational field.
Fe  qE
Similarly for electric forces
we can define the strength
of the electric field E.
14
For a point charge of charge Q, the
magnitude of the force per unit charge
at a distance r (the electric field) is:
Fe k Q
E
 2
q
r
The electric field at a point in space is found by adding all
of the electric fields present.
Enet   Ei
i
Be careful! The electric
field is a vector!
15
Example: Find the electric field at the point P.
P
x
q1 = +e
q2 = 2e
x=0m
x=1m
x=2m
E is a vector. What is its direction?
Place a positive test charge at the point of interest. The
direction of the electric field at the location of the test
charge is the same as the direction of the force on the
test charge.
16
Example continued:
q1 = +e
P
x
q2 = 2e
Locate the
positive test
charge here.
P
x
q1 = +e
q2 = 2e
Direction of E due
to charge 2
Direction of E due
to charge 1
17
Example continued:
The net electric field at point P is:
Enet  E1  E2
The magnitude of the electric field is:
Enet  E1  E2
18
Example continued:
E1 
k q1
E2 
k q2
r2
r2
9 10

9

9 10

9

Nm2 /C2 (1.6 1019 C)
10

3
.
6

10
N/C
2
(2 m)

Nm2 /C2 (2 *1.6 1019 C)
9

2
.
9

10
N/C
2
(1 m)
Enet  E1  E2  2.5 109 N/C
The net E-field is
directed to the left.
19
Electric field lines
Electric field lines are a useful way to indicate what the
magnitude and direction of an electric field is in space.
Rules:
1. The direction of the E-field is tangent to the field lines at
every point in space.
2. The field is strong where there are many field lines and
weak where there are few lines.
3. The field lines start on + charges and end on  charges.
4. Field lines do not cross.
20
Pictorial representation of the rules on the previous slide:
21
§16.5 Motion of a Point Charge in a
Uniform E-Field
A region of space with a uniform
electric field containing a particle
of charge q (q > 0) and mass m.
22
FBD for the
charge q
y
Fe
x
Apply Newton’s 2nd Law and
solve for the acceleration.
F
x
 Fe  m a
Fe  qE  m a
q
a E
m
One could now use the kinematic equations to solve for
distance traveled in a time interval, the velocity at the end of
a time interval, etc.
23
Example: What electric field strength is needed to keep an
electron suspended in the air?
y
FBD for the
electron:
Fe
x
w
To get an upward force on the electron, the electric field
must be directed toward the Earth.
24
Example continued:
Apply Newton’s 2nd Law:
F
y
 Fe  w  0
Fe  w
qE  eE  m g
mg
E
 5.6 1011 N/C
e
25
§16.6 Conductors in Electrostatic
Equilibrium
Conductors are easily polarized. These materials have free
electrons that are free to move around inside the material.
Any charges that are placed on a conductor will arrange
themselves in a stable distribution. This stable situation is
called electrostatic equilibrium.
26
When a conductor is in electrostatic equilibrium, the E-field
inside it is zero.
Any net charge must reside on the surface of a conductor
in electrostatic equilibrium.
27
Just outside the surface of a conductor in electrostatic
equilibrium the electric field must be perpendicular to the
surface.
If this were not true, then any surface
charge would have a net force acting
on it, and the conductor would not be
in electrostatic equilibrium.
28
Any excess charge on the
surface of a conductor will
accumulate where the
surface is highly curved
(i.e. a sharp point).
29
Summary
You need to remember:
•Properties of Conductors/Insulators
•Charge Induction
•Coulomb’s Law
•The Electric Field
•Motion of a Point Charge in an Electric Field
30