Transcript Chapter 15

Chapter 16
Electric Forces and
Electric Fields
Fundamental Forces of Nature
A Bit of History
• Ancient Greeks
– Observed electric and magnetic phenomena as
early as 700 BC
• Found that amber, when rubbed, became electrified
and attracted pieces of straw or feathers
• Magnetic forces were discovered by observing
magnetite attracting iron
A Bit More History
• William Gilbert
– 1600
– Found that electrification was not limited to
amber
• Charles Coulomb
– 1785
– Confirmed the inverse square relationship of
electrical forces
History Final
• Hans Oersted
– 1820
– Compass needle deflects when placed near an electrical current
• Michael Faraday
– A wire moved near a magnet, an electric current is observed in the
wire
• James Clerk Maxwell
– 1865-1873
– Formulated the laws of electromagnetism
• Hertz
– Verified Maxwell’s equations
Properties of Electric Charges
• Two types of charges exist
– They are called positive and negative
– Named by Benjamin Franklin
• Like charges repel and unlike charges attract one
another
• Nature’s basic carrier of positive charge is the proton
– Protons do not move from one material to another
because they are held firmly in the nucleus
More Properties of Charge
• Nature’s basic carrier of negative charge is the
electron
– Gaining or losing electrons is how an object
becomes charged
• Electric charge is always conserved
– Charge is not created, only exchanged
– Objects become charged because negative charge
is transferred from one object to another
Properties of Charge, final
• Charge is quantized
– All charge is a multiple of a fundamental unit of
charge, symbolized by e
• Quarks are the exception
– Electrons have a charge of –e
– Protons have a charge of +e
– The SI unit of charge is the Coulomb (C)
• e = 1.6 x 10-19 C
Conductors
• Conductors are materials in which the
electric charges move freely
– Copper, iron, aluminum and silver are good
conductors (metals)
– When a conductor is charged in a small region,
the charge readily distributes itself over the
entire surface of the material
Insulators
• Insulators are materials in which electric
charges do not move freely
– Glass and rubber are examples of insulators
– When insulators are charged by rubbing, only the
rubbed area becomes charged
• There is no tendency for the charge to move into other
regions of the material
Charging by Conduction
• A charged object (the rod) is
placed in contact with another
object (the sphere)
• Some electrons on the rod can
move to the sphere
• When the rod is removed, the
sphere is left with a charge
• The object being charged is
always left with a charge having
the same sign as the object
doing the charging
Charging by Induction
• When an object is connected to
a conducting wire or pipe
buried in the earth, it is said to
be grounded
• A negatively charged rubber
rod is brought near an
uncharged sphere
• The charges in the sphere are
redistributed
– Some of the electrons in the
sphere are repelled from the
electrons in the rod
Coulomb’s Law
• Mathematically,
q1 q2
F  ke
r2
• ke is called the Coulomb Constant
– ke = 8.99 x 109 N m2/C2
• Typical charges can be in the µC range
– Remember, Coulombs must be used in the equation
• Remember that force is a vector quantity
Coulomb’s Law F  k
q1 q2
e
r
2
• Coulomb showed that an electrical force has the
following properties:
– It is inversely proportional to the square of the
separation between the two particles and is along the
line joining them
– It is proportional to the product of the magnitudes of
the charges q1 and q2 on the two particles
– It is attractive if the charges are of opposite signs and
repulsive if the charges have the same signs
Vector Nature of Electric Forces
• Two point charges are
separated by a distance r
• The like charges produce a
repulsive force between them
• The force on q1 is equal in
magnitude and opposite in
direction to the force on q2
Vector Nature of Forces, cont.
• Two point charges are
separated by a distance r
• The unlike charges
produce a attractive force
between them
• The force on q1 is equal in
magnitude and opposite
in direction to the force
on q2
Electrical Forces are Field Forces
• This is the second example of a field force
– Gravity was the first
• Remember, with a field force, the force is exerted by
one object on another object even though there is
no physical contact between them
• There are some important differences between
electrical and gravitational forces
Electrical Force Compared to
Gravitational Force
• Both are inverse square laws
• The mathematical form of both laws is the
same
• Electrical forces can be either attractive or
repulsive
• Gravitational forces are always attractive
18.5 Coulomb’s Law
COULOMB’S LAW
The magnitude of the electrostatic force exerted by one point charge
on another point charge is directly proportional to the magnitude of the
charges and inversely proportional to the square of the distance between
them.
F k
q1 q2
  8.851012 C2 N  m2 
r2
k  1 4o   8.99109 N  m2 C2
18.5 Coulomb’s Law
Example 4 Three Charges on a Line
Determine the magnitude and direction of the net force on q1.
18.5 Coulomb’s Law
F12  k
F13  k
q1 q2
r
2
q1 q3
r
2
8.9910

9
8.9910







N  m 2 C2 3.0 106 C 4.0 106 C
0.20m2
9
N  m 2 C2 3.0 106 C 7.0 106 C
0.15m2
 

F  F12  F13  2.7 N  8.4N  5.7N
 2.7 N
 8.4 N
Superposition Principle Example
• The force exerted by
q1 on q3 is F13
• The force exerted by
q2 on q3 is F23
• The total force exerted
on q3 is the vector
sum of F13 and F23
Electrical Field
• Maxwell developed an approach to discussing
fields
• An electric field is said to exist in the region of
space around a charged object
– When another charged object enters this electric
field, the field exerts a force on the second
charged object
Direction of Electric Field
• The electric field
produced by a
negative charge is
directed toward the
charge
– A positive test charge
would be attracted to
the negative source
charge
Electric Field, cont.
• A charged particle,
with charge Q,
produces an electric
field in the region of
space around it
• A small test charge,
qo, placed in the field,
will experience a force
See example 15.4 & 5
Electric Field
F  ke
q1 q2
r2
• Mathematical Definition,
F k eQ
E
 2
qo
r
• The electric field is a vector quantity
• The direction of the field is defined to be the
direction of the electric force that would be
exerted on a small positive test charge placed
at that point
Example 6 A Test Charge
The positive test charge has a magnitude of
3.0x10-8C and experiences a force of 6.0x10-8N.
(a) Find the force per coulomb that the test charge
experiences.
(b) Predict the force that a charge of +12x10-8C
would experience if it replaced the test charge.
(a)
(b)
F 6.0 108 N

 2.0 N C
8
qo 3.0 10 C


F  2.0 N C 12.0 108 C  24108 N
18.6 The Electric Field
Example 10 The Electric Field of a Point
Charge
The isolated point charge of q=+15μC is
in a vacuum. The test charge is 0.20m
to the right and has a charge qo=+15μC.
Determine the electric field at point P.

 F
E
qo
F k
q1 q2
r2
18.6 The Electric Field
F k
q qo
r2
8.9910

9
E


N  m 2 C 2 0.80106 C 15106 C
0.20m 2
F
2.7 N

 3.4 106 N C
-6
qo 0.8010 C

 2.7 N
18.6 The Electric Field
q qo 1
F
E
k 2
qo
r qo
The electric field does not depend on the test charge.
Point charge q:
Ek
q
r2
18.6 The Electric Field
Example 11 The Electric Fields from Separate Charges May Cancel
Two positive point charges, q1=+16μC and q2=+4.0μC are separated in a
vacuum by a distance of 3.0m. Find the spot on the line between the charges
where the net electric field is zero.
Ek
q
r2
18.6 The Electric Field
Ek
q
r2
E1  E 2


1610 C
4.0 10 C
k
k
6
d2
6
3.0m  d 
2
2
2


2.0 3.0m  d  d
d  2.0 m
Electric Field Line Patterns
• Point charge
• The lines radiate
equally in all
directions
• For a positive source
charge, the lines will
radiate outward
Electric Field Lines, cont.
• The field lines are related to the field as
follows:
– The electric field vector, E, is tangent to the
electric field lines at each point
– The number of lines per unit area through a
surface perpendicular to the lines is proportional
to the strength of the electric field in a given
region
Electric Field Line Patterns
• For a negative source
charge, the lines will
point inward
Electric Field Line Patterns
• An electric dipole
consists of two equal
and opposite charges
• The high density of
lines between the
charges indicates the
strong electric field in
this region
Electric Field Line Patterns
• Two equal but like point
charges
• At a great distance from the
charges, the field would be
approximately that of a single
charge of 2q
• The bulging out of the field
lines between the charges
indicates the repulsion
between the charges
• The low field lines between the
charges indicates a weak field
in this region
Electric Field Patterns
• Unequal and unlike
charges
• Note that two lines
leave the +2q charge
for each line that
terminates on -q
Property 4
• On an irregularly
shaped conductor, the
charge accumulates at
locations where the
radius of curvature of
the surface is smallest
(that is, at sharp
points)
Rules for Drawing Electric Field Lines
• The lines for a group of charges must begin on
positive charges and end on negative charges
– In the case of an excess of charge, some lines will
begin or end infinitely far away
• The number of lines reflects the magnitude of
the charge
• No two field lines can cross each other
Electric Field in a Conductor
Four Properties
1. The electric field is zero everywhere inside the
conducting material
2. Any excess charge on an isolated conductor
resides entirely on its surface
3. The electric field just outside a charged conductor
is perpendicular to the conductor’s surface
Van de Graaff
Generator
• An electrostatic generator
designed and built by
Robert J. Van de Graaff in
1929
• Charge is transferred to
the dome by means of a
rotating belt
• Eventually an electrostatic
discharge takes place
F
E
q
2300 N/C
Find the charge
on the ball if the
system is at
equilibrium.
1m
Fig. P15.50, p. 494
Electric Flux—
A measure of E field density
• Field lines penetrating an
area A perpendicular to the
field
• The product of EA is the flux,
Φ
• In general:
– ΦE = E A cos θ
– A is perpendicular to E
θ
Example: Find the electric flux through a 0.2m2 area
where θ=20 deg, and the electric field is 30N/C.
Gauss’s Law
Electric Field of a Charged Thin Spherical Shell
• The calculation of electric flux through a surface
ΦE = E A cos θ =keq (4r2) = 4keq = q
r2
εo
Where:
εo = 1/4ke
εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2
Gauss’ Law
• Gauss’ Law states that the electric flux through any
closed surface is equal to the net charge Q inside the
surface divided by εo
Q
E 
o
– εo is the permittivity
of free space and equals 8.85 x 10-12
C2/Nm2
– The area in Φ is an imaginary surface that the electric field
permeates. It does not have to coincide with the surface of
a physical object
Chapter 16 Summary
F  ke
q1 q2
r2
F k eQ
E
 2
qo
r
ke is called the Coulomb Constant
ke = 8.99 x 109 N m2/C2
Units: N/C
ΦE = E A
Units: Nm2/C A is perpendicular to E
Q
E 
o
εo is the permittivity of free
space and equals 8.85 x 10-12
C2/Nm2
Electric Field of a Nonconducting Plane
Sheet of Charge
• Use a cylindrical Gaussian
surface
• The flux through the ends
is EA, there is no field
through the curved part
of the surface
• The total charge is Q = σA

E
2 o field is uniform
• Note, the
Direction of Electric Field, cont
• The electric field
produced by a positive
charge is directed
away from the charge
– A positive test charge
would be repelled
from the positive
source charge