Download The Electric Field

Unit 6
Electric Forces and
Electric Fields
· Electric Charge
· Conduction and Induction
· Electric Force (Coulomb's Law)
• Electric field, shielding
1 The Origin of Electricity
The electrical nature of matter is inherent
in atomic structure.
mp  1.673 1027 kg
mn  1.675 10 27 kg
me  9.1110 31 kg
e  1.60 10 19 C
Coulombs—unit for electric charge
Electric Charge
It has been known since ancient times that when certain
materials are rubbed together, they develop an attraction for
each other. (This can be seen today when you take clothes
out of a dryer)
In ancient Greece - people noticed that when thread was
spun over a spindle of amber, the thread was attracted to
the
spindle.
The Greek word for amber was "elektron," hence this force
was called electric.
Electric Charge
In the 18th century, American Ben Franklin noticedw hen a rubber
rod is rubbed by animal fur, the rod acquires a negative charge,
and the animal fur acquires a positive charge.
When a glass rod is rubbed by silk, the rod acquires a positive
charge and the silk obtains a negative charge. Thus, two
rubber rods after being charged would repel each other, while
a rubber rod would be attracted to a glass rod.
No new charge is created - instead, it is just separated - the
positive charge acquired by one object is exactly equal in
magnitude and opposite in sign to the charge lost by the other
object.
1 The Origin of Electricity
In nature, atoms are normally
found with equal numbers of protons
and electrons, so they are electrically
neutral.
By adding or removing electrons
from matter it will acquire a net
electric charge with magnitude equal
to e times the number of electrons
added or removed, N.
q  Ne
1 The Origin of Electricity
Example 1 A Lot of Electrons
How many electrons are there in one coulomb of negative charge?
q  Ne
q
1.00 C
18
N 
 6.25 10
-19
e 1.60 10 C
The Nature of Charge
Like energy and momentum, charge is neither created nor
destroyed, it is conserved.
Opposite charges attract and like charges repel.A s a result
negatively charged electrons are attracted to the positive
nucleus.
Despite the great mass difference, the charge on an electron
is exactly equal in magnitude to the charge on a proton, and
its magnitude is denoted by "e.“
An electron is said to have a charge of -e and
a proton a charge of +e.
Measurement of Charge
The electron was discovered by J.J. Thomson in 1897, and in a
series of experiments between 1909 and 1913, Robert Millikan
and his graduate student, Harvey Fletcher, established the value
of the charge, "e," on an electron.
2. Charged Objects and the Electric Force
It is possible to transfer electric charge from one object to another.
The body that loses electrons has an excess of positive charge, while
the body that gains electrons has an excess of negative charge.
2 Charged Objects and the Electric Force
LAW OF CONSERVATION OF ELECTRIC CHARGE
During any process, the net electric charge of an isolated system remains
constant (is conserved).
2 Charged Objects and the Electric Force
Like charges repel and unlike
charges attract each other.
2 Charged Objects and the Electric Force
1. An atom in its normal (non-ionic) state has no
charge. This is due to the fact that atoms:
A have only neutrons.
B have no protons or electrons.
C have equal numbers of protons and electrons.
D have an equal number of protons and neutrons.
2. What object moves freely within the entire atom?
A Electron.
B Neutron.
C Proton.
D Nucleus.
3. An atom is composed of:
A a central nucleus that is surrounded by neutrons.
B an even distribution of electrons and protons in a spherical shape.
C a central nucleus surrounded by electrons.
D a central nucleus containing protons and electrons.
3. Conductors and Insulators
Not only can electric charge exist on an object, but it can also move
through an object.
Substances that readily conduct electric charge are called electrical
conductors.
Materials that conduct electric charge poorly are called electrical
insulators.
Solids
Solids are a form of matter whose nuclei form a fixed structure.
Nuclei, and their protons and neutrons, are "locked" into
position.
Solids are classified as either conductors, insulators or
semiconductors.
In conductors, some electrons are free to move through the
solid and are not bound to any specific atom.
In insulators, electrons are bound to their atoms, and may
move short distances, but much less than the electrons in a
conductor.
Semiconductors, depending on their situation, act as either
conductors or insulators.
4. Charging by Contact and by Induction
Charging by contact.
4. Charging by Contact and by Induction
Charging by conduction
involves conductors that
are insulated from the
ground, touching and
transferring the charge
between them. The
insulator is necessary to
prevent electrons from
leaving or entering the
spheres from Earth.
Total Charge = -4Q
(identical spheres very far apart)
Question1: If a conductor carrying a net charge of 8Q is
brought into
contact with an identical conductor with no net charge,
what will be the charge on each conductor after they are
separated?
Question2: Metal sphere A has a charge of -2Q and an
identical
metal sphere B has a charge of -4Q. If they are brought
into contact with each other and then separated, what is
the final charge on sphere B?
4 Charging by Contact and by Induction
Charging by induction.
4 Charging by Contact and by Induction
The negatively charged rod induces a slight positive surface charge
on the plastic.
Conduction Summary
Through physical contact, a charged object will transfer a
portion of its charge to a neutral object. Because of the
Conservation of Charge, the amount of charge on the initially
charged object will decrease.
For example, a positively charged object will transfer positive
charge to a neutral object, leaving it with a net positive charge.
The amount of positive charge on the initial object will
decrease.
Similarly, a negatively charged object will transfer negative
charge to a neutral object.
Induction Summary
A charged object will be brought close to a neutral object, but it will
not touch it. The neutral object will be grounded - it will have an
electrical conducting path to ground. The charged object will repel
similar charges on the neutral object to the ground.
Thus, the neutral object will be left with a charge opposite to the
initially charged object. The initial object will not lose any charge the extra charge comes from the ground. As long as the ground is
disconnected before the initial object is removed, the neutral object
will gain charge.
If the ground were left in place, once the initially charged object was
removed, the neutral object will pass its gained charge back to the
ground.
1.
Sphere A carries a net positive charge, and sphere
B is neutral. They are placed near each other on an
insulated table. Sphere B is briefly touched with a
wire that is grounded. Which statement is correct?
A Sphere B remains neutral.
B Sphere B is now positively charged.
C Sphere B is now negatively charged.
D The charge on sphere B cannot be determined
without additional information.
2.
If a positively charged rod touches a neutral conducting sphere and is
removed, what charge remains on the sphere? What happens to the
magnitude of the charge on the rod?
A The sphere becomes positive and the rod's net charge stays the
same.
B The sphere becomes positive and the rod's net charge decreases.
C The sphere becomes negative and the rod's net charge stays the
same.
D The sphere remains neutral and the rod's net charge stays the same.
Demo
Static electric charge:
https://www.youtube.com/watch?v=QxZ6AWLpnUw
Van de Graaf generator experiment:
https://www.youtube.com/watch?v=ubZuSZYVBng
5. The Electroscope
The electroscope
measures electrical charge
(both sign and magnitude).
The conductor rod is
insulated from the glass
container.
When the scope is neutral,
the leaves hang down to
due to their own mass.
Electroscopes can be charged
by conduction or induction.
A neutral electroscope will become
negatively charged when touched by
a negatively charged object.
Negative electrical charge will
distribute across the electroscope
and the gold leaves will repel, since
they have the same charge, and like
charges repel.
The bar is moved away and there is now a negative net
charge on the scope. Since negative charge moved from
the rod to the electroscope, the rod now has less negative
charge (Conservation of Charge).
1. When a negatively charged rod touches the top of a
neutral electroscope, the gold leaves separate. What is
the charge on the leaves?
A Negative
B Positive
C Neutral
2. What is the source of the charge that is moved to the gold leaves?
A The charged bar.
B The ground.
C The glass surrounding the leaves.
6. Coulomb’s Law
Electrical Force:
In the late 18th Century,
several physicists (Joseph
Priestly and John Robison)
reasoned (and Robison
measured) that the force
between two objects
followed the same principles
as the gravitational force and
that the force between two
charged objects depends on
the inverse square of the
distance between them
Charles Coulomb published a
paper (1785), based on detailed
experiments, that definitively
proved the above, and that the
force was also proportional to
the size of the charges.
He used a torsion balance
which was based on the same
principle as Henry Cavendish's
experiment that measured the
gravitational constant.
Coulomb’s Law
6 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 C 2 N  m 2 
r2
k  1 4o   8.99 109 N  m 2 C 2
Coulomb's Law is used to calculate the magnitude of the
force.
Each object exerts the same force on the other - except in
opposite directions (Newton's third law applies to all forces,
not just mechanical ones).
Since electrical force, like all forces, is a vector, you need to
specify the direction of the force magnitude determined by
Coulomb's Law.
This is done by looking at the sign of both charges
(like charges repel & opposite charges attract).
6 Coulomb’s Law
Example 3 A Model of the Hydrogen Atom
In the Bohr model of the hydrogen atom, the electron is in orbit about the
nuclear proton at a radius of 5.29x10-11m. Determine the speed of the
electron, assuming the orbit to be circular.
F k
q1 q2
r2
6 Coulomb’s Law
F k
q1 q2
r2

8.99 10
9

N  m C 1.60 10
2
2
5.29 10
11
m

19
C

2
2
 8.22 10 8 N
F  mac  mv2 r
v  Fr m 
8.22 10 N5.29 10
8
9.1110 kg
-31
11
m
  2.18 10
6
ms
Electrical Force relationship
to Gravitational Force
Both forces are expressed using a similar mathematical
formula, where the magnitude of the force decreases as
1/r 2.
Electrical force can be attractive or repulsive (like charges
repel, opposite charges attract).
Gravitational force is always attractive.
The electrical force is on the order of 1036 times stronger
than the gravitational force!
2.
A +20.0 μC point charge is located 20.0 cm away from a
-40.0 μC point charge. What is the force on each due to
the other?
3.
What is the distance between two charges +7.8 μC and
+9.2 μC if they exert a force of 4.5 mN on each other?
4.
A -4.2 μC charge exerts an attractive force of 1.8 mN
on a second charge which is a distance of 2.4 m away.
What is the magnitude and sign of the second charge?
5.
Two equal negatively charged objects repel each other with a force of
18 mN. What is the charge on each object if the distance between them
is 9 cm?
How many extra electrons are on each object?
6 Coulomb’s Law
Example 4 Three Charges on a Line
Determine the magnitude and direction of the net force on q1.
6 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  8.4 N  5.7N
 2.7 N
 8.4N
Superimposition of
Electrical Forces
Follow this procedure:
1. Assume all charges, other than the one that the initial net
force is being calculated for, are immobile - this will allow the
determination of the direction of the individual initial forces.
2. Draw a free body diagram for each charge, using the fact that
opposite charges attract and like charges repel.
3. Use Coulomb's Law to find the magnitude of each force.
4. Sum the forces, taking into account that they are vectors with
direction and magnitudes. Use the free body diagrams to assign
signs to the forces - if they point to the right, they are positive; if they
point to the left, they are negative.
7. The Electric Field
The positive charge experiences a force which is the vector sum of the
forces exerted by the charges on the rod and the two spheres.
This test charge should have a small magnitude so it doesn’t affect
the other charge.
The Electric Field
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
The Electric Field
DEFINITION OF ELECRIC FIELD
The electric field that exists at a point is the electrostatic force experienced
by a small test charge placed at that point divided by the charge itself:

 F
E
qo
SI Units of Electric Field: newton per coulomb (N/C)
7 The Electric Field
It is the surrounding charges that create the electric field at a given point.
The Electric Field
Example 7 An Electric Field Leads to a Force
The charges on the two metal spheres and the ebonite rod create an electric
field at the spot indicated. The field has a magnitude of 2.0 N/C. Determine
the force on the charges in (a) and (b)
The Electric Field




(a)
F  qo E  2.0 N C 18.0 108 C  36 108 N
(b)
F  qo E  2.0 N C 24.0 108 C  48 108 N
The Electric Field
Electric fields from different sources
add as vectors.
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
The Electric Field
F k
q qo
r2
8.99 10

E
9
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
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
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
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
4.03.0m  d   d 2
2
d  2.0 m
The Electric Field
THE PARALLEL PLATE CAPACITOR
charge density
Parallel plate
capacitor
E
q


o A o
   8.85 10 12 C 2 N  m 2 
8. Electric Field Lines
Electric field lines or lines of force provide a map of the electric field
in the space surrounding electric charges.
8. Electric Field Lines
Electric field lines are always directed away from positive charges and
toward negative charges.
8 Electric Field Lines
Electric field lines always begin on a positive charge
and end on a negative charge and do not stop in
midspace.
8 Electric Field Lines
The number of lines leaving a positive charge or entering a
negative charge is proportional to the magnitude of the charge.
8 Electric Field Lines
9 The Electric Field Inside a
Conductor: Shielding
At equilibrium under electrostatic conditions, any
excess charge resides on the surface of a conductor.
At equilibrium under electrostatic conditions, the
electric field is zero at any point within a conducting
material.
The conductor shields any charge within it from
electric fields created outside the conductor.
9 The Electric Field Inside a Conductor: Shielding
The electric field just outside the surface of a conductor is perpendicular to
the surface at equilibrium under electrostatic conditions.
9 The Electric Field Inside a Conductor: Shielding
Conceptual Example 14 A Conductor in
an Electric Field
A charge is suspended at the center of
a hollow, electrically neutral, spherical
conductor. Show that this charge induces
(a) a charge of –q on the interior surface and
(b) a charge of +q on the exterior surface of
the conductor.