Transcript 15ElectricForcesFiel..

ELECTRIC
FORCES
AND
ELECTRIC
FIELDS
Classwork problems
Coulomb’s law
1,3,8,9,10,11,13
Electric Fields
19,21,23,25,27-29
Field Lines 30,32-35
Van deGraff 36,39
Gauss’s law 41,45,47
Physics II, Pg 1
OBJECTIVES
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After studying the material of this chapter, the student
should be able to:
1. State from memory the magnitude and sign of the
charge on an electron and proton and also state the
mass of each particle.
2. Apply Coulomb's law to determine the magnitude of
the electrical force between point charges separated
by a distance r and state whether the force will be one
of attraction or repulsion.
3. State from memory the law of conservation of
charge.
4. Distinguish between an insulator, a conductor and a
semi-conductor and give examples of each.
Physics II, Pg 2
OBJECTIVES
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5. Explain the concept of electric field and determine the
resultant electric field at a point some distance from two
or more point charges.
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6. Determine the magnitude and direction of the electric
force on a charged particle placed in an electric field.
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7. Sketch the electric field pattern in the region between
charged objects.
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8. Use Gauss's law to determine the magnitude of the
electric field in problems where static electric charge is
distributed on a surface which is simple and
symmetrical. (Not at this time!)
Physics II, Pg 3
KEY TERMS AND PHRASES
static electricity
conductor
electric charge
semiconductor
positive charge
induced charge
negative charge
charging by contact
law of conservation of charge
Coulomb's law
electron
dielectric(no)
proton
dielectric constant(no)
e
permittivity of free space(no)
neutron
electric field
insulator
electric field pattern
lines of force
Physics II, Pg 4
CONCEPTS AND EQUATIONS
ELECTRIC CHARGE
 There are two types of ELECTRIC CHARGE, arbitrarily called
POSITIVE and NEGATIVE
 Rubbing certain electrically neutral objects together (e.g., a glass
rod and a silk cloth) tends to cause the electric charges to separate.
In the case of the glass and silk, the glass rod loses negative
charge and becomes positively charged while the silk cloth gains
negative charge and therefore becomes negatively charged. After
separation, the negative charges and positive charges are found to
attract one another.
Physics II, Pg 5
ELECTRIC CHARGE
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If the glass rod is suspended from a string and a second
positively charged glass rod is brought near, a force of
electrical repulsion results. Negatively charged objects
also exert a repulsive force on one another. These results
can be summarized as follows: UNLIKE CHARGES
ATTRACT, LIKE CHARGES REPEL
Physics II, Pg 6
CONSERVATION OF ELECTRIC CHARGE
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In the process of rubbing two solid
objects together, electrical charges
are NOT created. Instead, both
objects contain both positive and
negative charges. During the
rubbing process, the negative charge
is transferred from one object to the
other and this leaves one object with
an excess of positive charge and
the other with an excess of negative
charge. The quantity of excess
charge on each object is exactly the
same.
Physics II, Pg 7
CONSERVATION OF ELECTRIC CHARGE
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This is summarized by the LAW OF
CONSERVATION OF ELECTRIC CHARGE: the
net amount of electric charge produced in any
process is zero. Another way of saying this is that
in any process electric charge CANNOT be created
or destroyed, however, it can be transferred from one
object to another.
Physics II, Pg 8
Subatomic Particles
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During the past century, the negative charges have been
shown to be carried by particles which are now called
ELECTRONS while the positive charge carriers are known
as PROTONS.
The SI unit of charge is the coulomb (C). The amount of
charge transferred when objects like glass or silk are rubbed
together is in the order of microcoulombs ( C).
1 C = 6.25 x 1018 electrons or protons and I C = 10-6 C.The
charge carried by the electron is represented by the symbol -e,
and the charge carried by the proton is +e. e = 1.6 x 10-19
coulomb
The mass of an electron is 9. II X 10-31 kg while mass of a
proton is 1.672 x10-27 kg.
A third particle, which carries no electrical charge, is the
NEUTRON. The neutron has a mass of 1.675 x 10-27 kg.
Physics II, Pg 9
Experiments performed early in this century have led
to the conclusion that protons and neutrons
are confined to the nucleus of the atom while
the electrons exist outside of the nucleus.
When solids
are rubbed together, it is the electrons which are
transferred from one object to the other.
The positive
charges, which are located in the nucleus, do not
move.
You may encounter discrepancies to this theory.
Physics II, Pg 10
INSULATORS, SEMICONDUCTORS AND
CONDUCTORS
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An INSULATOR is a material in which the electrons are
tightly held by the nucleus and are not free to move
through the material. There is no such thing as a perfect
insulator, however, examples of good insulators include
substances such as glass, rubber, plastic and dry wood.
Physics II, Pg 11
INSULATORS, SEMICONDUCTORS AND
CONDUCTORS
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A CONDUCTOR is a material through which electrons are
free to move through the material. Just as in the case of the
insulators, there is no such thing as a perfect conductor.
Examples of good conductors include metals, such as
silver, copper, gold and mercury.
Physics II, Pg 12
INSULATORS, SEMICONDUCTORS AND
CONDUCTORS
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A few materials, such as silicon, germanium and carbon,
are called SEMICONDUCTORS. At ordinary
temperatures, there are a few free electrons and the
material is a poor conductor of electricity. As the
temperature rises, electrons break free and move through
the material. As a result, the ability of a semiconducting
material to conduct improves with temperature.
Physics II, Pg 13
CHARGING BY INDUCTION
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If a negatively charged rod is brought near an uncharged
electrical conductor the negative charges in the conductor
travel to the far end of the conductor (see diagram).
Physics II, Pg 14
CHARGING BY INDUCTION
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The positive charges are not free to move and a charge is
temporarily INDUCED at the two ends of the conductor.
Overall, the conductor is still electrically neutral and if the
rod is removed a re-distribution of the negative charge
would occur.
Physics II, Pg 15
CHARGING BY INDUCTION
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If the metal conductor is touched by a person's finger or a
wire connected to ground, it is said to be "grounded" . The
negative charges would flow from the conductor to ground.
If the ground is removed and then the rod is removed, a
permanent positive charge would be left on the conductor.
The electrons would move until the excess positive charge
was uniformly distributed over the conductor.
Physics II, Pg 16
CHARGING BY CONTACT
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If the rod touches the metal conductor, some of the
negative charges on the rod transfer to the metal. This
charge distributes uniformly over the metal. The metal has
been charged by CONTACT and a permanent charge
remains when the rod is removed.
Physics II, Pg 17
Coulomb’s Law
Physics II, Pg 18
COULOMB'S LAW
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COULOMB'S LAW states that two point charges exert a
force (F) on one another that is directly proportional to the
product of the magnitudes of the charges (Q) and inversely
proportional to the square of the distance (r) between their
centers. The formula relating the force to the charges and
the distance is
Physics II, Pg 19
COULOMB'S LAW
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In the case of objects in which the electric charge is
distributed in such a way that they can be considered to act
like "point" charges, e.g., small metal spheres with uniform
charge distribution,the distance r is measured from the
center of one object to the center of the second object.The
value of k given above is for two point charges separated
by a distance (r) in a vacuum and to a good approximation
dry air. The constant may also be expressed in terms of
the permittivity of free space
Physics II, Pg 20
COULOMB'S LAW
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The proportionality constant (k) can only be used if the
medium which separates the charges is a vacuum. If the
region between the point charges is not a vacuum then the
value of the proportionality constant to be used is
determined by dividing k by the DIELECTRIC CONSTANT
(K). For a vacuum (& dry air) K = 1, for distilled water K =
80, and for wax paper K = 2.25 and
You can ignore the BIG K for 99.99% of your problems
Physics II, Pg 21
Solving Problems involving Coulomb’s Law
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The following is an outline of the steps to be followed in
attempting to solve the type of problems found in this
chapter.
For problems involving Coulomb's law:
1. Complete a data table listing the charge on each
object and the distance between the objects. If more than
two charged objects are given, draw a diagram showing the
position of each object.
2. If the objects touch then charge transfer occurs and
the law of conservation of charge must be applied to
determine the charge on each object.
3. If more than two charges are given it may be
necessary to use the methods of vector algebra discussed
in Chapter 2 to solve the problem.
4. Apply Coulomb's law and solve the problem.
Physics II, Pg 22
ELECTRIC FIELD
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If an electric charge experiences an electric force at a particular
point in space, it is in the presence of an ELECTRIC FIELD. The
magnitude of the electric field (E) at any point in space can be
determined by the ratio of the force (F) exerted on a test charge
placed at the point to the magnitude of the charge on the test
particle (q).
E = F/q The units of electric field are Newton/coulomb
Physics II, Pg 23
Gravity and Electric Fields
g=F/m
E=F/q
Physics II, Pg 24
Gravity and Electric Fields
F=GMm/r2 g=F/m g= GM/r2
F=kQq/r2 E=F/q E=kQ/r2
Physics II, Pg 25
ELECTRIC FIELD
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Electric field is a vector quantity, the direction of the vector
is in the same direction as the direction of the force vector if
the test charge is positive, and directed opposite from the
force vector if the test charge is negative. For a single
point charge (Q) the electric field a distance (r) from the
charge is given by E = k Q/r2
Physics II, Pg 26
Electric Field Lines
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In order to visualize the path taken by a charged particle
placed in an electric field, ELECTRIC FIELD LINES, also
known as LINES OF FORCE, are drawn. The following
diagrams represent the electric field patterns for certain
arrangements of charge.
Physics II, Pg 27
Rules For drawing Electric Field Lines
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The lines must begin on positive charges and terminate on
negative charges, or at infinity in the case of excess charge
The number of lines drawn leaving a positive charge or
approaching a negative charge is proportional to the magnitude of
the charge.
No two field lines can cross
Physics II, Pg 28
Electric Field for two equal and opposite point
charges
Physics II, Pg 29
Electric Field for two positive charges
Physics II, Pg 30
Electric Field for two unequal and opposite charges
Physics II, Pg 31
Electric Field Lines
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Since a POSITIVE TEST CHARGE is arbitrarily chosen to
analyze the field, electric field lines are drawn away from
an object with the excess of positive charge and toward an
object with an excess of negative charge. In diagrams c, d
and e the electric field lines start on the positive charge and
terminate on the negative charge.
Physics II, Pg 32
Electric Field Lines
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The electric field is strongest in regions where the lines are
close together and weak where the lines are further apart.
Thus, in diagrams (a) and (b), the field is strongest close to
the point charges.
Physics II, Pg 33
Electric Field Lines
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In diagram (c) the field weakens as the lines diverge as
they leave the positive charge and strengthens as the lines
converge on the negative charge. In diagram (e), two
parallel plates of opposite charge produce an electric field
where the lines are parallel near the center of the plates. In
this region the electric field is uniform and E is constant in
magnitude and directions start on the positive charge and
terminate on the negative charge.
Physics II, Pg 34
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Coulomb's law can be used to predict that the electric field inside a
closed conductor is zero. An example of a closed conductor is a
hollow metal sphere which contains an excess of static electric
charge. The charge on the conductor tends to reside on its outer
surface. Inside the conductor, the electric field is zero. Outside the
conductor, the electric field is not zero and the electric field lines
are drawn perpendicular to the surface.
Physics II, Pg 35