Chapter
15 Electric Forces and Electric Fields
15.1 Properties of Electric
Charges
It is
possible to transfer electric charge from one object to another by rubbing. (Static Electricity)
Electric charge
is an intrinsic property of proton and electrons, only two types of charge have
been discovered, positive and negative.
I will use
a symbol q for a charge. The unit of charge q, [q], is C (coulomb).
The
electron carries charge -e and the
proton carries charge +e.
e = 1.60 x 10-19 C
The charge on an electron or a proton (e) is the smallest amount of free charge that has been discovered
(quantized). Thus, any charge of
magnitude of q is an integer multiple
of e; q = Ne.
Properties of Electric
Charges
1. Unlike charges
attract one another and like charges repel one another.
2. Electric charge
is always conserved.
3. Charge is
quantized that is, it exists in discrete packets that are integral multiples
of the electronic charge.
4. The force between
charged particles varies as the inverse square of their separation.
15.2 Insulators and
Conductors
Substances
(materials) that readily conduct electric charge are called electrical conductors.
(Metals such as copper, aluminum, silver, and gold)
Materials
that conduct electric charge poorly are known as electric insulators.
(Dielectrics such as rubber, plastic, and wood)
The
difference between electrical conductors and insulators is related to atomic
structure.
<Charging by Conduction (by touching)>
The object
being charged in this process is always left with a charge having the same sign
as the object doing the charging (Figure 15.3).
<Charging by Inducting (without touching)>
When a
conductor is connected to Earth by means of a conducting wire, it is said to be
grounded.
Figure
15.4
15.3 Coulombs Law
Coulomb's Law
The magnitude F of the electrostatic force exerted by one point charge on another
point charge is directly proportional to the magnitudes q1 and q2
of the charges and inversely proportional to the square of the distance r between them
F = (15.1)
where ke
is a proportionality constant called the Coulomb constant (ke = 8.99 x 109 Nm2/C2). The electrostatic force is directed along
the line joining the charges, and it is attractive if the charges have unlike signs and
repulsive if the charges have like signs.
The unit
of F, [F], is N (newton).
Examples
<The Superposition Principle>
It is
convenient to deal with a three-charges problem in parts.
First,
find the magnitude and direction of the force exerted on q1 by q2
(12).
Second,
find the magnitude and direction of the force exerted on q1 by q3
(13).
The net
force on q1 is the vector sum of these forces.
Examples
15.4 The Electric Field
Similar to
Gravitational force, the electrostatic force (Coulomb force) is capable of
acting through space, producing an effect even when there is no physical
contact between the objects involved.
Since no physical contact is required for the electrostatic interaction,
we assume that there exists an electric field around a charged object. When another charged object enters this
electric field, forces of an electrical nature arise.
Definition of the Electric Field
The strength of the electric field is
defined as the electrostatic force experienced by a small test charge qo placed at that point
divided by the charge itself.
|| || /| qo| (15.4)
The electric field is a vector, and its
direction is the same as the direction of the force on a positive test charge.
The unit of is N/C (newton per
coulomb).
<Point Charges>
The
magnitude of the electric field produced by a point charge q is
E = ke (15.5)
At a
particular point in space, each of the surrounding charges contributes to the
net electric field that exists there.
To determine the net field, it is necessary to obtain the various
contributions separately and then find the vector sum
of them all.
Examples
15.5 Electric Field Lines
A
convenient aid for visualizing electric field patterns is to draw lines
pointing in the direction of the electric field vector at any point. (Electric field lines)
1.
The
electric field vector, , is tangent to the electric
field line at each point.
2.
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.
The rules
for drawing electric field lines:
1.
The
lines must begin on positive charges (or at infinity) and must terminate on
negative charges or, in the case of an excess of charge, at infinity.
2.
The
number of lines drawn leaving a positive charge or approaching a negative
charge is proportional to the magnitude of the charge.
3.
No two field lines can cross each other.
See
Figures 15.13, 14, 15, and 16.
Example
15.6 Conductors in Electrostatic Equilibrium
Properties of an isolated conductor
1. The electric
field is zero everywhere inside the conductor.
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 conductors
surface.
4. On an irregularly
shaped conductor, the charge tends to accumulate at locations where the radius
of curvature of the surface is smallest that is at sharp points.
Figure
15.20
Example
15.7 The Millikan Oil-Drop Experiment (Reading
Assignment)
15.8 The Van De Graaff Generator (Reading
Assignment)
15.9 The Oscilloscope (Reading Assignment)
Figure
15.24
15.10 Electric Flux and Gausss Law (Reading
Assignment)
The electric flux, FE, is the total electric
field line (E) passing through a
surface with an area A; FE = EA. It is an important
concept in physics.
Figure
15.26