Electrostatics
Electrostatics, as the name implies, is the study of
stationary electric charges. A rod of plastic rubbed
with fur or a rod of glass rubbed with silk will
attract small pieces of paper and is said to be
electrically charged. The charge on plastic rubbed
with fur is defined as negative , and the charge on
glass rubbed with silk is defined as positive .
Electric charge
Electrically charged objects have several important
characteristics:
Like charges repel one another; that is, positive
repels positive and negative repels negative.
Unlike charges attract each another; that is,
positive attracts negative.
Charge is conserved. A neutral object has no net
charge. If the plastic rod and fur are initially
neutral, when the rod becomes charged by the
fur, a negative charge is transferred from the fur
to the rod. The net negative charge on the rod is
equal to the net positive charge on the fur.
A conductor is a material through which electric
charges can easily flow. An insulator is a material
through which electric charges do not move easily,
if at all. An electroscope is a simple device used to
indicate the existence of charge. As shown in Figure
1, the electroscope consists of a conducting knob
and attached lightweight conducting leaves—
commonly made of gold foil or aluminum foil.
When a charged object touches the knob, the like
charges repel and force the leaves apart. The
electroscope will indicate the presence of charge
but does not directly indicate whether the charge is
positive or negative.
Figure 1
An electroscope reports the presence of charge.
A large charge near a neutral electroscope can
make the leaves move apart. The electroscope is
made of conducting material, so the positive
charges are attracted to the knob by the nearby (but
not touching) negatively charged rod. The leaves
are left with a negative charge and therefore deflect.
When the negative rod is removed, the leaves will
fall.
Now, consider touching the electroscope knob with
a finger while the charged rod is nearby. The
electrons will be repulsed and flow out of the
electroscope through the hand. If the hand is
removed while the charged rod is still close , the
electroscope will retain a charge. This method of
charging is called charging by induction (see
Figure 2).
Figure 2
Charging an electroscope by induction.
When an object is rubbed with a charged rod, the
object shares the charge so that both have a charge
of the same sign. In contrast, charging by induction
gives an object the charge opposite that of the
charged rod.
Even though the charges are not free to travel
throughout the material, insulators can be charged
by induction. A large charge nearby—not touching—
will induce an opposite charge on the surface of the
insulator. As shown in Figure 3, the negative and
positive charges of the molecules are displaced
slightly. This realignment of charges in the insulator
produces an effective induced charge.
Figure 3
Induction of surface charge on an insulator by a
nearby charged object.
Coulomb's law
Coulomb's law gives the magnitude of the
electrostatic force ( F ) between two charges:
where q 1 and q 2 are the charges, r is the distance
between them, and k is the proportionality constant.
The SI unit for charge is the coulomb. If the charge
is in coulombs and the separation in meters, the
following approximate value for k will give the force
in newtons: k = 9.0 × 10 9 N · m 2/C 2. The
direction of the electrostatic force depends upon
the signs of the charges. Like charges repel, and
unlike charges attract.
Coulomb's law can also be expressed in terms of
another constant (ε 0), known as the permittivity of
free space:
When the permittivity constant is used, Coulomb's
law is
The most fundamental electric charge is the charge
of one proton or one electron. This value (e) is e =
1.602 × 10 −19 coulombs. It takes about 6.24 × 10
18 excess electrons to equal the charge of one
coulomb; thus, it is a very large static charge.
For a system of charges, the forces between each
set of charges must be found; then, the net force on
a given charge is the vector sum of these forces.
The following problem illustrates this procedure.
Example 1: Consider equal charges of Q whose
value in coulombs is not known. The force between
two of these charges at distance X is F . In Figure ,
three charges (3 Q ) are placed at point A , which is
a distance X from point B. One charge (Q) is placed
at point B, which is X /2 distance from point C,
which has one charge. What is the net force on the
charge at point B?
Figure 4
Arrangement of point charges for the example.
Solution: This problem can be solved through
proportional reasoning. The force of 3 Q on the one
charge at B will be 3 F . Because the single charge
is one‐half X from B, the force will be four times
greater than at a distance X , that is, 4 F . The forces
of 3 F and 4 F are at right angles, and therefore, the
resultant force is 5 F , or
The direction is found from the tangent: θ −1 = tan
4/3 = 53°
Electric fields and lines of force
When a small positive test charge is brought near a
large positive charge, it experiences a force directed
away from the large charge. If the test charge is far
from the large charge, the electrostatic force given
by Coulomb's law is smaller than when it is near.
This data of direction and magnitude of an
electrostatic force, due to a fixed charge or set of
fixed charges, constitutes an electrostatic field. The
electric field is defined as the force per unit charge
exerted on a small positive test charge (q 0) placed
at that point. Mathematically,
Note that both the force and electric field are vector
quantities. The test charge is required to be small
so that the field of the test charge does not affect
the field of the set charges being examined. The SI
unit for electric field is newtons per coulomb (N/C).
Figure 5 is a pictorial representation of the electric
fields surrounding a positive charge and a negative
charge. These lines are called field lines or lines
Distance
TDistance is a scalar quantity that refers to "how
much ground an object has covered" during its
motion. Displacement is a vector quantity that refers
to "how far out of place an object is"; it is the
object's overall change in position.of
force .
Figure 5
Electric field lines of (a) positive and (b) negative
point charges.
Figure 6 shows the electric fields for opposite
charges, similar charges, and oppositely charged
plates.
Figure 6
Electric field lines of (a) two opposite
charges, (b) two like charges, and (c)
two oppositely charged plates.
The rules for drawing electric field lines for any
static configuration of charges are
The lines begin on positive charges and
terminate on negative charges.
The number of lines drawn emerging from or
terminating on a charge is proportional to
