PHYSICS - Electrostatics
Electrostatics, or electricity at rest, involves electric charges, the forces between them, and their behavior in materials.
The fundamental rule at the base of all
electrical phenomena is that
like charges repel
and
opposite charges attract.
22.1 Electrical Forces and Charges
The helium nucleus is composed of two protons and
two neutrons. The positively charged protons attract
two negative electrons.
22.1 Electrical Forces and Charges
22.1 Electrical Forces and Charges
An object that has unequal numbers of
electrons and protons is electrically charged.
22.2 Conservation of Charge
A charged atom is called an ion.
• A positive ion has a net positive charge; it has lost
one or more electrons.
• A negative ion has a net negative charge; it has
gained one or more extra electrons.
22.2 Conservation of Charge
• Innermost electrons tightly bound to the nucleus.
• Outermost electrons are bound very loosely.
• How much energy is required to tear an electron away
from an atom varies for different substances.
22.2 Conservation of Charge
When electrons are
transferred from the fur to the
rod, the rod becomes
negatively charged.
22.2 Conservation of Charge
Electric Charge is Quantized
22.2 Conservation of Charge
● Any object that is electrically charged has an excess
or deficiency of some whole number of electrons.
● This means that the charge of the object is a whole-
number multiple of the charge of an electron.
Electrons are neither created nor destroyed but are
simply transferred from one material to another. This
principle is known as conservation of charge.
22.2 Conservation of Charge
If you scuff electrons onto your shoes while walking
across a rug, are you negatively or positively
charged?
22.2 Check Question
Coulomb’s law states that (for charged particles or
objects that are small compared with the distance
between them), the force between the charges varies…
… directly as the product of the charges and…
… inversely as the square of the distance between
them.
22.3 Coulomb’s Law
Recall from Newton’s law of gravitation...
22.3 Coulomb’s Law
For charged objects...
Where:
d is the distance between the charged particles.
q1 represents the quantity of charge of one particle.
q2 is the quantity of charge of the other particle.
k is the proportionality constant.
22.3 Coulomb’s Law
The SI unit of charge is the coulomb, abbreviated C.
A charge of 1 C is the charge of 6.24 × 1018 electrons.
22.3 Coulomb’s Law
The Electrical Proportionality Constant
The proportionality constant k in Coulomb’s law is
similar to G in Newton’s law of gravitation.
k = 9,000,000,000 N·m2/C2 or 9.0 × 109 N·m2/C2
22.3 Coulomb’s Law
22.3 Coulomb’s Law
Because most objects have almost exactly equal
numbers of electrons and protons, electrical forces
usually balance out.
Between Earth and the moon, for example, there is no
measurable electrical force.
In general, the weak gravitational force, which only
attracts, is the predominant force between astronomical
bodies.
22.3 Coulomb’s Law
• Materials through which electric charge can flow
are called conductors.
• Metals are good conductors for the motion of
electric charges because their electrons are
“loose.”
22.4 Conductors and Insulators
• Electrons in other materials—rubber and glass,
for example—are tightly bound and remain with
particular atoms.
• They are not free to wander about to other
atoms in the material.
• These materials, known as insulators, are poor
conductors of electricity.
22.4 Conductors and Insulators
In power lines, charge flows much
more easily through hundreds of
kilometers of metal wire than
through the few centimeters of
insulating material that separates
the wire from the supporting
tower.
22.4 Conductors and Insulators
• Semiconductors are materials that can be
made to behave sometimes as insulators and
sometimes as conductors.
22.4 Conductors and Insulators
• Superconductors are materials that at certain low
temperatures acquire zero resistance to the flow of
charge.
22.4 Conductors and Insulators
Two ways electric charge can be transferred are
➔ by friction
➔ by contact
22.5 Charging by Friction and Contact
• Electrons can be transferred from one material to another
by simply touching.
• When a charged rod is placed in contact with a neutral
object, some charge will transfer to the neutral object.
• This method of charging is called charging by contact.
22.5 Charging by Friction and Contact
If a charged object is brought near a conducting
surface, even without physical contact, electrons will
move in the conducting surface. This is called
charging by induction.
22.6 Charging by Induction
22.6 Charging by Induction
The charge on the spheres has been redistributed, or induced.
22.6 Charging by Induction
22.6 Charging by Induction
Charge Induction by Grounding
22.6 Charging by Induction
22.6 Charging by Induction
Charge Induction by Grounding
22.6 Charging by Induction
Charge Induction by Grounding
22.6 Charging by Induction
Charge Induction by Grounding
22.6 Charging by Induction
Charge Induction by Grounding
When we touch the metal surface with a finger, charges
that repel each other have a conducting path to a
practically infinite reservoir for electric charge—the
ground.
When we allow charges to move off (or onto) a
conductor by touching it, we are grounding it.
22.6 Charging by Induction
Charging by induction occurs
during thunderstorms.
22.6 Charging by Induction
• The primary purpose of the
lightning rod is to prevent a
lightning discharge from
occurring.
• If lightning does strike, it may be
attracted to the rod and short-
circuited to the ground, sparing
the building.
22.6 Charging by Induction
Lightening Rods
How an Electrophorus Works
Charge polarization can occur in insulators that are
near a charged object.
22.7 Charge Polarization
a. When an external negative charge is brought closer
from the left, the charges within a neutral atom or
molecule rearrange.
22.7 Charge Polarization
a. When an external negative charge is brought closer
from the left, the charges within a neutral atom or
molecule rearrange.
b. All the atoms or molecules near the surface of the
insulator become electrically polarized.
22.7 Charge Polarization
22.7 Charge Polarization
22.7 Charge Polarization
Electric Dipoles
Many molecules—H2O, for
example—have a little more
negative charge on one side
of the molecule than on the
other.
Such molecules are said to be
electric dipoles.
22.7 Charge Polarization
In summary, objects are electrically charged in three ways.
• By friction, when electrons are transferred by friction
from one object to another.
• By contact, when electrons are transferred from one
object to another by direct contact without rubbing.
• By induction, when electrons are caused to gather or
disperse by the presence of nearby charge without
physical contact.
22.7 Charge Polarization
You can sense the force field that surrounds a
charged Van de Graaff generator.
22.8 Electric Fields
22.8 Electric Fields
gThe distance
between field lines
indicates
magnitudes.
22.8 Electric Fields
FG = mg
FG
22.9 Electric Field Lines
EE
22.8 Electric Fields
FG = mg
FG
FE = qE
FE
The direction of an electric field at any point, by
convention, is the direction of the electrical force on
a small positive test charge placed at that point.
22.8 Electric Fields
a. The field lines around a single positive charge extend to infinity.
22.9 Electric Field Lines
a. The field lines around a single positive charge extend to infinity.
b. For a pair of equal but opposite charges, the field lines emanate
from the positive charge and terminate on the negative charge.
22.9 Electric Field Lines
a. The field lines around a single positive charge extend to infinity.
b. For a pair of equal but opposite charges, the field lines emanate
from the positive charge and terminate on the negative charge.
c. Field lines are evenly spaced between two oppositely charged
capacitor plates.
22.9 Electric Field Lines
22.9 Uniform Electric Fields
Between two parallel plates containing equal but
opposite charges, the electric field is uniform.
Both the magnitude and direction of the field is the
same at all points between the plates.
+ + + + + +
+ + +
- - - - - -
- - -
E
22.9 Uniform Electric Fields
+ + + + + +
+ + +
- - - - - -
- - -
E+
-
q
qFE
FE
FE= qE
22.9 Example
+ + + + + +
+ + +
- - - - - -
- - -
-oil
drop
FE
FG
Robert Millikan determined the charge on an electron by suspending
negatively charged oil drops in a uniform electric field created by two charged
plates. Determine the charge on the oil drop in terms of its mass (m), the
electric field (E) and the gravity of Earth (g).
22.9 Example
When an electron is released from rest in a uniform electric field E,
it reaches a velocity of v after traveling a distance of x. In terms of
v, what will be the electron’s velocity if the magnitude of the electric
field is doubled while traveling the same distance?
22.9 Electric Fields of Point Charges
So far we have two equations for the electrical force:
FE= qE AND
As with gravity, we can set these equal to each other and solve
for E to determine the strength of the electric field at a given
position. The result should look very familiar from our study of
gravity...
22.9 Electric Fields of Point Charges
22.9 Example
A conducting sphere contains a charge q. The electric field at a set
distance from the center of the sphere is E. If the charge on the
sphere and the distance from the sphere are both doubled, by what
factor would the electric field change?
22.9 Superposition of Electrical Fields
A +8 coulomb charge is located 2 meters to the left of the origin. A
-4 coulomb charge is located 2 meters to the right of the origin.
Determine the magnitude and direction of the electric field at point
P located at the origin.
+
8 C P 4C
-
-2 -1 0 1 2
22.9 Superposition of Electrical Fields
Two negative charges, 4 coulombs and 16 coulombs, are
separated by a distance of 1 meter. Determine the location, as
measured from the 4-coulomb charge, where the electric field is
zero.
-
4 C 16C
-
1 meter
22.10 Electric Shielding
Consider a charged metal sphere.
Because of repulsion, electrons
spread as far apart as possible,
uniformly over the surface.
A positive test charge located exactly
in the middle of the sphere would feel
no force. The net force on a test
charge would be zero.
22.10 Electric Shielding
22.10 Electric Shielding
How to Shield an Electric Field
There is no way to shield gravity, because gravity
only attracts. Shielding electric fields, however, is
quite simple.
• Surround yourself or whatever you wish to
shield with a conducting surface.
• Put this surface in an electric field of whatever
field strength.
• The free charges in the conducting surface will
arrange on the surface of the conductor so that
fields inside cancel.
22.10 Electric Shielding
22.11 Electrical Potential Energy
• Imagine moving multiple
charges from A to B. For
each charge we move,
there is a gain in PE.
• So it makes sense to talk
about difference in
potential energy per
charge.
22.11 Electrical Potential Energy
Difference in potential energy per charge
POTENTIAL DIFFERENCE
ELECTRIC POTENTIAL
VOLTAGE
22.11 Electrical Potential Energy
Difference in potential energy per charge
Joules
Coulomb
22.11 Electrical Potential Energy
1 Joule / Coulomb = 1 Volt
22.11 Electrical Potential Energy
22.11 Electrical Potential Energy
22.11 Electrical Potential Energy
22.11 Electrical Potential Energy
V = Ed
CAUTION: This equation is only for uniform electric fields. For
example, for the field between two parallel charged plates.
E = V
d
Electric potential
is not the same as
electrical potential energy.
Electric potential is
electrical potential energy per charge.
22.12 Electric Potential
22.12 Electric Potential
If there were twice as much charge on one of the
objects, would the electrical potential energy be the
same or would it be twice as great? Would the
electric potential be the same or would it be twice as
great?
22.12 Electric Potential
22.12 Example
d
P
+ + + + +
- - - - - -
6 V
4 V
2 V
0 V
-+
22.12 Example
Two charged plates with a 20 newton per coulomb
electric field are separated by a distance of 10
centimeters. A proton is located at the midpoint
between the plates.
A) Determine the potential difference between the
charged plates.
B) Determine the potential acting on the proton.
22.12 Potential of Point Charges
+q
E
6 V
4 V
2 V
V = kq
r
E = kq
r2
22.12 Example
A +4 coulomb charge is located 4 meters to the left of
the origin. A -4 coulomb charge is located 4 meters
to the right of the origin. Determine the electric
potential at point P located at the origin.
22.12 Electric Potential Energy
UE = qV
Once we know the electric potential of a point in
space, it’s easy to find the electric potential energy of
any amount of charge.
Since V is simply difference in potential energy PER
CHARGE, we only need to multiply by how much
charge we have to find the total potential energy.
22.12 Work of Electricity
WE = 𝚫K = -𝚫UE = -q𝚫V = -q (Vf - Vi)
|W | = |q| ● |(Vf - Vi)|
22.12 Example
The diagram above shows the equipotential lines in a
region of space. Determine the work done on a 2-
coulomb charge that is moved from point A to point
B.
-4 V -2 V 0 V 2 V 4 V 6 V
+
AB
22.12 Conservation of Energy
Don’t forget that you can still apply what you already
know about energy to solve electric potential problems.
See below:
-
-
-
+
+
+
-
Two charged plates have a
potential difference of V. An
electron of mass m and charge
e is initially at the negative plate.
It accelerates through the
potential difference. Determine
the electron’s max speed, v, in
terms of the given variables.
22.13 Electrical Energy Storage
A capacitor is a
device that can
store electrical
energy.
22.13 Electrical Energy Storage
22.13 Capacitance
Capacitance, C, is measured in farads (F) and is a
measure of the ability of a capacitor to store charge and
energy.
Capacitance is proportional to the area of one of the
plates, A and inversely proportional to the distance of the
plate separation, d.
Epsilon is a constant known as the permittivity of free
space and = 8.85 x 10-12 C2/Nm2
22.13 Capacitance
Other formulas you might need for capacitance:
22.13 Capacitance
Other formulas you might need for capacitance:
UC =
22.14 The Van de Graaff Generator
22.14 The Van de Graaff Generator