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Chapter 16: Electric Forces and Fields1
Section 1: Electric Charge
Properties of charge
Have you ever noticed:
Static cling
Rubbing your feet against the carpet and then
touching a door knob or light switch
Fly-away hair after combing
These experiences are the result of electrical charges.
2 kinds of electric charge
o Positive charge
o Negative charge
 Like charges repel
 Unlike charges attract
o Ex. Electrostatic painting  negatively
charged paint droplets are attracted to the
positively charged target object (less wasted
Electric charge is conserved
Remember your chemistry …
Parts of the atom:
Protons (+ charge)
Neutrons (no charge; neutral)
o Nucleus (center of the atom)
Electrons (― charge)
o Outside the nucleus; in motion
o Easily transferred
When protons = electrons, no net charge
If an electron is transferred from a neutral atom
to another, both atoms have acquired a charge
o Lose an electron, + charge
o Gain an electron, ― charge
o Both are now called ions
Charge has a natural tendency to be transferred
between unlike materials.
Rubbing the materials together increases the
area of contact
Enhances the charge-transfer process
Only a small portion of the total available charge
is transferred from one object to another
Charge transferred to a second object = the
charge “lost” by the first object
o + charge is equal in magnitude to ― charge
Principle of Conservation of
Electric charge is
conserved; no charge is
created or destroyed.
Fundamental laws of
Chapter 16: Electric Forces and Fields2
Electric force is quantized
Transferring electric charge
Robert Millikan’s oil-drop experiment
When charged by rubbing, the charge
does not move into other regions of the
When some materials (like copper,
aluminum, silver) become charged in
one small area, the charge distributes
itself over the entire surface of the
Demonstrated that when an object is
charged, its charge is always a
multiple of a fundamental unit of
charge, represented by e.
o + e, +2e, +3e, etc.
o Electrons have a charge of –e
o Protons have the charge of +e
o Value of e = 1.60 x 10-19C
o C = coulomb, the SI unit of
o -1 C (as in 1 C of electrons)
contains 6.2 x 1018 electrons
Charging by contact
Charging by contact – materials become
charged when rubbed together
Insulators can be charged by contact
Like charges repel
Unlike charges attract
Conductors can be charged by contact if you
hold a metal with an insulated material and
then rub it.
Without the insulator, the charges
that are produced by rubbing move
through the metal, then through your
body (also a conductor), and ends up
in the Earth (going to ground or being
The Earth is considered to be an
infinite reservoir for electrons
because it can accept an unlimited
amount of electrons.
Classify materials based on their
ability to transfer electric charge
Electrical conductors: materials
in which electric charges move
o Metals
Electrical insulators: materials in
which electric charges do not
move freely
o Glass, rubber, silk, plastic
Semiconductors: electric
properties are somewhere
between conductors and
o Pure state – insulators
o When specific materials are
added as impurities,
become conductors
Superconductors have zero
electrical resistance when they
are at or below a certain
o Can conduct electricity
indefinitely without heating
Charging by induction
When a charged rod is brought near a
neutral (uncharged) sphere, the
electrons in the charged rod repel the
electrons in the sphere, causing the
charge in the sphere to be redistributed.
Region nearest to the rod now has
an excess of positive charge
Induction: process of charging a
conductor by bringing it near
another charged object while the
conductor is grounded.
Chapter 16: Electric Forces and Fields3
Process similar to charging by induction
Works on insulators
In the presence of a charged object,
positive charge shifts slightly away
from the negative charge – resulting in
a more positive charge on one side
and a more negative charge on the
other (polarization)
Insulator has no net charge, but is still
able to attract or repel objects due to
Section 2: Electric Force
Coulomb’s Law
Electric force: the force that two charged objects exert on each other, causing an
acceleration either toward or away from each other
The closer the two charges are, the greater the force
Amount of charge on the objects affects the magnitude of the electric force
There is a relationship between distance, charge, and electric force
Coulomb’s law:
Force is a vector quantity
Electric force = Coulomb constant x (charge 1)(charge 2)
Felectric = kC(q1q2)
kC = Coulomb constant = 8.99 x10 N•m
Force between 2 objects
always acts along the line
that connects their
centers of charge
Coulomb’s law applies only
to point charges or
particles, and to spherical
distributions of charge.
o r = distance between
centers of the spheres
Chapter 16: Electric Forces and Fields4
Practice 16A
The electron and proton of a hydrogen atom are separated, on average, by a distance of
about 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force
that each particle exerts on the other.
What you need to know, but may not remember (or know where to find the info):
me = 9.109 x 10-31 kg
mp = 1.673 x 10-27 kg
Conceptual question
Consider two forces, F1 = F and F2 = ―F
acting on two charged particles separated by
a distance, d. Explain the change in forces
under these conditions:
Distance between the 2 particles
Charge on one particle doubles
Charge on both particles doubles
Charge on both particles doubles,
distance between the particles also
G = 6.673 x 10-11 N•m2/kg2
Resultant force on a charge is a vector sum
of the individual forces on that charge
Coulomb’s law gives the electric force
between any pair of charges.
Still applies when there are more than
two charges present
Resultant force on any single charge is
the vector sum of the individual forces
exerted on that charge by all of the
other individual charges present.
o Called principle of
o Find the magnitudes of the
individual electric forces
o Add the magnitudes as we did
 Straight line – add/subtract
 Not in a line, but right
angles, Pythagorean theorem
 Not in a line, not 90°,
components and
Pythagorean theorem
Chapter 16: Electric Forces and Fields5
Practice 16B
Consider three point charges at the corners of a triangle, as shown below, where q1 = 6.00 x
10-9C, q2 = -2.00 x 10-9C, and q3 = 5.00 x 10-9C. Find the magnitude and direction of the
resultant force on q3.
An object in equilibrium
Net external force acting on a body in equilibrium must be zero.
Equilibrium position of a charge is the location where the net electric force on the
charge is zero.
To find this position:
Find the position where the electric force from 1 charge is equal and opposite the
electric force from another charge.
Set the forces (found by Coulomb’s law) equal to each other and then solving for
the distance between either charge and the equilibrium position.
Chapter 16: Electric Forces and Fields6
Practice 16C
Three charges lie along the x-axis. One positive charge, q1 = 15 μC, is at x = 2.0 m, and
another positive charge, q2 = 6.0 μC, is at the origin. At what point on the x-axis must a
negative charge, q3, be placed so that the resultant force on it is zero?
Electric force is a field force
Field force: a force that is exerted by one object on another without physical contact
Gravitational force is another example
Electrical forces:
Can be attractive or repulsive
o Gravity is only attractive
Electrical force is MUCH stronger than gravitational force
o Only a small amount of charge is required to overcome the gravitational
force (balloon on hair trick)
Chapter 16: Electric Forces and Fields7
Section 3: The Electric Field
Electric Field Strength
Electric Field:
No physical contact between objects required
Acts through space
Set up by a charged object in the space around it
o Second charged object enters the field of the first charged object, and
interacts with the electric field
Electric field strength is defined as the magnitude of the electric force acting on a
small, positively charged particle (q0) that enters the field of a much larger positive
E = Felectric
units are the ratio of force to charge, so N/C (newtons per coulomb)
Direction of E (electric field) is defined as the direction of the electric force that
would be exerted on a small positive charge (test charge)
o Direction of E depends on the sign of the charge producing the field
Electric field strength depends on charge and
To find the electric field strength from a
point charge, consider a small test charge, q0,
located a distance, r, from charge q.
Coulomb’s law:
Felectric = kCqq0
Combine this value for Felectric in the Electric
field strength equation:
E = Felectric = kCqq0
E is a vector
E = kCq
If q is positive, the field due to
q radiates outward
If q is negative, the field is
directed toward q
Electric field due to more than
one charge is calculated by
using the principle of
Depends only on the charge,
q, setting up the field, and the
distance, r, from that object
to a specific point in space.
Electric field = Coulomb con. x charge producing field
Chapter 16: Electric Forces and Fields8
Practice 16D
A charge q1 = +7.00 µC is at the origin, and a charge q2 = -5.00 µC is on the x-axis 0.300
m from the origin. Find the electric field strength at point P, which is on the y-axis
0.400 m from the origin.
Chapter 16: Electric Forces and Fields9
Electric field lines
Electric field lines drawn in the direction of the electric field are a convenient aid for
visualizing electric field patterns.
Electric field lines are NOT physical lines – they do not physically exist
Field lines are a visual representation of the field that would be experienced by a
positive test charge
Cannot be observed directly; only the effects of the field can be observed.
Represent both the strength and the direction of the field at different points in
Field lines make it easier to visualize the net field at each point when the field is
the result of more than one charge.
How to draw electric field lines
Number of lines is proportional to the strength of the electric field
Closer the lines, the stronger the field; the farther apart the field lines, the weaker
the electric field
Drawing is two-dimensional, but reality is three-dimensional (like porcupine quills)
No two field lines can cross each other
o At every point in space, the electric field vector points in a single direction
and any field line at that point also points in the same direction.
o Positive charge: electric field lines radiate outward because a positive test
charge would be repelled; the lines are directed away from the positive
charge toward infinity
o Negative charge: electric field lines are directed inward toward the charge
 Lines are closer together as the lines get nearer the charge, indicating
that the field strength is increasing
 Field strength equation is inversely proportional to distance squared
Rules for drawing electric field lines
1. The lines must begin on positive charges or at infinity and must terminate on
negative charges or 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 from the same field can cross each other.
Chapter 16: Electric Forces and Fields10
Electric dipole
2 equal and opposite point charges
Number of lines that begin on the
positive charge must equal the
number of lines that terminate on
the negative charge
Points very near the charges are
nearly radial
High density of lines between the
charges indicate a strong electric
Unequal, opposite charges
Positive charge is twice the
magnitude of the negative charge
Number of field lines leaving +2q is
twice the number of field lines
terminating on –q.
The other field lines terminate at
At great distances, the electric field
pattern equals that of a single
charge, +q.
Two equal positive charges
Close to either charge, the lines are
nearly radial
Same number of lines emerges from
each charge (equal in magnitude)
At great distances from the charges,
the electric field equals that of a
single change of magnitude 2q.