CHAPTER 16
Electric Forces and Electric Fields
Electric Charge:
• Atoms are made of equal numbers of protons (positive
charge) and electrons (negative charge)
• We say something is “electrically charged” if it contains
unequal amounts of positive and negative charge
• In this class (as was the case in chemistry) objects
become charged by gaining or losing electrons. They do
not gain or lose protons.
Observations Regarding Charge
• Like charges (or charged objects) repel each other
• Unlike charges (or charged objects) attract each other
• We can positively charge an object by removing some
electrons
and
We can negatively charge an object by adding some
electrons
• Charge is conserved. If an object becomes positively
charged, then some other object (s) must have become
negatively charged
• Charge comes in discrete amounts.
Every proton has the exact amount of positive
charge as every other proton
Every electron has a similar amount of negative
charge
Trivia Question:
Who decided that protons have positive charge and
electrons have negative charge?
Ben Franklin
Terms:
Insulator: Material that does not allow electrons to freely
flow through it (Ex: plastic, rubber, glass)
Conductor: Material that does allow electrons to freely flow
through it (Ex: metals)
How does an object obtain a net charge (uneven
amounts of protons and electrons)?
• It always either gains or loses electrons. Protons never
move to or from an object under normal conditions.
• Ways to transfer electrons
(Ex: the “shock you feel when you touch
Friction
your car after you have just driven it)
Conduction (Ex: direct contact with a charged object)
Induction (Ex: obtaining a charge due to the
influence of nearby charged object
Charging by Conduction
Charging by Induction
Charged Particle Brought Near Uncharged Conductor
Positively
Charged Particle
Uncharged
Conductor
Negative charges
migrate towards
positively charged
objects
Fe Fe
Attractive Forces Result
Charged Particle Brought Near Uncharged Conductor
Negatively
Charged Particle
Uncharged
Conductor
Negative charges
migrate away from
negatively charged
objects
Fe Fe
Attractive Forces Result
Electric Force (Fe)
Fe 
q1 q2
r2
q1 = charge producing the field
q2 = small charge influenced by the
field produced by q1
r = distance between the two charges
Question:
How do you change a proportionality into an equality?
Answer:
Add a proportionality constant.
k q1 q2
Fe =
Coulomb’s Law
2
r
Fe = Newtons
q1 = coulombs of charge
q2 = coulombs of charge
r = distance between centers of charged objects
k = 9.0x109 Nm2/C2
Coulomb is new basic unit (m, s, kg, C)
+1 coulomb = charge of 6.3 x 1018 protons
Example Problem (Coulombs Law Application)
Determine Fe and Fg between a hydrogen atom proton and
its orbiting electron (r = .53x10-10 m)
a) Fe part:
Apply Coulomb’s Law Fe = kq12q2
r
q1 = proton = 1 / 6.3x1018C
good # to remember
q1 = 1.6x10-19C
q2 = electron = -1.6x10-19C
(9.0x109Nm2/C2)(1.6x10-19C)(-1.6x10-19C)
Fe =
(.53x10-10 m)2
Fe = 8.2 x 10-8 N
b) Fg part:
Apply Universal Law of Gravitation Fg = G m21 m2
r
-11
2
2
-27
(6.67x10 Nm /kg )(1.67x10 kg)(9.11x10-31kg)
Fg =
(.53x10-10m)2
Fe is much
Fg = 3.6 x 10-47 N
Fe/Fg = 2.3 x 1039 larger force
than Fg
Electric Fields
Charged particles exert a force on other charged particles
(Fe) just like massive objects exert a force on other massive
objects (Fg).
Field lines are used to show the strength and direction of
the electric field (E)
• field lines point in the direction that a small positive
test charge would move if placed in the field.
• like charges repel. Unlike charges attract
• field lines never cross.
Why?
• closer lines indicate stronger fields
• field lines are a way humans visualize something
we cannot sense. Field lines are only a model.
• Field is 3-dimensional, not 2.
• Lines spread out through ever
increasing spheres surrounding
the charge.
• Area of sphere = 4r2
Distance from
charge (m)
Example: 12 field lines:
Approximate
Strength of
2
Surface Area (m ) field (lines/m2)
1.0
2.0
12 m2
48 m2
12/12
12/48
3.0
r
108 m2
12/108
Field strength proportional to 1/r2
1
 1/22
 1/32
 1/r2
Electric Force (Fe)
k q1 q2
Fe =
r2
Proportional to
product of charges
Proportional to inverse
of distance squared
[ ]
kq1 q
2
r2
Fe = E1 q2
E1 = electric field
caused by object 1
(N/C)
Fe =
Gravitational Force (Fg)
G m1 m2
Fg =
r2
Proportional to
product of masses
Proportional to inverse
of distance squared
[
]
Gm1 m
2
r2
Fg = g1 m2
g1 = gravitational field
caused by object 1
(N/kg) or (m/s2)
E and g
Not forces
Are vectors
Similar concepts
Different units
Fg =
Superposition (Addition of E-fields)
Example Problem: (Point between 2 charges)
r1=2.0cm
E2
q1
-25C
E1
r2=8.0cm
P
q2
+50C
Calculate E1 at P
k q1
E1 =
r2
(9.0x109Nm2/C2)(-25x10-6C)
E1 =
(2.0x10-2m)2
E1 = 5.6x108 N/C (left)
A second charge is placed in the vicinity of P.
Calculate E2 at P.
E2 = 7.0x107 N/C (left)
ET (at P) = E1 + E2
ET = 6.3 x108 N/C (left)
Electrostatics with Conductors in Equilibrium
In Equilibrium:
Conductors:
Charges are not moving.
Materials that contain charges (electrons)
that are not bound to any atom and are
free to move about within the material.
For a conductor in electrostatic equilibrium:
1. The electric field is zero everywhere inside the conductor.
Reasoning:
If an E-field did exist, then electrons
E
would move and in the static condition
Spherical
they are not moving. Hence, there
conductor
must not be an E-field inside the
conductor.
2. Excess charge resides entirely on the surface of the
conductor.
Reasoning:
Repulsive forces cause charges to distance themselves from
each other causing them to migrate to the surface.
3. The electric field outside a charged
x
conductor is perpendicular to the surface.
Reasoning:
Spherical
conductor
If this were not the case (as shown), a
component of the E-field vector parallel
to the surface would cause the charge to
move. However, the charge is not moving (static equilibrium)
and so the E-field must be perpendicular to the surface.
4. Excess charge tends to accumulate at sharp points on the
surface.
Work is
being done
in two
places.
Can you
name
them?
1. Positive charge is “sprayed”
onto the moving belt at point
“A”. (Actually, electrons are
pulled off the belt onto an
electrode.)
2. Charge moves up the
rotating belt and is scraped
off by a wire brush at point
“B”. (Actually, electrons
move onto the belt from the
sphere.)
3. Positive charge builds up on
the sphere and spreads itself
out on the sphere exterior
surface.
4. At some point the resulting
E-field becomes strong
enough to ionize air and
charge leaks off to the air.