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Charge Properties
•  Conservation
–  Charge is not created or destroyed, only
transferred.
–  The net amount of electric charge produced in any
process is zero.
Charge Properties
•  Conservation
–  Charge is not created or destroyed, only
transferred.
–  The net amount of electric charge produced in any
process is zero.
•  Quantization
–  The smallest unit of charge is that on an electron
or proton. (e = 1.6 x 10-19 C)
•  It is impossible to have less charge than this
•  It is possible to have integer multiples of this
charge
Charge Properties
•  Conservation
–  Charge is not created or destroyed, only
transferred.
–  The net amount of electric charge produced in any
process is zero.
•  Quantization
–  The smallest unit of charge is that on an electron
or proton. (e = 1.6 x 10-19 C)
•  It is impossible to have less charge than this
•  It is possible to have integer multiples of this
charge
What is meant by quantization of charge?
•  Discovered in 1911 by Robert A. Millikan in the oil drop experiment
•  The unit of charge is so tiny that we will never notice it comes in
indivisible lumps. The fact that charge comes in discrete
amounts, only divisible by a constant, is what is meant by
quantization.
•  Example: Suppose in a typical experiment we charge an object up
with a nanoCoulomb of charge (Q = 10-9 C). How many
elementary units of charge is this?
Elementary unit of charge
= 1 particle (a proton or electron)
1 × 10 −9 C × 1unit, or particleof charge = 0.625 x 1010 = 6.25 x 109 particles
1.6 × 10 −19 C
Six billion units of charge!!
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Conductors and Insulators
•  Conductor
•  Insulator
•  Semiconductor
transfers charge on contact
does not transfer charge
might transfer charge
Calculating the Magnitude of Electrical Force
Look familiar?
Compare
Similarities:
Both equations show an inverse square relationship between force and
separation distance.
And both equations show that the force is proportional to the product of the
quantity that causes the force - charge in the case of electrical force and
mass in the case of gravitational force.
Differences:
First, a comparison of the proportionality constants - k versus G - reveals
that the Coulomb's law constant (k) is significantly greater than Newton's
universal gravitation constant (G). Subsequently, a unit of charge will
attract a unit of charge with significantly more force than a unit of mass
will attract a unit of mass.
Second, gravitational forces are only attractive; electrical forces can be
either attractive or repulsive.
Direction
Coulomb's Law
•  The force between
two charges gets
stronger as the
charges move
closer together.
•  The force also gets
stronger if the
amount of charge
becomes larger.
Coulomb's Law
•  The force between
two charges is
directed along the
line connecting
their centers.
•  Electric forces
always occur in
pairs according to
Newton’s third law,
like all forces.
Coulomb's Law
•  The force between
charges is directly
proportional to the
magnitude, or
amount, of each
charge.
•  Doubling one charge
doubles the force.
•  Doubling both
charges quadruples
the force.
Coulomb's Law
•  Doubling the distance
reduces the force by a factor
of 22 = (4), decreasing the
force to one-fourth its original
value (1/4).
•  This relationship is called an
inverse square law because
force and distance follow an
inverse square relationship.
•  The force between charges
is inversely proportional to
the square of the distance
between them.
Q values are often on the order of 10-9 or possibly 10-6
Coulombs. For this reason, charge is often expressed in units of
microCoulomb (µC) and nanoCoulomb (nC).
If a problem states the charge in these units, it is advisable to
first convert to Coulombs prior to substitution into the Coulomb's
law equation.
The following unit equivalencies will assist in such conversions:
1 Coulomb = 106 µC (microCoulomb)
1 Coulomb = 109 nC (nanoCoulomb)
Calculating force
•  Two balls are each given a static
electric charge of one tenthousandth (0.0001) of a coulomb.
•  Calculate the force between the
charges when they are separated by
one-tenth (0.1) of a meter.
•  Compare the force with the weight of
an average 70 kg person.
•  Two balls are each given a static electric charge of one tenthousandth (0.0001) of a coulomb.
•  Calculate the force between the charges when they are separated by
one-tenth (0.1) of a meter.
•  Compare the force with the weight of an average 70 kg person.
F = 9000 N
away from each other
Fg = mg = 70 kg (9.8 m/s2) = 686 N
•  The weight of a 70 kg person:
•  F = mg = (70 kg)(9.8 N/kg) = 686 N
•  The force between the charges is 13.1 times
the weight of an average person!
(9,000 ÷ 686).
Coulomb’s Law
Two Positive Charges
•  What is the magnitude of the force between a positive & negative
charge, each 1 nanoCoulomb, and 1cm apart?
q2
q1
r
1 nC
1 nC
1 cm
(Equivalent to the weight
of a long strand of hair)
•  What is the direction of the force?
1 nC
1 cm
1 nC
Some atoms hold on to their electrons more tightly than others do.
How strongly matter holds on to its electrons determines its place
in the triboelectric series.
If a material is more apt to give up electrons when in contact with
another material, it is more positive in the triboelectric series. If a
material is more apt to "capture" electrons when in contact with
another material, it is more negative in the triboelectric series.
The following table shows you the triboelectric series for many
materials you find around the house. Positive items in the series
are at the top, and negative items are at the bottom:
Human hands (usually too moist, though)
Very positive
Rabbit Fur
Glass
Human hair
Nylon
Wool
Fur
Lead
Silk
Aluminum
Paper
Cotton
Steel _____________________________________________Neutral
_________
Wood
Amber
Hard rubber
Nickel, Copper
Brass, Silver
Gold, Platinum
Polyester
Styrene (Styrofoam)
Saran Wrap
Polyurethane
Polyethylene (like Scotch Tape)
Polypropylene
Conductors and Insulators
•  Conductor
•  Insulator
•  Semiconductor
transfers charge on contact
does not transfer charge
might transfer charge
Conductors and Insulators
3 ways to charge objects
1. Charging by Friction
Human hands (usually too moist, though)
Very positive
Rabbit Fur
Glass
Human hair
Nylon
Wool
Fur
Lead
Silk
Aluminum
Paper
Cotton
Steel _____________________________________________Neutral
_________
Wood
Amber
Hard rubber
Nickel, Copper
Brass, Silver
Gold, Platinum
Polyester
Styrene (Styrofoam)
Saran Wrap
Polyurethane
Polyethylene (like Scotch Tape)
Polypropylene
2. Charging by Induction
3. Charging by Conduction
Electroscope
The electroscope typically consists of a
conducting plate or knob, a conducting base
and either a pair of conducting leaves or a
conducting needle.
Charging by Conduction (cont’d)
Electroscopes
Electroscope Example
•  Suppose that a negatively charged balloon
is used to charge an electroscope.
•  Explain, in terms of electron movement, what is
happening in each step.
Coulomb’s Law
Where Q1 and Q2 are the amount of charge and k is a
proportionality constant
Charges produced by rubbing ordinary objects
(such as a comb or a plastic ruler) are typically
around a microcoulomb or less:
Coulomb’s Law
The charges carried by the proton and electron are
equal in size. However, the mass of the proton is
2000 times the mass of the electron.
Example
Suppose you could place a free proton on the
ground, and wished to place a second one
directly above the first so that the weight of the
second proton would be exactly balanced by the
electric repulsion between them. How far apart
must the protons be?
0.12 m
Defining Electric Field Strength
•  Electric field strength is a vector quantity
•  An electric charge, Q, creates an electric field. We will
refer to this electric charge as the source charge.
•  The strength of the source charge's electric field could be
measured by any other charge placed somewhere in its
surroundings. The charge that is used to measure the
electric field strength is referred to as a test charge, q.
•  A force, F, is felt by the test charge q.
Electric Field Strength
•  The magnitude of the electric field is
simply defined as the force per charge on
the test charge.
Units of N/C
Another equation for E
•  The electric field strength is not dependent upon the quantity of q
•  In the formula for electric field strength E = F/q, substitute Coulomb’s Law in for F
• 
•  q was cancelled from both numerator and denominator of the equation. The new
formula shows that the electric field strength is dependent upon
–  the quantity of charge on the source charge (Q) and
–  the distance of separation (d) from the source charge.
Example 2
•  Tiny droplets of oil acquire a small negative charge while
dropping through a vacuum (pressure = 0) in an experiment. An
electric field of magnitude 5.92 x 104 N/C is present.
a) One particular droplet is observed to remain suspended
against gravity. If the mass of the droplet is 2.93 x 10-15 kg,
find the charge carried by the droplet.
b) Another droplet of the same mass falls 10.3 cm from rest
in 0.250 s, again moving through a vacuum. Find the
charge carried by the droplet.
First, lets draw a picture. Which way must the
arrows be pointing in my electric field?
Example 2
•  Tiny droplets of oil acquire a small negative charge while dropping
through a vacuum (pressure = 0) in an experiment. An electric field of
magnitude 5.92 x 104 N/C is present.
a) One particular droplet is observed to remain suspended against
gravity. If the mass of the droplet is 2.93 x 10-15 kg, find the charge
carried by the droplet.
E
mg = Fe = Eq
(2.93 × 10 −15 kg)(9.8m /s2 )
q = mg / E =
−5.92 × 10 4 N /C
= - 4.85 x 10-19 C
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Example 2
•  Tiny droplets of oil acquire a small negative charge while dropping
through a vacuum (pressure = 0) in an experiment. An electric field
of magnitude 5.92 x 104 N/C points straight down.
b) Another droplet of the same mass falls 10.3 cm from rest in
0.250 s, again moving through a vacuum. Find the charge
carried by the droplet.
Fe
F = ma = F - F
net
e
= Eq - mg
g
Now find the acceleration, a, of the droplet.
Δy = vit + ½ at2
a = 2Δy/t
2=
€
Fg
2(−0.103m)
2
=
-3.3
m/s
0.25 2 sec 2
ma + mg (2.93 × 10 −15 kg)(−3.3m /s2 + 9.8m /s2 )
-19 C
=
3.22
x
10
=
q=
−5.92 × 10 4 N /C
E €
Equations - Summary
•  Coulomb’s Law
–  units: N
•  Electric Field Strength
–  units: N/C
•  Electric Field Strength
(a second equation)
There is a parallel (similarity) between g and E
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A note about k
It was pointed out (by a scientist long ago) that k can
be written in terms of 1/4π and a new constant, ε :
1
k=
4 πε
Where ε is called the permittivity.
Materials with high ε are easily polarized and, therefore,
good electric insulators (electric insulators cancel E fields).
When the charges (q) are in air (similar
enough to a vacuum), ε is written as ε0 .
This has been the assumption for the
cases/equations discussed so far.
So, in the equations (for Coulomb’s Law
and E field), k can be written as k0 :
1
k0 =
4 πε 0
where εo = 8.8541878 x 10-12 C2/Nm2
So, you may see Coulomb’s Law written as:
Q1Q2
= k0 2
r
And Electric Field Intensity:
€
2
Q2
= k0 2
r
But if the experiment is
performed in a medium
other than air, we use a
tabulated value of ε
instead of the εo in ko
Where Q1 is the test charge,
and Q2 is the source charge.
Example 3
A point-charge of 10 µC is surrounded by
water (permittivity is 7.1 x 10-10 C2/Nm2).
Calculate the magnitude of the electric
field 20 cm away.
−6 ⎞
⎛
1
10 × 10 C
1 Q=
Q
⎜
⎟
−10
2
2
E =k 2 =
2 4 π (7.1 × 10
) ⎝ 0.2 m ⎠
4 πε r
r
€
E = 28,020.2 N/C
€
€
Charge cannot be transferred through air
Electric Fields
•  All charged objects create an electric field which
extends outward into the space which surrounds
it.
•  The charge alters that space, causing any other
charged object that enters the space to be
affected by this field.
•  The strength of the electric field is dependent
upon how charged the object creating the field is
and upon the distance of separation from the
charged object.
•  Electric force acts through a field.
•  An electric field is a region in space
around a charged object that causes a
stationary charged object to experience an
electric force.
•  One way to show an electric field is by
drawing electric field lines.
•  Electric field lines point in the direction of
the electric force on a positive charge.
•  The electric field lines around a positive
charge point outward.
•  The electric field lines around a negative
charge point inward.
Electric Field Lines
Electric Field Lines
•  Electric field lines never cross one another.
•  Field lines show both the direction of an electric
field and the relative strength due to a given
charge.
•  More lines are drawn for greater charges to
indicate greater force.
Direction of Electric Fields
•  By convention, the test charge is assumed positive when
assigning direction arrows to field lines.
•  Since like charges repel and opposites attract, electric field
vectors will always point
–  away from positive source charges
–  toward negative source charges
•  Electric Field lines do not cross
•  The electric field is stronger when the lines are located closer
to one another.
Electric Field Lines
Like charges (++)
Opposite charges (+ -)
This is called an electric dipole.
Electric Field Lines
Examples
What is the direction of the electric field at point C?
1)  Left
2)  Right
3)  Zero
y
C
x
Examples
What is the direction of the electric field at point C?
1)  Left
Red is negative
2)  Right
Blue is positive
3)  Zero
Away from positive charge (right)
Towards negative charge (right)
Net E field is to right.
y
C
x
Comparison:
Electric Force vs. Electric Field
•  Electric Force (F) - the actual force felt by a
charge at some location.
•  Electric Field (E) - found for a location only –
tells what the electric force would be if a charge
were located there.
•  Both are vectors, with magnitude and
direction. Add x & y components.
Examples
What is the direction of the electric field at point A?
1)  Up
2)  Down
3)  Left
4)  Right
5)  Zero
A
y
B
x
Examples
What is the direction of the electric field at point A?
1)  Up
Red is negative
2)  Down
Blue is positive
3)  Left
4)  Right
5)  Zero
A
y
B
x
Examples
What is the direction of the electric field at point A, if
the two positive charges have equal magnitude?
1)  Up
2)  Down
3)  Right
4)  Left
5)  Zero
A
y
B
x
Examples
What is the direction of the electric field at point A, if
the two positive charges have equal magnitude?
1)  Up
Red is negative
2)  Down
Blue is positive
3)  Right
4)  Left
A
5)  Zero
x
Concept Check
Example 4 A positive point charge +q is fixed
in position at the center of a
square, as the drawing shows. A
second point charge is fixed to
either corner B, corner C, or
corner D. The net electric field
at corner A is zero. (a) At which
corner is the second charge
located?
(b) Is the second charge positive or
negative?
(c) Does the second charge have a
greater, a smaller, or the same
magnitude as the charge at the
center?
Example 5
Two point charges q1 = -6.15 nC, and q2 = -10.5 nC are separated by 25.0 cm.
(a) Find the net electric field these charges produce at point A.
(b) Find the net electric field these charges produce at point B.
EA = 6990 N/C, to right
EB = 6306.4 N/C = 6310 N/C, to right
Example 6
A proton travels horizontally to the right at 4.50 x 106 m/s.
a) Find the magnitude and direction of the weakest electric
field that can bring the proton uniformly to rest over a
distance of 3.20 cm. Note: mp= 1.67 x 10-27 kg, qp = 1.6 x 10-19
b) How much time does it take the proton to stop after
entering the field?
Use v 2 = v 2 + 2ax
f
i
ma
−v i 2 −(4.5 × 10 6 ) 2
F = ma = Eq → E =
, where a =
=
q
2x
2(0.032m)
v f − vi
t=
since v f = v i + at 2
a
0 − 4.5 × 10 6
t=
−3.16 × 1014
E = 3.3 x 106 N/C, left
a = -3.16 x 1014 m/s2
t = 1.4 x 10-8 sec
-3 nC
q1 3m
5 cm
E1
+6 nC
•
+
q2
E2 A 4 m
Signs of the charges are used only to find direction of E
-3 nC
q1 3m
E1
5m
+6 nC
+
q2
•
E2 A 4 m
E1
E R = E 2 + E1 ; tan φ =
E2
2
2
ER
φ
E2
E1
ER
E2
φ
E1
E1 = 3.00 N/C, North
E2 = 3.38 N/ C, West
N 2
N 2
N
E = ((3.00 ) + (3.38 ) ) = 4.52
C
C
C
N
3.00
C
tan φ =
N
3.38
C
Resultant Field: ER = 4.52 N/C; 138.40
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