Download Charging

Science knows of four forces that
exist in nature.
The Strong Force
The Electromagnetic Force
The Weak Force.
Gravity
The strong and weak forces are short range
forces, that is, they only act over very small
distances (like inside the nucleus of an atom).
Gravity and the electromagnetic forces are long
range forces and can act over very large distances.
Perhaps the most startling thing about the
electric force is how strong it is compared to
gravity
It is approximately 3x1047 times stronger
than gravity.
Actually, it’s not that the
electric force is so strong,
it’s that gravity is so weak.
Rules of Electrostatics
1. There are two kinds of charge that exist in nature
(positive charge and negative charge)
• unlike charges attract one another
• like charges repel one another.
2. The force between charges varies as the
inverse square of the distance, and directly
with the charges. (Coulomb’s Law)
3. Charge is conserved.
4. Charge is quantized. (quantized means
small discrete packets that can not be
further subdivided. For example, you can
have 1 or 2 electrons, but never 1.5
electrons)
The basic unit of positive charge is the proton.
(Although protons are ultimately made up of quarks)
The basic unit of negative charge is the
electron. It is almost always electrons that are
moving when charge “flows”
The SI unit of charge is the Coulomb ( C).
Charge of 1e- = 1 proton = 1.6x10-19 Coulombs
Q
Jeff rubs a piece of fur on glass rod, giving the rod a
negative charge. What is the most likely thing that
happens?
1) Protons are removed from the rod
2) Electrons are added to the rod
3) The fur is also charged negatively
4) The fur is left neutral
Jeff rubs a piece of fur on glass rod, giving the rod a
negative charge. What is the most likely thing that
happens?
1) Protons are removed from the rod
2) Electrons are added to the rod
3) The fur is also charged negatively
4) The fur is left neutral
Conductors & Insulators
Conductors are materials
in which charges are free to
move. Metals are a good
example.
Insulators are materials in which charges
can not move. Glass, plastics, and wood, are
examples.
Q
Which of the following best characterizes electrical
conductors?
1) Low mass density
3) Poor heat conductors
5) All of the above
2) High tensile strength
4) charges move freely
Which of the following best characterizes electrical
conductors?
1) Low mass density
3) Poor heat conductors
5) All of the above
2) High tensile strength
4) charges move freely
Consider the “pith” ball…
+- +
+
+ + +-
Charges are balanced, so the
ball is neutral
Consider the “pith” ball…
-
--
- - - --
- +
+
++
+
+
-
Consider the “pith” ball…
-
--
- - - --
-
-
+
-
+ ++
-- +
- +
Consider the electroscope
Consider the electroscope
+ ++
+ ++ +
++ +
++
Charging by conduction—A physical transfer
of charge
+ ++ +
+ + ++
+ ++ + +
Explain
+
what
+
+ +
happens in
++
+
+
+
++ +
+ +
pictures &
words
Consider the electroscope
+ ++ +
+ + ++
+ ++ + +
+
-- --- - -- + ++
+
++
+ +
Polarized
but Still
neutral
Electrons transfer
from the scope to
the rod
+ ++ +
+ + ++
+ ++ + +
+- --- - -- + ++
+
++
+ +
Scope is left positive.
+
+ +
++
+
+
+
++ +
+ +
I can tell it is
charged
because the
leaves repel
each other.
Charging by Induction - A transfer of charge, but
only two neutral objects touch
+ + + + + + + + + + + + Be ready
to explain
what
happens in
pictures &
words
Consider the electroscope
Charging by Induction
+ + + + ++ + + + + + +
-- --- - -- + ++
+
++
+ +
Still
neutral
Charging by Induction
+ + + + ++ + + + + + +
-- --- - -- + ++
+
++
+ +
Charging by Induction
+ + + + ++ + + + + + +
-- --- - -- These charges
flow from the
ground to the
electroscope.
-
-
+
+
+
- - ++
+ +
These
charges
remain
held in
place
Charging by Induction
http://regentsprep.org/Regents/physics/phys03/aeleclab/ind
uct.htm
+ + + + ++ + + + + + +
-- --- - -- The
electroscope
is now
charged.
-
-
- - -
-
Explain
what
happens in
pictures &
words
These
charges
now spread
out.
Q
An uncharged conductor is supported by an
insulating stand. I pass a positively charged rod near the
left end of the conductor, but do not touch it. The right
end of the conductor will be…
1) Negative
4) Attracted
2) Positive
3) Neutral
5) Depends on the materials.
An uncharged conductor is supported by an
insulating stand. I pass a positively charged rod near the
left end of the conductor, but do not touch it. The right
end of the conductor will be…
1) Negative
2) Positive
3) Neutral
5) Depends on the materials.
4) Attracted
An uncharged conductor is supported by an
insulating stand. I pass a positively charged rod near the
left end of the conductor, but do not touch it. The right
end of the conductor will be…
1) Negative
2) Positive
3) Neutral
5) Depends on the materials.
+ + ++ +++
- - --
+
++
+ +
4) Attracted
Charles Augustin de Coulomb
(1736-1806)
Force between
charges….
Coulomb’s Law
To determine the
direction of the
force, look at the
charges.
kQ1Q2
F
2
d
Where:
Also seen as “q”
k = Coulomb’s Constant
(9.0x109 N m2/C2)
Q = Charge in Coulombs

d = Distance between charges Q
Coulomb’s Law
The significance of Coulomb’s Law goes far
beyond the description of the forces acting between
charged balls or rods. This law correctly describes
the forces that…
* Binds the electrons of an atom to its nucleus
* Binds atoms together to form molecules
* Binds atoms or molecules together to
form solids and liquids
Example
Two charges, + 2.0x10-5 C and –3.0x10-5 C are
5.0 m apart. Calculate the force between them.
kQ1Q2 9 10 (2 10

F
2
5
d
9
5
2
= .22 N
5
)(310 )
Another Example
(draw the picture)
Find the net force on the 5.0 nC charge.
0.10m
-3.0 nC
5.0 nC
0.30m
-6.0 nC
Another Example
(draw the picture)
Find the net force on the 5.0 nC charge.
5.0 nC
-3.0 nC
0.10m
F-3
F6
0.30m
-6.0 nC
(9 ´10 9 )(5´10-9 )(6 ´10-9 )
-6
F6 =
=
3.0
´10
N
2
(.3)
9
9
9
(9 10 )(5 10 )(310 )
5
F3 
1.3510 N
2
(.1)
-6
Fnet = F6 + F-3 = 3.0x10 -1.35x10

-5
= - 1.05x10-5 N
= 1.05x10-5 N
Q
Two point charges are 4 cm apart. They are moved
to a new separation of 2 cm. By what factor does the
resulting mutual force between them change?
1) ½
2) 2
3) ¼
4) 4
5) depends on
the charges
Two point charges are 4 cm apart. They are moved
to a new separation of 2 cm. By what factor does the
resulting mutual force between them change?
1) ½
2) 2
3) ¼
4) 4
5) depends on
the charges
Q
If the size of the charge value is tripled for both of two
point charges maintained at a constant separation, the
mutual force between them will be changed by what factor?
1) 9.0
2) 3.0
3) 1/3
4) 6.0
5) 1/9
If the size of the charge value is tripled for both of
two point charges maintained at a constant separation, the
mutual force between them will be changed by what
factor?
1) 9.0
2) 3.0
3) 1/3
4) 6.0
5) 1/9
Define the concept of a field
A field is an area or volume that has a
number, representing some quantity,
assigned to every location.
That number can be a scalar
or a vector.
A football field has
numbers assigned in
one dimension
A weather map is an example of a
scalar field.
For example, the
Every point on
temperature
in
NP
the map has a
o
is
about
75
scalar quantity
associated
with it.define a field in
We can also
In this case, it’s
terms
of
vectors.
temperature.
Vector Field Examples - Has an amount and a
direction associated with each position.
Example: Earth has a
Gravitational Field
The Electric Field (E) is a vector field
• Any charge will set up an electric field around it.
•It exerts an electric force on any other charged
object within the field.
•It is defined as the force per positive charge.
Don’t confuse the charge that creates the
field with the charge that reacts to the field
Look at phet “Charges and Fields”
All electric charges set up an electric field around
themselves. To determine the direction of an electric
field at any given point, a positive point charge or test
charge is used.
A positive point charge is like a point or an infinitely
small spot that has a single positive charge.
Convention states that when testing an electric field,
always use a positive point charge, never a negative
one.
Draw the electric field around a positive charge.
Electric field for a positive charge
+
Draw the electric field for a negative charge.
Rules for Drawing Electric Fields
1. The lines must begin on positive
charges and end 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 amount of
charge.
3. Field lines may not cross or touch
each other.
This implies that the
vector sum has two
values---which it can’t
4. Field lines must meet conductors or
charges perpendicular to the surface of
the conductor or charge.
Example: 2 charges
Less Charge
Example: Charge & Plate
This is an
equipotential
line. Do not
worry about it
for now.
Q
Back to Earth’s
Gravitational Field:
Mass CREATING
the field
Near the surface of the Earth, Earth’s gravitational field is
9.8 N/kg downwards,
toward Earth’s surface.
Mass EXPERIENCING
the field
Do larger masses experience
a larger gravitational field
from Earth?
What two variables does gravitational field depend on?
GM 2 
GM 1M 2
Fg 
 M 1  2 
2
 R 
R

Calculation of a
Gravitational Field (on
Earth 9.8 m/s2)
Consider a positive charge in
space.
+
The Electric Field is used to
describe the effect of this charge at
some point in space.
Consider a positive charge in
space.
+
+
10 N
If a positive point charge (+1) is
placed at that point, a force will be
exerted on it by the original
charge.
Let’s say, the force is 10 N.
Consider a positive charge in
space.
E = 10 N/C
+
Then we can say, whenever a charge is
placed at that point, for every coulomb of charge,
it will have a force of 10 N act on it.
We say the electric field at that point
is 10 N per coulomb.
Consider a positive charge in
space.
+
If a 3 C charge is placed there, the force
on it would be 3 C x 10 N/C or 30 N.
In general, we say F = Q E
Another equation
for EXPERIENCES
This charge
the field
Electric Field:
 kQ1Q2
F
2
d
This charge
According to
Coulomb’s Law:
Another way to
CREATES the
calculate
electric force is
field
this:
 
F  EQ
 kQ
F 2 Q
d
Therefore, this
part of Coulomb’s
Law must
calculate the
Electric Field
Q
The electric field produced by a point or
spherical charge is given by….
The direction of
 kQ
E 2
d
the electric field
is based on the
direction of
force for a
positive charge.
K = Coulomb’s Constant (9.0x109 N m2/C2)
Q = The charge producing the field.
Given in Coulombs
d = The distance to the point in question
Q
What is the electric field 20.00 m to the
right of a (+) 0.0025 C point charge?
E=?
20.00 m
+
.0025 C
 kQ
E 2
d
9.0 10 .0025C 
9
E
20.00 m
2
2
= 5.6x104 N/C
Q
The electric field produced by a point charge is 16
N/C at a distance of 10. m. At what distance will the
field be 4.0 N/C?
1) 20.m
2) 5.0m
3) 25m
4) 40.m
5) 32m
The electric field produced by a point charge is 16
N/C at a distance of 10.m. At what distance will the
field be 4.0 N/C?
1) 20.m
2) 5.0m
3) 25m
4) 40.m
kQ
E 2
d
N (9.0 10 9 Nm 2 /C 2 )Q
16 
2
C
(10.m)
Q  1.778107 C
5) 32m
N (9.0 10 Nm /C )(1.77810 C)
4.0 
2
C
d

d  20.m
9
2
2
7
Two charges, +Q and –Q, are located two
meters apart as shown. Which vector best
represents the direction of the electric field
at the point above them?
1
2
3
4
+
-
Two charges, +Q and –Q, are located two meters
apart as shown. Which vector best represents
the direction of the electric field at the point
2
above them?
3
1
4
+
-
Two charges, +Q and –Q, are located two meters
apart as shown. Which vector best represents
the direction of the electric field at the point
above them?
+
-
Two charges are along the x-axis. Q1 is 3.0 m from the
origin and has a charge of -12.0µC. Q2 is 4.5 m from the
origin and has a charge of +4.0µC. (all charges are along
the positive x-axis)
a) Calculate the electric field 8.0 m from the origin.
3.0 m
0.0 m
-
Q1 = - 12.0x10-6C
+
E=?
Q2 = + 4.0x10-6C
𝑘𝑄1
𝐸1 =
𝑑2
9 × 109 (−12.0 × 10−6 )
𝐸1 =
5.02
𝐸1 = 4320 𝑁/𝐶
8.0 m
4.5 m
𝑘𝑄2
𝐸2 =
𝑑2
9 × 109 (+4.0 × 10−6 )
𝐸2 =
3.52
𝐸2 = 2939 𝑁/𝐶
0.0 m
4.5 m
3.0 m
-
Q1 = - 12.0x10-6C
+
Q2 = + 4.0x10-6C
𝐸1 = 4320 𝑁/𝐶
𝐸2 = 2939 𝑁/𝐶
= 1381 𝑁/𝐶
𝐸𝑡𝑜𝑡𝑎𝑙 = 1400 𝑁/𝐶
8.0 m
E=?
b) What force will a - 9.0 mC charge experience if it
is placed 8.0 m from the origin?
0.0 m
4.5 m
3.0 m
-
Q1 = - 12.0x10-6C
+
Q2 = + 4.0x10-6C
8.0 m
-
Q3 = - 9.0x10-6C
E = 1381 N/C 
F = QE
F = (-9.0x10-6C)(1380N/C)
F = 0.012 N
Two charges, - 4.0 μC and - 5.0 μC, are separated by a
distance of 20.0 cm. What is the electric field intensity
halfway between the charges?
Two point charges, separated by 1.5cm, have charges of
+2 and -4C. Suppose we determine that 10 field lines radiate
out from the +2C charge. If so, what might be inferred about
the -4C charge with respect to field lines?
1) 20 radiate out
4) 10 radiate in
2) 5 radiate out
5) 5 radiate in
3) 20 radiate in
Two point charges, separated by 1.5cm, have charges of
+2 and -4C. Suppose we determine that 10 field lines radiate
out from the +2C charge. If so, what might be inferred about
the -4C charge with respect to field lines?
1) 20 radiate out
4) 10 radiate in
2) 5 radiate out
5) 5 radiate in
3) 20 radiate in
A quick thought
experiment:
Given: Several hundred packs of
M&M’s
A Scale
How could you
determine the mass of
one M&M
without opening the
M&M bag?
A few assumptions:
1. All M&Ms have the same
mass.
2. There are no broken M&M’s in
the bag
3. The mass of the package is
minimal.
4. The number of M&M’s per
pack varies considerably.
Experiment with M & M's
Mass (g)
Smallest difference
100
equals 1.0 grams
90
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
Pack Number
9
10 11 12
This is exactly what was
done to determine the charge
Darn oil drops
of an electron.
make a mess!
•In 1909 Robert Millikan
measured the charge of
an electron using an oil
drop experiment
•In 1923 he received the
Nobel Prize for his work.
Millikan’s set up:
Negatively charged oil drops are attracted to
the positively charged plate. The more charge
the oil drop has, the more attracted to the plate
it is.
Charged oil drop in an electric field
Millikan varied the
electric field in
between the plates,
until the electric force
on the “target” oil drop
balanced the force of
gravity and the oil drop
stayed suspended
between the plates.
F = QE
F = mg
Example: A 3.2x10-8 kg oil drop is suspended in an electric
field of strength 1.31x1011 N/C. (a) What is the charge on the
oil drop? (b) how many extra electrons does the oil drop have?
Fg  Fe
mg  QE
m
11 N
(3.2 10 kg)(9.8 2 )  (1.3110
)Q
s
C
8
Q  2.4 10 C  1electron

18


1.6 10 C
19
15electrons
Shocking Fingers and Lightning Rods
On a regularly shaped object, charges are evenly
spread.
On an irregularly shaped object, charge tends to
accumulate at areas of largest curvature/smallest
radii.
Small radius,
large curvature
Big radius, small
curvature
In other words,
charge accumulates at
sharp points
Ben Franklin invented the
lightning rod.
Q
At what point is the charge per unit area greatest
on the surface of an irregularly shaped conducting
object?
1) Where the surface curves inward
2) Where the surface is flat
3) Where the curvature is greatest (smallest radius)
4) Where the curvature is least (largest radius)
At what point is the charge per unit area
greatest on the surface of an irregularly shaped
conducting object?
1) Where the surface curves inward
2) Where the surface is flat
3) Where the curvature is greatest
4) Where the curvature is least
2. Faraday Cage
http://www.youtube.com/watch?v=Zi4kXgDBFhw
The Electric Field inside a conducting surface is
zero.
Conducting
Cup
Insulating Stand
The Electric Field inside a conducting
surface is zero.
Charged Ball
+
The Electric Field inside a conducting
surface is zero.
Polarized
Charged
-+
+-+
++- + -+
-+
+-+
+ + + +
The Electric Field inside a conducting
surface is zero.
The negative
Charge
remains on
the outside
only
+
+
+
+
+ + + +
+
+
+
+
+
charges from
the polarized
inside get
neutralized as
the positive
ball comes in
contact with
them. The
charge from
the positive
ball is now left
on the outside
of the cup.
A negative charge comes close to the conductor
and the conductor polarizes.
-
-
-
+
+
- +
+
+
- + + +
+ + - +
+
+ - +
+
+
+
+
+
But not all the
negative charge
can accumulate
on the far side
because then the
far side would be
“too” negative so
some stays in the
center leaving
the center
neutral.
The rod touches, the electrons transfer,
and the outside is left negative while the
inside is still neutral.
-
-
-
+
+
- +
+
+
- + + +
+ + -+
+
+ - +
+
+
+
+
+
+
+
+
+ - +- + -+ + + - +
+ -+
- +
- +
+
- +
- +
+
+
-
A faraday Cage is a metal enclosure in which
charge will always flow to the outside, thus
leaving the inside neutral.
A faraday Cage is a metal enclosure in which
charge will always flow to the outside, thus
leaving the inside neutral.
Not only do Faraday cages block charge, they more
importantly block electromagnetic radiation.
Applications of a Faraday Cage
1. Microwave Oven
2. Electronic shielding
3. Lightning protection
During a lightning storm
you are relatively safe
in…
A metal framed building.
A car. (not a convertible
however)
Watch Car being Struck by Lighting