Transcript electric field

Static Electricity
“Electrostatics”
•
“Static”- not moving. Electric
charges that can be collected an
held in one place
–
–
–
Examples: sparks on carpet, balloon
against hair, lightning, photocopier
History: ancient Greeks made little
sparks when rubbing amber with fur
(Greek word for amber: “elektron”)
Electric charge, “q”, is measured in
Coulombs, C. One Coulomb is charge
is a dangerously high charge. An
average lightning bolt has about 10
Coulombs of charge.
Atomic View
–
Proton: in nucleus
•
Positive charge
•
q = + 1.6 x 10-19 C
–
Electron: outside nucleus
•
Negative charge
•
q = - 1.6 x 10-19 C
–
Protons and Electrons have the same amount of
charge but a proton has much more mass!
Neutron: in nucleus, has no charge
Molecules
–
–
•
•
2 or more atoms bonded together
usually atoms and molecules are neutral,
but if they have a net charge, they are called
IONS
•
Behavior of charges
– Unlike charges attract
– Like charges repel
– A neutral object will attract both positive
and negative charges
Charles Coulomb, mid 1700’s, studied and published papers
about the electrostatic force between 2 charged objects.
Hmmm..
+++
---
Ben Franklin was the
first to use the terms
“positive” and
“negative” to describe
electrical charge. Mid
1700’s
Robert Millikan
First determined the “elementary charge”- the
charge on an electron or proton. (early 1900’s)
Materials
Conductors
•
Substances that have
easily moveable electric
charges
•
Most familiar conductors
are metals that have “free
electrons”
•
Positive ions may also be
mobile
–
Insulators
•
Charges cannot move
easily
•
Examples: plastic, wood,
glass
Semiconductor: used in
computers
Conduction is an intermediate
magnitude between a
conductor and an insulator
Superconductor: NO
resistance to the flow of
electrons. So far, no
material is a superconductor
except at extremely low
temperatures.
–
Water: insulator or conductor?
•
•
•
•
–
PURE water does NOT conduct
electricity
Impurities or ions in water can allow conduction
The purer the water, the lower the conductivity
(the conduction of electricity is called
ELECTROLYTIC behavior- )
Air: insulator or conductor?
•
•
•
Usually an insulator, thankfully
When strong forces are present, electron’s can be
stripped from air molecules, creating ions
example: lightning
Lightning
An electrical discharge between the clouds
and the ground or between two clouds.
As the electrons flow through the ionized
air, they generate so much heat that a
PLASMA is produced. We see that plasma
and call it LIGHTNING!
The air around the lightning expands so
rapidly from the heat that it creates a
strong pressure wave of air molecules
(that’s sound!)
We call that THUNDER!
How much electrical charge is flowing
through a lightning bolt?
Typically around 10 Coulombs of charge.
How many electrons, each with a negative
charge of 1.6 x 10-19 C, does it take to
have 10 C of charge?
10 C / 1.6 x 10-19 C =
6.25 x 1019 electrons !
How many electrons are flowing in a 12 C
lightning bolt?
7.5 x 1019 electrons
The Earth is able to absorb much electrical
charge.
Touching a charged object to the Earth in
order to discharge it is called
GROUNDING
•
Methods to electrically charge an
object
– Conduction:
• Direct contact: will transfer
electrons, such as touching your
car door in the winter
• Friction: rubbing your feet against
carpet, hair against a balloon
– Induction: no direct contact
• Start with a neutral object. Then, bring an electrically charged object
near, but not in contact with, a neutral object
• The charges in the neutral object will be “induced” to separate to get
closer or farther from the charged object.
• If provided a pathway, the separated electrons will leave.
• The object is now positively charged.
•
Static devices
– Electroscope: the
separation of metal
leaves indicates the
presence of static
charge
– Van de Graaff
generator: charge is
delivered by a rubber
belt to a metal dome
– Electrophorus a device
used to transfer electric
charge
•
Coulomb’s Law
–
–
Calculates the magnitude of the electric
force between two charges
Each charge experiences equal but
opposite forces
q1q2
F k 2
d
where k is a constant, k = 9 x 109 N·m2/C2
Coulomb’s Law looks VERY similar to
Newton’s Universal Law of Gravitation
FG
m1m2
d
2
Fk
q1q 2
d
2
Differences:
1. Gravitational Force is based on MASS.
Coulomb’s law is based on CHARGE.
2. Gravity is ALWAYS an attractive force.
The Electric Force can attract and repel.
3. “G” is a tiny number, therefore gravity force is a small
force.
“k” is a huge number, therefore electric force is a large
force.
Fk
q1q 2
d
2
Both laws are INVERSE SQUARE LAWS
“The Force varies with the inverse of the
distance squared.”
At twice the distance,  d2 = 22 in denominator
= ¼ the Force,
At three times the distance, 32 in denominator,
= 1/9 the Force
At half the distance,  (1/2)2 in denominator
= 4 times the Force
Now if one CHARGE, q, doubles…. The Force
doubles since they are directly related.
Remember….Force is a
VECTOR!
Electric Fields
A gravitational field
surrounds all masses.
An electric field surrounds
all charges.
The stronger the electric
charge, the stronger the
electric field surrounding
it.
Electric Field- the region around
every electric charge
The electric field around a charge can be
represented by
Electric field lines
Electric fields exist, but electric field lines
don’t really exist but provide a model of
the electric field.
Electric Field Lines
Electric field lines always point OUT of a positive
charge and INTO a negative charge
To indicate a stronger
electric field, just draw
MORE lines.
The farther apart the lines,
the weaker the field.
Since the electric field, E,
has both magnitude and
direction, it is a vector.
+2q
- 4q
+
One way to measure the strength of a
gravitational field is to release a mass in
the field and measure how strength of the
force exerted on it.
One way to measure the strength of an
electrical field is to release a charge in
the field and measure the strength of the
force exerted on it.
So… the strength of the electric field, E, is
given by
Electric Field = Force ÷ charge
E=F÷q
For example:
A 0.5 C charge experiences a force of 20 N
when placed in an electric field.
What is the strength of the electric field, E?
E=F÷q=
20 N ÷ 0.5 C =
40 N/C
The electric field near a charged
piece of plastic or styrofoam is
around 1000 N/C.
The electric field in a television
picture tube is around 10,000 N/C.
The electric field at the location of the
electron in a Hydrogen atom is
500,000,000,000 N/C!
The further you go from an electric
charge, the weaker the field
becomes.
• The electric field
INSIDE a hollow
conductor is ZERO
even if there are
charges on the
OUTSIDE of the
conductor!
Electric Shielding
There is no way to shield from
gravity, but there is a way to
shield from an electric field….
Surround yourself or whatever
you wish to shield with a
conductor (even if it is more
like a cage that a solid surface)
That’s why certain electric
components are enclosed in
metal boxes and even certain
cables, like coaxial cables have
a metal covering.
The covering shields them from
all outside electrical activity.
Michael Faraday, 1791-1867
Michael Faraday
demonstrated that the
electrostatic charge only
resides on the exterior of a
charged conductor, and
exterior charge has no
influence on anything
enclosed within a conductor.
This was one of many
contributions he made to
electromagnetic theory.
“Faraday Cage”
Are you safe from lightning inside
your car?
Why or why not?
Accelerating Charges
A charge placed in an electric field will
experience an electric force,
F = Eq
This force will make the charge accelerate
according to Newton’s Second Law
F = ma
What direction will a charge accelerate?
+
+
+
+
+
+
+
+
+
-
Positive charges will
accelerate in the same
direction as the
electric field.
Negative charges will
accelerate in the
opposite direction of
the electric field.
The Electric Field can
also be determined by
using Coulomb’s Law:
F
E 
q
k
q1q 2
d
q
2
k
q
d
2
Electric Potential Energy
d
Energy stored up
between 2 charges
separated by a
distance d:
q1q 2
UE  k
d
Unit: Joules
Changing the Electric Potential
Energy
If you raise or lower a mass in a
gravitational field, you change the
gravitational potential energy, UG.
If you move a charge in an electric field,
you change the
electric potential energy, UE.
Move a mass, m
Through a gravitational field, g
A distance, h
Gravitational Potential Energy, mgh
Move a charge, q
Through an electrical field, E
A distance, d
Electrical Potential Energy, qEd
The work energy required to move a charge through
an electric field is given by
+++
+++
+++
W = qEd
Two Ways to Find Electric Potential
Energy ?
q1q 2
UE  k
d
OR
Are these the same thing???
Which equation should be used??
qEd
Conversion of energy
Moving a mass or
moving a charge
takes
work energy
that is converted to
potential energy
Work = mgh
Or
Work = qEd
If you release an object
in a gravitational field,
its gravitational potential
energy is converted to
kinetic energy.
If you RELEASE a charge in an electrical
field, its potential energy is converted to
kinetic energy!
UE = ½ mv2
E
-
Examples
What is the potential
energy stored
between 2 charges of
3 C and 4 C
separated by 2 m?
5.4 x 1010 J
q1q 2
UE  k
d
It takes 2.43 x 10-15 J of work to move an
electron as distance of 2 m in an electric
field. What is the strength of the field?
W = qEd
E = 7600 N/C
The electron is then released. What is the
maximum velocity it will achieve?
2.43 x 10-15 J = W = qEd = ½ mv2
v = 7.3 x 107 m/s
If two charges are placed close to each
other and held in place, there is an electric
potential energy stored between them.
+
+
Two charges in an electric
+
field at the same location
+
+
+
will have twice as much
electric potential energy as
+
one charge;
Five charges will have five
time the potential energy,
and so on…
Electric potential energy
It is often convenient to
charge
consider the
electric potential energy per
charge.
Electric potential energy
charge
The concept of the electric potential energy
per charge has a special nameElectric Potential
Unit: Joule/coulomb.
However, it gets its own unit called a volt.
1 volt = 1 joule / coulomb
Since electric potential is measured in volts,
it is commonly called Voltage.
Electric Potential = Voltage
Voltage
Voltage can be thought of as a kind of pressureElectrical Pressure
Voltage is also called Electric Potential
Think of the water supply at your housesometimes you have high water pressure-water
flows quickly- and sometimes low water
pressure- water flows slowly.
With Higher Voltage (pressure), charges are able
to flow more quickly
Rub a balloon on your hair and it
becomes negatively charged, perhaps to
several thousand volts.
Does this mean that there’s a lot of
electrical energy?
Well, the charge transferred to the
balloon is typically less than a millionth of
a Coulomb (Remember, one Coulomb is charge is
a HUGE amount of charge)
There’s a LOT of difference
Voltage = Energy / charge
between Voltage and Energy!
Energy = Voltage x charge
Energy = 3000 V x 0.000001 C
Energy = 0.003 J
That’s not much energy!
High Voltage does not
necessarily mean that there’s a
lot of useful energy or that
something is dangerous.
High Voltage is not necessarily
dangerous- a Van de Graaff
generator can have more than
400,000 V, but there’s not much
charge that is transferred to you
from the globe.
Low Voltage is not necessarily safe.
Our houses are wired with 120V
and you can be killed from that
electricity.
Voltage (potential) is not the
dangerous part of electricity. The
dangerous part is how many
charges are flowing- the “current”.
The Electric Potential (Voltage), V, changes
as you move from one place to another
in an electric field
The change in Potential (“pressure”), called
the “Potential Difference” is given by
DV = Ed
Electric Field
3 meters
For example, the potential
difference between two
locations separated by 3
meters in a 4000 N/C electric
field is given by
DV = Ed = 4000 N/C x 3 m =
12,000 V
The work energy required to move a charge, q,
through an electric field, E, a distance d, is given by
+++
+++
+++
W = qEd = qDV
Sometimes, a charge is said to be located “at
ground”.
The potential (voltage) at “ground” is zero.
Vground = 0 Volts
There is another unit for very tiny amounts of
energy associated with atoms and sub-atomic
particles. It is called an “electron-Volt” or eV.
One electron-Volt is the amount of work energy
required to move one electron through 1 Volt of
potential difference.
In other words, 1 eV = W = qDV
= 1.6 x 10-19 C x 1V
So the conversion between eV’s and Joules is
1 eV = 1.6 x 10-19 J
V = ??
q
The Electric Potential, V, due to a point
charge, q, is given by
q
Vk
d
The potential will have the same sign
as the charge- there can be a large
positive and a large negative potential
At very great distances away from a charge…
d is very large…
q
Vk
d
The Potential, V, due to that charge is virtually ZERO.
Potential due to more than one
charge
Potential is NOT a vector…. (yea!!!)….So
The potential due to a group of point
charges is given by
q
V  k
d
Example
What is the potential halfway
between 2 charges of 3mC
and 4mC located 16 cm
apart?
787500V
What would be the potential
if the 4mC charge were
negative?
-112500 V
q
V  k
d
+
Higher V
Lower V
-
The potential near a positive charge will
be higher (it’s positive!) than the
potential near a negative charge (it’s
negative!).
• Therefore a positive charge will
accelerate from high to low V
• A negative charge will accelerate from
low to high V
Capacitors:
Electric Energy Storage
-
+
-
+
A device consisting of two
conductors placed near,
but not touching each
other in which electric
charge and energy can be
stored.
Capacitors are Used in
– camera flashes
– defibrillators
– Computers: tiny capacitors
store the 1’s and 0’s for the
binary code
– Many keyboards have a
capacitor beneath each key that
records every key stroke.
– Virtually every electronic device
Leyden Jar, the first
“capacitor”
Dutch physicist
Pieter van
Musschenbroek of the
University of Leyden
– The capacitance, C, measures how much
charge can be separated in the capacitor
per volt and is measured in farads, F.
– One farad is a very large capacitance, so
generally you will see mF, mF, nF, pF
Capacitance x Voltage = Charge separated
CV = q
Parallel-Plate capacitors
the capacitance is increased by placing an
insulating material, a dielectric, between
the two plates. It is NOT dependent on
the voltage of the battery.
The capacitance is given by
-
+
C=
e o A
d
-
+
A = area of plates
eo = permittivity of free space
 = dielectric constant
(air or vacuum,  = 1)
d = distance between the plates
Energy stored in a capacitor
Energy U = ½ CV2
Substituting from CV = q will yield other
equations for U.
Parallel-Plate capacitors
The Electric Field inside a
capacitor,
-
+
-
+
q
E
eo A
• Move to a sturdy building or car.
• Do not take shelter in small sheds, under isolated
trees, or in convertible automobiles.
• Get out of boats and away from water.
• Telephones lines and metal pipes can conduct
electricity. Unplug appliances if possible and
avoid using the telephone (unless it is an
emergency) or any electrical appliances.
• Do not take a bath or shower.
• If you are caught outdoors and
unable to find shelter:
• Find a low spot away from trees,
fences and poles.
• If you are in the woods, take
shelter under the shorter trees.
• If you feel your skin tingle or your
hair stand on end, squat low to
the ground on the balls of your
feet. Place you hands on your
knees, put your head down and
try to make yourself the smallest
target possible while minimizing
your contact with the ground.