Download neutral - Mr Bernabo at Affton High School

ELECTRIC CHARGE
Chapter 16
Just as the mass of the earth
exerts an invisible force on
you because of your mass.
Any two objects which
have an electric charge
also exert a force on
each other.
The electron on the comb is not moving so it is called:
STATIC ELECTRICITY
the study of stationary charges is called:
ELECTROSTATICS
Gravity
Which type of force is
generally stronger?
Electrical Force
little comb
paper
BIG EARTH
If I had two 1 kg piles of electrons separated by 1 m
1m
1 kg
e-
1 kg
e-
Their masses would attract each other due to gravity with a force of:
.000000000067 N
Their Charges would repel each other with an Electrical force of:
270,000,000,000,000,000,000,000,000,000,000 N
In Mechanics, a fundamental concept was
MASS.
We never really said what it is, just how it
behaves.
Gravity
Inertia
Momentum
Energy
With Electrostatics, a fundamental concept
is
CHARGE
We won’t define what it is or why it acts as
it does, just how it behaves.
There are ONLY 2 types of charges
Positive (+)
Negative (-)
LIKE CHARGES REPEL
+
+
-
-
OPPOSITE CHARGES ATTRACT
-
+
Charge maze game applet
All charge in the universe comes from two particles
Electrons (-)
Protons(+)
How can an atom be neutral?
+ +
-
Neutral
+ +
2 protons & 2 electrons
How does an atom become a
positive ion?
-
positive 2 protons & 1 electrons
+ +
CATION
Negative?
-
-
+ +
ANION
-
negative 2 protons & 3 electrons
The charge of an electron is equal &
opposite the charge on a proton
-
+
if an electron is -1
a proton is exactly +1
The smallest amount of
charge possible is the
charge on 1 electron
or 1 proton
the charge on any object is
a multiple of this amount
-
+
Our charge cannot not be split into a smaller piece of charge
Conservation of Charge
Charge is not created or destroyed,
but it can move from 1 object to another
Some materials are very good at holding onto their
own electrons or stealing them from other objects.
Like:
Plastics and Rubber
Others don’t hold on to their electrons well and
tend to lose them.
Like:
hair or glass
They start
When
two out
materials
with NO
areNET
rubbed,
CHARGE.
usually electrons get
stolenare
Why
bythey
one the
neutral?
of the objects.
cloth
glass
+ +
- - - +
+
+
+
-
After the electrons move. What it the charge on each
object?
cloth
glass
+
+ +
- - - + +
+
-
Negative
Positive
If a piece of Plastic is rubbed on the same cloth
(neutral again)
cloth
rubber
+ +
- -
+
-
+
+
+
-
If a piece of Plastic is rubbed on the same cloth
(neutral again)
cloth
rubber
+
+ + +
+
- - +
-
They both end up charged
cloth
rubber
+
+ + +
- +
+
-
Positive
Negative
CHARGE IS NOT CREATED
It is only transferred between OBJECTS
2+
0
+ +
- - - +
+
-
+
+
0
+
+
+
0+0=0
e-s
2+
+
+
2+ + 2- = 0
2e-s
thus CHARGE IS CONSERVED
0+0=0
(2+) + (2-) = 0
0=0
Initial = Final
RECAP
How does an object become
negatively charged
It GAINS Electrons
positively charged
It LOSES Electrons
An object DOES NOT gain protons to become positively charged.
This would be a NUCLEAR REACTION.
John Travoltage applet
BEN FRANKLIN FOUND THAT
+
+
+
Repel
+
+
-
-
+
-+
+
-
+
+
Repel
-+
+
-
+
+
-
+ Attract +
+
+
-
-
So he knew that the charges were different
+
+
+
I dub thou charge on the
glass rod POSITIVE.
and Rubber rod shall be
NEGATIVE
-
+
-+
+
-
This were arbitrary
1-
1+
- + -
The smallest charge
an object can have is
1 electron
+
charge is QUANTIFIED
(comes in chunks)
The SI unit of CHARGE is a COULOMB (C)
The smallest possible AMOUNT charge is
(the charge on 1 electron)
e = 1.60 x
-19
10
C
All Net charge is a multiple of this amount
In other words charge is quantized, it only come in
discrete packets or quantities.
How many electrons do I need to have 1 full
coulomb of charge?
e = 1.60 x
-19
10
C
Millikan oil drop video clip ( in folder)
Video via you tube
The force exerted between two charged objects is
Charge on object #1 (C)
F12 = F21 (N)
k Q1 Q2
F=
2
r
r
Q1
Q2
Charge on
object #2 (C)
distance
between (m)
Coulomb’s Constant=
8.988 109 N m2
C2
k Q1 Q2
F=
2
r
This equation is known as COULOMB’S LAW
k Q1 Q2
F=
2
r
1
k = 4pe
0
A fundamental constant known as
THE PERMITTIVITY OF FREE SPACE
= 8.85 10-12 C2/N m2
So in some cases you will see Coulomb’s law written like this.
If so I would think that you will be given eo
Q
Q
1
1 2
F = 4pe r2
0
You generally will need a direction for the force. I typically
use a picture to determine direction and simply put in the
charges without their signs.
k Q1 Q2
F=
2
r
Force of Gravity
6.667 10-11 (little)
Coulombic Force
8.988 109(BIG)
k Q1 Q2
G m1 m2
F=
F
=
2
2
r
r
Proportional to mass
Proportional to charge
BOTH FOLLOW INVERSE SQUARE LAW
Force of Gravity
Coulombic Force
k Q1 Q2
G m1 m2
F=
F
=
2
2
r
r
Always attractive
Mass is always positive
Can be attractive
or repulsive
Charge can be positive
or negative
What is the magnitude of electrostatic
force on a 1s electron in a helium atom
due to the nucleus. The distance from
electron to the nucleus is .53 x 10-10 m
What is the direction of the force on the electron?
What is the magnitude and direction of the force on the nucleus?
How would the force change if the radius was doubled?
How would the force change if the nucleus had two protons?
What if the charge on both were doubled?
A fixed proton and an electron are
separated by some distance. When the
electron is released released the ......
The force on the e- them will_______
increase
increase
The acceleration of the e- will_______
increase
The velocity of the e- will_______
A fixed electron and another electron are
separated by some distance. When the
electron is released released the ......
The force on the e- them will_______
decrease
decrease
The acceleration of the e- will_______
increase
The velocity of the e- will_______
Page 497: 1, 2, 5
2.7 N
http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html
Coulomb’s Law only gives us the force between two
particles. If more than 2 are present the forces just add
or subtract
Find the Resultant Force on Particle #2
Q3 = -21.5 mC
Q1 = -15.4 mC
-
.50 m
+
.65 m
Q2 = +80.6 mC
F2,1 = 44.6 N
FNET = 7.7 N
+
+
F2,3 = 36.9 N
-
F=
k Q1 Q2
r2
If the particles are not in a line, you can
still add the forces together.
Remember adding vectors?
+
1
+
2
3
-
Let’s look at the direction of the forces on PARTICLE #2
How would we find the Total Force on #2?
+
1
+
2
3
-
F2,3
F2,1
How would we find the Total Force on #2?
Resultant Force
F21
F23
Find the Resultant Force on Particle #2
-
Q1 = -2.5 x 10-5 C
.65 m
Q3 = +1.4 x 10-5 C
+
.50 m
+
Q2 = +8.6 x 10-5 C
Problems:
Honors Physics
Page 497: 11, 14
2.96 x 105 N
Electrons can travel
easily through some
materials
but are STUCK in
place in others
Conductor- electrons travel easily
Insulator- electrons are tightly bound
Electricity will travel hundreds of miles through
metal wire (conductor) rather than a few
centimeters of glass (insulator).
If a charge is placed on a conductor, the like
charges repel each other and excess charge
migrates to the surface of a conductor to get as
far as possible
- from other like charges.
- -
Negatively charged
metal sphere
+
+
+
+
+
+
Positively charged
metal sphere
--- - - - - - - - - - -- - - - - - - - - - --
If a charge is placed on a INSULATOR, electrons are stuck where
they land. So charged patches can be seen.
---- --
-- -- ------- --
like your black slate desk top
What would have happened to cause a positive patch your desk?
Friction (rubbing) is not the only an
object can be charged
Starting with a negatively charged sphere and a neutral one
separated by air
Negative Metal Sphere
-
-
- -
Note: the extra electron on
this sphere repel each
other and spread out
Neutral Metal Sphere
They electrons
If they are
(repelling)
brought into
are contact
able to spread out further,
charging the other sphere!
-
-
- -
Note the spheres would
now repel each other
The second sphere was charged by CONDUCTION.
CONDUCTION- Charging by contact.
-
-
COPPER
-
- -
The charge was CONDUCTED, through the copper
-
-
Glass
- -
NO CONDUCTION THROUGH AN INSULATOR
How would a neutral object become positively
charged by conduction?
positively charged, fewer
electrons than protons
Neutral
+
-+
+
-
+
- +-
-+
+
-
+
-+
-
+
-+
How would a neutral object become positively
charged by conduction?
Neutral
positive
+
-+
+
-
positive
+
- +-
-+ +-
+
-
+
-+
+
Electron leave the neutral object
a negative
object
brought
near
(but notside
touching)
a neutralside.
one
TheIfneutral
object
will is
end
up with
a positive
and a negative
Negative
-
- -
Neutral
+
-+
+
-
+
- +-
-+
it is still neutral
but now polar
This movement of charge (without contact)
is called induction
The
If neutral
theIfsphere
a negative
object
moves
will
object
back,
endisupthe
brought
with
sphere
a near
positive
is still
a neutral
side
neutral
and
onebut
a negative
not polar
side
Negative
Neutral
-
- -
+
+
+
- -+
-+
+
The process of induction will cause a charged object
to attract a neutral one
-
-
+
+
-+
- -
-
+
-+
- +-
Attract
-
- -
---
++
+
+
+
+
Distance
Why are the attractive forces stronger than the repulsive ones?
Neutral objects are attracted to charged objects
Charged comb attracts neutral
bits of paper.
Charged comb attracts
neutral water molecules.
Demo soda can- attraction by induction
Here a sphere shows an induced polarity, they attract.
Will they be attracted or repelled after they touch?
Attract
-
- -
+ ++ +- ++
-++
++ - + +- -
NOW THEY BOTH HAVE A NET NEGATIVE CHARGE!!!!
REPEL
Two neutral metal spheres are in contact.
If a negatively charged sphere is brought near…..
What would happen if this sphere moved back away?
-
- -
+
-+
+
-
-+ ++
+
- +-
+
-
+
- +-
-+
INDUCTION can be used to create a “permanent” charge on an object
2 neutral metal spheres in contact, and a charged one is brought close.
-
- -
+
-+
+
-
-+ ++
+
- +-
+
-
+
- +-
-+
When the spheres are separated. They remain charged even if the left
sphere is removed. WHY?
Are the charges on the
remaining spheres equal
and opposite?
- -
+
+
+
+
+
+
+ -+
-++
-+
- -+ -
The earth is neutral (and really big). So it
acts like a charge reservoir. If a negatively
charged object touches a conductor which
is “grounded”….
--
neutral
Electrons will flow to the earth. The earth
is so big it is still essentially neutral & so is
the object
--neutral
If a positively charged object touches a
conductor which is “grounded”….
+
+ +
+
+
-+
neutral
+-
-+
-+
+
+
-
-
Electrons from the earth flow to the
positive object. Again both objects are now
neutral
-+
+ +
e-’s
neutral
Charging by induction and grounding
-
+
-
+
-
+
+
+
+
- -+
+
Charging by induction and grounding
-
+
+
+
+
+
+
-+--- +
- - --
What would the charge be on the can if a
positively charged rod was used instead?
+
+
+
+
+
+
+
-
+
-
+
+
+
+
-- ++
-
+
-+
What would the charge be on the can if a
positively charged rod was used instead?
+
+
+
+
+
+
-+
-+
+
-
+
-- ++
-
+
-+
+
+
The hand acts as a GROUND in this experiment
Demo soda can- attraction by induction
(rolling)
Demo 2 soda cans & van de graaf)
alligator clip
alligator clip
ground
attraction by induction, repulsion after conduction, neutralization by grounding
Charging an object by induction & grounding
-
-
- -
animation
-
---
++
- -
- -
+
+
+
+
+
+
+
+
+
+
+
+
+
the right sphere
is grounded
+
+
+
Earth Ground
both spheres are
now charged
neutral
-
-
+
+
-
Positive
+
+
+
-+
-
-
+
-
Negative
+
+
neutral
+
+
+
+ - -
+
+
-+
-
-
+
+
+
+
+
+
+
+
+
+
+
+ - -
+
+
+
+ - -
These spheres have been charged by INDUCTION
animation
an ELECTROSCOPE is a device used to detect charge
INSULATORS
Metal ball & Rod
Rubber Stopper
Glass Flask
Thin Metal
Foil Strips
It can start out neutral
+
-+ -
-+
+-+
If a negatively charged object is brought near
- - - -- - - -- - - +
+
Electrons are repelled
down to the foil strips
+
-+
+
- -
The negatively charged
foil strips repel each other
(charged by induction)
If the rod is taken away, electrons redistribute themselves again
+
-+ -
-+
+-+
If a negatively charged object is brought near again.
And then touches
- - - -- - - -- - - +
+
+
-+
+
- -
Electrons will move from the rod to the electroscope
Now the electroscope
is negatively charged
by:
contact
or
conduction
- - +
- -+
+
-+
+
- -
Even if the rod is removed, the negative charge
remains and the leaves STILL repel each other
+
- -+
+
-+
+
- -
If a positively charged rod is brought near
+ + + + + + +
+
- -+
+
-+
+
- -
If a positively charged rod is brought near
Electrons migrate
from the leaves
toward the positive
rod reducing their
repulsion
+ + + + + + +
--+--+-
-
+
+-+
Powder Painting
PHOTOCOPIERS
Copy Machine (animation)
LASERPRINTERS
Electrostatic Precipitators
Problems involving static charge
Electronics
lightning
winter and door knobs
Problems and Questions:
1.) At automobile toll-collecting stations a thin metal wire sticks up from the road and makes
contact with cars before they reach the toll collector. What is the purpose of this wire?
2.) Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to
conducting electricity?
3.) Would it be necessary for a charged body to actually touch the ball of the electroscope for the
leaves to diverge? Explain.
4.) Strictly speaking, when an object acquires a positive charge, what happens to its mass? If it
acquires a negative charge?
5.) How can you charge an object negatively with only the help of a positively charged object?
6.) Which of the two would be safer: a house with no lightning rod , or , a house with a lightning
rod not connected to the ground? Explain.
7.) Why is a good conductor of electricity also a good conductor of heat?
8.) If you rub an inflated balloon against your hair and place it against the wall, it will stick.
Explain.
9.) How are electrically neutral atoms and molecules able to electrically attract each other?
10.) Five pith balls are tested against each other, Ball A attracts B and repels C. Ball D has no
effect on E. Are all the pith balls charged? What charges are on the pith balls?
11.) Describe the process of putting a negative charge on an electroscope by induction. Use
diagrams as necessary and explain the motion of the electrons in the electroscope in terms of
attractive and repulsive forces between
the charges.
Static Electricity Lab
Triboelectric series



























Human Hands (if very dry)
Leather
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 (scotch tape)
Polypropylene Vinyl (PVC)
Silicon
Teflon
ELECTRON GIVERS (Positive)
ELECTRON STEALERS (Negative)
WHAT 3 types of things can exert a force
without physical contact with the other object
Electric Charge
Magnets
Gravity(mass)
Electric Charge
Magnets
Gravity(mass)
Exert a force without
contact through a vacuum
That really bugs me.
A charge creates a FIELD,
and the field exerts a
force on objects in it
-
+
Electric Field
Electric, Magnetic, and Gravitational Fields are FORCE FIELDS
An ELECTRIC FIELD cannot be seen directly. But it can be felt.
An electric field is mapped out by placing a POSITIVE “test
particle” in it and measuring the force on the test particle.
2+
Compare the
magnitude and
direction of the
force felt by the
particles
+
3
+
1
To show each Force vector at every
possible location would be too messy.
applet
Electric Field Vector Map (applet)
FIELD LINES are used to simplify the picture
Arrows point in
the direction of the
force a positive
test charge would
feel at that location
FIELD LINES are used to simplify the picture
Lines are CLOSE
where Field is
STRONG
and FURTHER
where field is
weaker
Why do field line arrow point TOWARDS a negative CHARGE
Compare the two sets of Field Lines
Field around 2 positive charges
+
+
what is the field midway
between the two charges?
applet
Field around 2 opposite charges
Field Lines are like a map.
How does is a topography map show elevation changes
They indicate the magnitude and direction of the Field (vector).
The direction FIELD LINE is also the direction of the FORCE
ON A POSITIVE TEST PARTICLE
Electric Field applet
Field Lines around charged parallel plates
Note evenly placed field lines within between charged plates
indicate a uniform strength electric field. I.e. same force but
continuous force on a charge object in the field
DO MORE HERE WITH INTERPRETING FIELD LINES
See ActFF025-fieldlines in maloney file
What would field lines look like outside of a charged metal ring?
-
-
-
-
-
-
-
-
-
-
-
-
What about on the inside?
Lets put a test charge in and see which way it is pulled.
-
-
-
-
-
-
-
-
+
No
Electric
Field on
the inside
-
-
-
-
Inside of a charge CONDUCTING object, there is no NET FORCE
and NO FIELD (no matter the shape of the object)
animation of hollow conductor
An electric field does not affect the inside
of a conductor. It is SHIELDED
The rubber tires DO
NOT PROTECT
YOU in a car.
The lightning just
jumped over 1,000 ft
through air (a few
inches of rubber are
no problem).
You are surrounded by a conductor and so the electric field
inside is ZERO.
The person is shielded from the electric field, perfectly safe.
This type of demo uses a Faraday Cage named for Michael Faraday.
We’ll see him later with magnetism
When determining the field around a charge, why should we
use a small test charge?
Object creating field to be measured
-
+
small test charge
BECAUSE the test charge creates its own field.
The field generated by a charge must be found by using
a test charge and looking for the force on it
F=
+q
Q
k Qq
r2
What would happen to the force
on the test particle if its charge
was doubled?
Did the electric Field from
particle 1 change?
The field generated by a charge must be found by using
a test charge and looking for the force on it
(Test Charge)
+q
Q
F=
k Qq
r2
The force measured on the test
particle depends on its own
charge
The ELECTRIC FIELD we are
measuring DOES NOT depend
on the test particle
Electric Field (N/C)
q(Test Charge)
+
Q
Force on Test Charge
E=
F
q
Charge on Test Charge (C)
So the charge of the
test particle is
divided out
E=
q
Q
F
q
Electric Field is 24 N/C here.
What would be the direction
and magnitude of force of a
2 C charge placed here?
F=
+q
Q
E=
E=
F
q
k Qq
q r2
k Qq
r2
+
Q
q
kQ
E= 2
r
The Strength of an electric Field:
Increases with the charge of the object creating it
Decreases with the square of the distance from the object creating it
a hammerhead shark
biting at an electrode
All living marine organisms generate an electric field around their
body and some animals possess a sensory system (the Ampullae of
Lorenzini) which enables them to detect weak electric fields and use
them to orient to cryptic prey.
What is the strength and direction of the
electric field 2.5 x 10-9 m to the right of
an electron?
Electric Fields can add or subtract just like FORCES
What is show is the “net” electric field
Here Two electric Fields are affecting our Test
Charge. What is the direction of each field at
its location?
Q1
-
E1
E2
Q2
-
+
Test Charge
Why is the field from particle 1 stronger at that point?
Will the Forces on the test particle add or subtract
+
E1 + E2 =
=
What is the direction of the two electric fields at the test charge?
Q1
-
E1
E2
Q2
+
+
Test Charge
Will the Forces on the test particle add or subtract
+
E1 + E2 =
=
10-11 m
5x10-11 m
Q2
+
Q1
e-
p+
What is the strength of the field at
the blue point?
And what is the force on a 1mC
charge at that location?
E1
+
E2
Q2
-
Q1
-
What direction would the net electric field point at the test charge?
Electric Field applet
Electric Field Strength (at a given location) tells
you the amount of FORCE per charge
-
+
2+
+
+
+
+
+
+
+
+
Both charges feel the same field strength but
different forces
Basic dialogue
Energy was useful in mechanics
Relate PE of charge and gravity
Use test + test particle to show low and high PE’s
Intro voltage, increase or decrease based on + particle
+ charges tend to go from high to low potentials,
-charges tend to go from low to high potentials
Voltage always based on differences, like energy
Usually ground is considered zero-tie to GPE
Similarly 2 masses on the surface of the earth
experience the same gravitational field strength
(9.8 m/s2)
but the one with twice the mass, experiences
twice the force
Field strength and Potential energy are related
but different....
What
happens
to the
Potential
Energy as
What
happens
to the
field strength
the as
object
is lifted
this case)?
the object
is (in
lifted?
Why does a rock lifted up on earth gain POTENTIAL ENERGY
You sure do
have potential,
son!!
The PE is the amount of Work done
to lift the object against the force of gravity.
PE = mgh = W = Fd
h
The FORCE of Gravity, can convert its height to Kinetic Energy
( it is in a gravitational field)
Weeeee
+
Gravitational
Potential Energy
Electric
Potential Energy
-
+
Both can be converted to KE
-
Work must be done to move
against a force to put them back
in the same spot
+
-
Does the Electric Potential Energy
increase or decrease?
1
-
+
2
-
+
Does the Electric Potential Energy
increase or decrease?
1
+
+
2
+
+
If 2 J of work was done to push
them closer. Then 2 J of electric
potential energy was gained
1
+
+
2
+
+
The monkey does work to bring the charges closer.
That energy can be converted to kinetic energy when released
UE
V= q
electric
potential
energy
electric potential
(in Volts or V)
electric potential is the Joules of energy per unit charge.
So one way of expressing volts is J/C
Remember if we say the rock has 9.8 J of Ug,
We really mean, it has 9.8 J of Ug compared to…
1 kg
1m
DUE
DV = q
We really mean than the difference in voltage is proportional
to the difference in potential energy between two locations.
Usually we consider one state to have an
energy of zero. Which is…
1 kg
1m
DUE
DV = q
We can only measure the voltage DIFFERENCE between
two position. Usually a grounded wire is considered to be a
a zero potential
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
What happens to the potential energy of the
particle as it is moved?
+
Potential energy increases
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
+
Low Voltage
+ High Voltage
+
+
+
Where would voltage (electric potential)
+
be higher?
+
+
+
+
+
+
+
+
+
+
+
+
+
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
+
Low Voltage
+ High Voltage
+
+
+
+
CHANGES IN VOLTAGE are ALWAYS
+
based on a POSITIVE test charge.
+
+
+
+
+
+
+
+
+
+
+
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
+
Low Voltage
+ High Voltage
+
+
+
+
+
+
+
+
+
+
Positive
charges
naturally
move
+
High to ______
Low potentials
+ from________
+
+
Know this
+
+
+
-
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
+
Low Voltage
+ High Voltage
+
+
+
+
+
+
+
+
+
+
Negative
charges
naturally
move
+
Low to ______
High potentials
+ from________
+
+
Know this
+
+
+
-
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
+
Low Voltage
+ High Voltage
+
+
+
+
+
+
+
+
+
+
The
two
charges
are
moved
from
+
+ low to high potentials.
Increases
+ The U of the + charge_________
E
+
Decreases
The UE of the + charge_________
+
+
+
-
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
or work
We say that the original position has no
energy, so its voltage is Zero
DUE
DV = q
or work
We say that the original position has no
energy, so its voltage is Zero
DUE
DV = q
or work
Since the voltage changed by 10 V,
we did 30 J of work to move the charges
DUE
DV = q
Gravitational potential energy
Lifting a rock that has twice the mass
Requires twice the work.
Moving a particle that has twice the charge also requires
twice the work, because it has twice the force.
UE
V= q
Electric Potential or Voltage is the electric
potential energy per charge.
This ONLY depends on the location /
strength of the electric field
not the “test charge”
The more Voltage DIFFRENCE, the Greater the difference in
ENERGY each electron has
Electric Field =
Voltage =
electric potential
Force
q
UE
q
electric
potential
energy
This particle has twice the potential energy but the
same electric potential (voltage). Energy per charge.
This just depends on location and the source charge!
-
2-
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Demo- Van de Graaff Generator
Charges in electric field have energy
Voltage is the energy per unit charge
(basically it just depends on location)
Electric Potential Energy (J)
UE
V= q
Charge (C)
Electric Potential (J/C or Volts)
OUR Van de Graaf Generator creates a voltage
of
50,000 V
or
50,000 J/C
WHY is there not that much energy
discharged when you get ZAPPED??
There is not that much CHARGE!!
Some Voltages (Potentials)
Lightning
Our VDG
Residential Electric
D battery
100,000,000 Volts
50,000 Volts
120 Volts
1.5 Volts
How much electric potential energy does 2
coulombs of charge have at 120 V
(standard household voltage).
UE
V= q
Rearranging
UE = V q
and more correctly written
DUE = qDV
A common unit of measuring very small
amounts of energy is an electron volt (eV)
UE = qV
1 eV= 1.60x10-19 C 1V
1 eV= 1.60x10-19 J
Potential Energy looks at a change in position.
Usually one state is said to have zero potential
DPE = mgDh
DPE = qDV
- - - -- - - -- - - DV
-
Dh
+ + + + + + +
How much PE does an electron have in a
lightning bolt about to strike?
Assume the voltage is 100,000,000 (108)Volts.
DUE = QDV
charge on an electron: 1.6x10-19 C
How fast is it moving when it strikes the ground?
mass of an electron: 9.1 x10-31 kg
A charge +2 C, is in a uniform electric field of 6 N/C between two
parallel plates as indicated in the diagram below. If the charge is
moved 3 meters
-- how much work was done,
--by how much did its energy change,
--What is the change in electric potential (& increase or --decrease),
--did it gain or lose electric potential energy?
3m
+
+
E = 6 N/C
A charge +2 C, is in a uniform electric field of 6 N/C between
two parallel plates as indicated in the diagram below. If the
charge is moved 3 meters how much work was done, by how
much did its energy change, did it gain or lose electric potential
energy.?
+
3m
+
E = 6 N/C
A charge +2 C, is in a uniform electric field of 6 N/C between
two parallel plates as indicated in the diagram below. If the
charge is moved 3 meters how much work was done, by how
much did its energy change, did it gain or lose electric potential
energy.?
E = 6 N/C
3m
+
45o
+
Solving this generically, a charge (q) in a uniform electric field (E)
moved a distance (d) parallel with the field.
F
E= q
Plugging in
for F…..
W=Fd
Solving for F
DUE = q E d
F= q E
E
+
W=qEd
+
And we all
know work =
the change in
….
DUE = qEd
The change in electric potential for a charge in a uniform
Electric field. Uniform meaning that field strength is constant
as is the case between parallel plates.
DUE = qEd
DUE
=V
q
V = Ed
And of course by V we really mean DV, a comparison
between two states… One usually taken to be Zero.
V=Ed
+
+
+
+
+
+
E
d
-
-
-
battery
-
-
-
The Field must be uniform for this to work
V=Ed
+
+
+
+
+
+
E
.11 m
-
-
-
12 V
battery
-
-
-
What is the strength of the electric field between the plates
More than one spot can have the same Potential (voltage)
Meaning if an electron was place in anywhere along 1 dashed line it would have the
same UE
These are indicated by EQUIPOTENTIAL LINES
Which electrons have the same electric potential?
-
-
-
Both electrons have the same potential energy.
Because they are the same distance from the charge
and the field strength is the same as well.
-
The voltage is the same
along an equipotential
line
Equipotential lines must be perpendicular to field
line…
For the equipotential lines shown, draw an electric field line
Voltage is based on energy per charge.
To find the voltage “at a given location”, we compare
it to a position where the voltage is considered to be
zero. Where would a positive test charge have the
least/Zero electric potential energy?
At infinite distance
+
To find the voltage “at a given location”, the amount
of work to bring a particle to that location from an
infinite distance is calculated.
from an infinite
distance
+
k Qq
F= 2
r
Work = F d
UE so
F
d
V=
V=
q
q
ra= ∞
+Q
rb
q
Fd
V=
q
k Qq d
= q r2
ra= ∞
+Q
rb
q
k Q dr
V= 2
r
The distance is really r
so...
ra= ∞
+Q
rb
q
kQ
V= r
The difference in voltage between the two locations
k
Q
k
Q
DVab = Vb - Va =
rb
ra
ra= ∞
+Q
rb
q
The change in voltage of a particle brought from infinite
distance (and zero force) to a distance r from the charge.
kQ
V= r
ra= ∞
+Q
rb
q
kQ
V= r
r
This equation yields the change in
voltage of a particle brought from
infinite distance to a distance r from
the charge. It can be thought of as
just the voltage at that location.
Or Voltage can be figured out by calculus
kQ
V= r
An electron is brought from an infinite distance to a
distance of 1 nm from a proton.
What is the voltage at that location?
Does the voltage depend on the electron being there?
How much work was done?
If a particle is moved from one location to another,
just find the voltage at both locations and subtract
them.
If the charge moved was 3 C,
how much work was done?
V1 = 4 V
V2= 9 V
What happens to the electric field as the
test particle is brought on an approaching
equidistant path.
+
+
-
A side note, electric potentials do have
signs based on the source charge.
Consider the test + charge brought in from infinity and
brought to the location below.
As it got closer to the two charges,
the red positive object caused its PE and V to....
the blue negative object caused its PE and V to....
+
+
-
What is the electric potential at a location 10
meters from the two charges below?
How much work was done to bring and electron to
this location?
2C
-3C
Common Misconceptions
Electric Potential Energy is not the same as Electrical Potential.
Electrical Potential can also be described by the terms, potential
difference, voltage, potential drop, potential rise.
The variable we use for potential difference is V and the unit for
potential difference is also V (volts). Don't let that confuse you when
you see V = 1.5V
The electron volt is not a smaller unit of the volt, it's a smaller unit of the
Joule.
The Electric Field inside of a conductor (charged or
not) must be 0. Why?
-
-
-
-
-
-
-
-
-
-
-
-
Why excess charge distributes itself out until the net
force on any excess charge is zero.
-
- - - - -
-
---
-
-
-
-
The electric field inside of a conductor is always zero,
EVEN if…
the conductor isn’t round
or a charge is placed inside a hollow conductor
Because the excess charge on a conductor can move
and will do so until there is no net force on them even
in a charge is placed inside a hollow conductor.
If there is no net force on the excess charge on the
outside of a hollow conductor due to charge inside….
(Newton’s 3rd law says).
F
E= q
In order to accomplish this, excess charge tends to concentrate
on the “sharper” parts of a hollow conductor. (probably not that
important). But the electric field inside each is still zero.
Is there an electric field outside the conductor?
This is an AP objective so copy this down
R
r
kQ
E = R2
(At the surface)
kQ
E = r2
(away from the surface)
Inside the conductor the electric field is zero
Back to electric potential (voltage). A change in voltage occurs
when work changes the electric energy of a charged particle.
How would I calculate the work involved to move a charge
particle in a hollow conductor?
+
+
E=0
+
+
+
+
+
+
+
F=0
+
W=0
+
DV = 0
+
+
+
+
+
+
The electric potential
in a hollow conductor
is constant
Would there be work to bring a charged particle from a distance
away from the conductor to inside of it?
YES
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Also an AP objective
R
r
kQ (At the surface and inside)
V= R
kQ Outside of the
V= r
sphere
Going back to conductors connected by wires
-
-
COPPER
-
- -
When equilibrium is established (this is assumed)…
The net force on any excess charge is zero which means anywhere
on or in a conductor means….
Zero
The net force on a charge particle is___________
Zero
The electric field is ____________
Constant
The electric potential is___________
AP objective
Explain why a conductor must be an
equipotential, and apply this principle
in analyzing what happens when
conductors are connected by wires.
Capacitors store energy in an electric field
They come in all shapes and sizes
Capacitors the energy for a camera flash
the energy is stored slowly and released QUICKLY
the capacitor from a camera being discharged by
“shorting the circuit”
BIG capacitors store energy to be used when you
Air conditioner starts up.
They are used in most electronic device like TV’s.
They retain their energy even when the power is off.
So be careful when digging around in one.
Conducting plates are connected to a battery (or another power source)
the plates do not touch and are separated by an insulator like air,
capacitor animation
When connected electrons flow building up charge on the plates
The Voltage across the plates will eventually be the same as the battery
1.5 V
-
+
+
+
+
e-
1.5 V
capacitor animation
e-
The total charge that can be stored in a capacitor is
Q = CV
voltage of power source
Stored Charge
(Coulombs)
Capacitance (farads, F)
a fudge factor based on the actual capacitor’s
size and materials
The greater the voltage source and capacitance
the more charge can be stored
The capacitance depends on the:
dielectric constant of
material between the
plates (page 514)
e0 =8.85x10-12 C2/Nm2
Ke0A
C=
d
A (area)
What will units on A and d be?
d
Table of dielectric constants
Inserting a dielectric
material between the
capacitor plates reduces the
electric field there
Material
Vacuum
Air(1 atm)
Air(100 atm)
Teflon
Polyethylene
Benzene
Mylar
Polyvinyl
chloride
Plexiglas
Neoprene
Glass
Germanium
Liquid
ammonia(-78°C
Glycerin
Water
Strontiun
titanate
Dielectric
Constant
1
1.00059
1.0548
2.1
2.25
2.284
3.1
3.18
3.4
6.7
7
16
25
42.5
80.4
310
Ke0A
C=
d
Q = CV
Inserting a dielectric material improves the capacitor by
1.) Increases the voltage you can apply
before a spark jumps between the plates
2.) Allows the plates to be closer together
without sparking. Reducing d increases C.
3.) By simply being there, increases the
capacitance by the factor “K”.
Ke0A
C=
d
Q = CV
Two metal plates are separated by some distance with air between
them forming a capacitor. They are connected to a 12 V battery.
If a dielectric material such as teflon is placed between them, what
happens to the amount of charged stored on the plates?
Good animation for this
Ke0A
C=
d
Q = CV
For a given applied voltage.....
As area of the plates increases the amount of charge
that can be stored
As distance between the plates increases the amount
of charge that can be stored
Capacitance DOES NOT depend on its voltage or
charge, just its structure. (like a storage tank)
Typical Capacitance ranges from
mF =
-6
10
F
pF = 10-12 F
To increase the area of the plates without making the capacitor huge,
the “plates” are sandwiched between a dielectric material and rolled up.
Capacitors are essentially parallel plates. What
does the electric field look like between two
charged electric plates.
UNIFORM
+
+
+
+
+
+
E
d
-
-
-
battery
-
-
-
What is the relationship between electric field inside a parallel plate
capacitor, the voltage, and plate separation.
V=Ed
+
+
+
+
+
+
E
d
-
-
-
V
V
battery
-
-
-
So as
Or…
voltage___ electric field ____
V
E= d
+
+
distance___ electric field ____
+
+
+
+
E
d
-
-
-
V
battery
-
-
-
What is the capacitance of two sheets of
aluminum foil, each .30 m x 1.5 m. Which
are separated by paper (K = 5.0) which is .50
mm thick.
What is the total charge, if connect to a 9.0 V battery?
A capacitor stores energy
What determines the amount of energy, for a
given capacitor
QV
UE = 2
Energy (J)
Charge on capacitor (C)
Voltage between
plates (V)
Since
Q = CV
plugging in for V
plugging in for Q
2
Q
QV
U=
=
=
2 2C
2
CV
2
How much energy was stored on our
aluminum foil capacitor (C= 4.0 x 10-8 F)
charged to 12 V?
Capacitance Problems
Honors Physics
Page 524: 32, 33, 39