ELECTRIC CHARGEChapter 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

Which type of force is generally stronger?

Gravity

Electrical Force

BIG EARTH

little comb

paper

1 m

If I had two 1 kg piles of electrons separated by 1 m

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

1 kge-

1 kge-

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

-

++

CATION

positive 2 protons & 1 electrons

-

++

ANION

--negative 2 protons & 3 electrons

How does an atom become a positive ion?

Negative?

The charge of an electron is equal & opposite the charge on a proton

-

+

if an electron is -1

a proton is exactly +1

- +

Our charge cannot not be split into a smaller piece of charge

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

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

When two materials are rubbed, usually electrons get stolen by one the of the objects.

+ + +---cloth

glass

+

+-

-

+-

They start out with NO NET CHARGE. Why are they neutral?

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

+

+-

-

+-

-

-

Negative

Positive

+ + +---

+

+-

-

+-

e-s

CHARGE IS NOT CREATED

+ + +

-

-

-

+

+

--+

-

2e-s

2+

2-

0

It is only transferred between OBJECTS

0

0 + 0 = 0 2+ + 2- = 0

thus CHARGE IS CONSERVED

0 + 0 = 0 (2+) + (2-) = 0

0 = 0

Initial = Final

negatively charged It GAINS Electrons

positively charged

How does an object become

An object DOES NOT gain protons to become positively charged.This would be a NUCLEAR REACTION.

RECAP

It LOSES Electrons

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

+ -

+

The smallest charge an object can have is

1 electron

charge is QUANTIFIED(comes in chunks)

1+

1- -

The SI unit of CHARGE is a COULOMB (C)

The smallest possible AMOUNT charge is

e = 1.60 x 10-19 C

All Net charge is a multiple of this amount

(the charge on 1 electron)

In other words charge is quantized, it only come in discrete packets or quantities.

e = 1.60 x 10-19 C

How many electrons do I need to have 1 full coulomb of charge?

Millikan oil drop video clip ( in folder)

Video via you tube

F =

The force exerted between two charged objects is

k Q1 Q2

r2

Q2Q1

r

Charge on object #1 (C)

Charge on object #2 (C)

distance between (m)

F12 = F21 (N)

F =k Q1 Q2

r2

Coulomb’s Constant= 8.988 109 N m2

C2

This equation is known as COULOMB’S LAW

F =k Q1 Q2

r2

k = 140

A fundamental constant known asTHE PERMITTIVITY OF FREE SPACE = 8.85 10-12 C2/N m2

F =Q1 Q2

r21

40

So in some cases you will see Coulomb’s law written like this.If so I would think that you will be given o

F =k Q1 Q2

r2

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.

F =k Q1 Q2

r2F =

G m1 m2

r2

Force of Gravity Coulombic Force

Proportional to mass Proportional to charge

8.988 109(BIG)6.667 10-11 (little)

BOTH FOLLOW INVERSE SQUARE LAW

F =k Q1 Q2

r2F =

G m1 m2

r2

Force of Gravity Coulombic Force

Always attractive Can be attractive or repulsive

Mass is always positive 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

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?

What is the direction of the force on the electron?

What is the magnitude and direction of the force on the nucleus?

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_______

The acceleration of the e- will_______

The velocity of the e- will_______

increase

increase

increase

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_______

The acceleration of the e- will_______

The velocity of the e- will_______

decrease

decrease

increase

Page 497: 1, 2, 5

2.7 N

http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html

- +

Q3 = -21.5 C

-Q2 = +80.6 C

Q1 = -15.4 C.50 m .65 m

Find the Resultant Force on Particle #2

Coulomb’s Law only gives us the force between two particles. If more than 2 are present the forces just add or subtract

+F2,3 = 36.9 NF2,1 = 44.6 N

+FNET = 7.7 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

23

-

+

Let’s look at the direction of the forces on PARTICLE #2

1

+ 23

F2,1

F2,3

How would we find the Total Force on #2?

F21

F23

How would we find the Total Force on #2?

Resultant Force

+

Q1 = -2.5 x 10-5 C

-

Q2 = +8.6 x 10-5 C

Q3 = +1.4 x 10-5 C

.50 m

.65 m

Find the Resultant Force on Particle #2

+

Problems:

Honors PhysicsPage 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

- - - - - - - - -- - - - - - - - - - --

- ----

like your black slate desk top

If a charge is placed on a INSULATOR, electrons are stuck where they land. So charged patches can be seen.

-- ----- -- ----- -- ----

What would have happened to cause a positive patch your desk?

Friction (rubbing) is not the only an object can be charged

-

-- -

--

Note: the extra electron on this sphere repel each other and spread out

Negative Metal Sphere Neutral Metal Sphere

Starting with a negatively charged sphere and a neutral oneseparated by air

-

-- -

--

If they are brought into contactThey electrons (repelling) are able to spread out further,charging the other sphere!

The second sphere was charged by CONDUCTION.CONDUCTION- Charging by contact.

Note the spheres would now repel each other

COPPER

-

-- -

--

The charge was CONDUCTED, through the copper

-

-- -

--

Glass

NO CONDUCTION THROUGH AN INSULATOR

How would a neutral object become positively charged by conduction?

-

--

--

-+

+ ++

++

Neutralpositively charged, fewer electrons than protons

-- -

-+

++

++

How would a neutral object become positively charged by conduction?

-

--

--+

+ ++

++

Neutral

- --

+

++

++-

Electron leave the neutral object

positivepositive

If a negative object is brought near (but not touching) a neutral one

-

--

--

-+-

-- -

--

+ ++

++

NeutralNegative

The neutral object will end up with a positive side and a negative side.

This movement of charge (without contact) is called induction

it is still neutral but now polar

If a negative object is brought near a neutral one

-

--

--

-+-

-- -

--

+ ++

++

NeutralNegative

The neutral object will end up with a positive side and a negative sideIf the sphere moves back, the sphere is still neutral but not polar

The process of induction will cause a charged object to attract a neutral one

-

-- -

--

+-

-- -

--

++

+

++

--

- -

-+-

-- -

--

++

+

++

Attract

Why are the attractive forces stronger than the repulsive ones?

Distance

                                                              Charged comb attracts neutralbits of paper.

                                             

Charged comb attractsneutral water molecules.

   

Neutral objects are attracted to charged objects

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

neutral

+++

- --

e-’s

+ +--+

+

+

-

-

-+

+

+

-

-

-

-

----

--

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)

ground

alligator clip

alligator clip

attraction by induction, repulsion after conduction, neutralization by grounding

--

- -

-+-

-- -

--

++

+

++

Earth Ground

+-

-- -

--

+++

++

the right sphere is grounded

+-

-- -

--

+++

++

both spheres are now charged

Charging an object by induction & grounding

animation

- --

-+

+

+

+

------

- --

-+

+

+

+

neutral neutral

------

- --

+

+

+

+

- -

-

+

+

+

+

Positive Negative

------

These spheres have been charged by INDUCTION

------

- --

+

+

+

+

- -

-

+

+

+

+

- --

+

+

+

+

- -

-

+

+

+

+

animation

Glass Flask

Rubber Stopper

INSULATORS

Metal ball & Rod

Thin Metal Foil Strips

an ELECTROSCOPE is a device used to detect charge

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:

contactor

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

Copy Machine (animation)

PHOTOCOPIERS 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 betweenthe 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 MagnetsGravity(mass)

Electric Charge MagnetsGravity(mass)

That really bugs me.

Exert a force without contact through a vacuum

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.

+

+

1

2

3

Compare the magnitude and direction of the force felt by the particles

To show each Force vector at every possible location would be too messy.

Electric Field Vector Map (applet)

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

applet

what is the field midway between the two charges?

Field around 2 opposite charges

Electric Field applet

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

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.

Inside of a charge CONDUCTING object, there is no NET FORCE and NO FIELD (no matter the shape of the object)

No Electric Field on the inside

animation of hollow conductor

An electric field does not affect the inside of a conductor. It is SHIELDED

You are surrounded by a conductor and so the electric field inside is ZERO.

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).

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 =k Q q

r2+

Q

q

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

+

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

(Test Charge)F =

k Q q

r2

Q

q

E =Fq+

Q

q(Test Charge)

So the charge of the test particle is divided out

Electric Field (N/C)

Charge on Test Charge (C)

Force on Test Charge

E =Fq

Electric Field is 24 N/C here.

What would be the direction and magnitude of force of a 2 C charge placed here?Q

q

+

Q

q

E =Fq

F =k Q q

r2

E =k Q q

q r2

+

E =k Q

r2

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

Q

q

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.

a hammerhead shark biting at an electrode

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 FORCESWhat 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

Q2

Test Charge

Will the Forces on the test particle add or subtract

E1 E2

Why is the field from particle 1 stronger at that point?

-

E1 + E2 =

+ =

What is the direction of the two electric fields at the test charge?

+Q1

Q2

Test Charge

Will the Forces on the test particle add or subtract

E1 E2

- +

E1 + E2 =

+ =

Q1Q2

- +

What is the strength of the field at the blue point? And what is the force on a 1mC charge at that location?

5x10-11 m

e-

10-11 m

p+

+

-Q1

Q2

E1 E2

-

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 mechanicsRelate PE of charge and gravityUse test + test particle to show low and high PE’sIntro voltage, increase or decrease based on + particle+ charges tend to go from high to low potentials,-charges tend to go from low to high potentialsVoltage always based on differences, like energyUsually 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 field strength as the object is lifted?

What happens to the Potential Energy as the object is lifted (in this case)?

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.

h

PE = mgh = W = Fd

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

-+

-

-

1

2

+

+

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

++

++

The monkey does work to bring the charges closer.That energy can be converted to kinetic energy when released

V =UE

qelectric potential (in Volts or V)

electric potentialenergy

electric potential is the Joules of energy per unit charge.So one way of expressing volts is J/C

1 kg

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 m

V =UE

qWe really mean than the difference in voltage is proportional to the difference in potential energy between two locations.

1 kg

Usually we consider one state to have an energy of zero. Which is…

1 m

V =UE

qWe 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 theparticle as it is moved?

Potential energy increases

++++++++++++++++++

__________________

+

Where would voltage (electric potential) be higher?

High Voltage Low Voltage

++++++++++++++++++

__________________

CHANGES IN VOLTAGE are ALWAYS based on a POSITIVE test charge.

High Voltage Low Voltage

++++++++++++++++++

__________________

High Voltage Low Voltage

+

-

Positive charges naturally move from________ to ______ potentialsHigh Low

Know this

++++++++++++++++++

__________________

High Voltage Low Voltage

+

-

Negative charges naturally move from________ to ______ potentialsHighLow

Know this

++++++++++++++++++

__________________

High Voltage Low Voltage

+

-

The two charges are moved from low to high potentials. The UE of the + charge_________The UE of the + charge_________

Increases

Decreases

V =UE

q

or workWe say that the original position has no energy, so its voltage is Zero

V =UE

q

or workWe say that the original position has no energy, so its voltage is Zero

V =UE

q

or workSince the voltage changed by 10 V,we did 30 J of work to move the charges

Gravitational potential energyLifting a rock that has twice the massRequires twice the work.

Moving a particle that has twice the charge also requires twice the work, because it has twice the force.

V =UE

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 = Forceq

Voltage =UE

q

electric potential

electric potentialenergy

2-

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!

++ +

+

++

+ + ++

-

++ +

+

++

+ + ++

Demo- Van de Graaff Generator

Charges in electric field have energy

Electric Potential (J/C or Volts)

Voltage is the energy per unit charge (basically it just depends on location)

Electric Potential Energy (J)

qV = UE

Charge (C)

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 100,000,000 Volts

Our VDG

120 VoltsResidential Electric

50,000 Volts

D battery 1.5 Volts

How much electric potential energy does 2 coulombs of charge have at 120 V (standard household voltage).

qV = UE

Rearranging

q= VUE

UE = qV

and more correctly written

UE = qV

A common unit of measuring very small amounts of energy is an electron volt (eV)

1 eV= 1.60x10-19 C 1V

1 eV= 1.60x10-19 J

PE = mgh

h

- -- - -- - - - - --

+ + + + + + +

-

PE = qV

V

Potential Energy looks at a change in position.Usually one state is said to have zero potential

How much PE does an electron have in a lightning bolt about to strike?Assume the voltage is 100,000,000 (108)Volts.

UE = QV

How fast is it moving when it strikes the ground?

charge on an electron: 1.6x10-19 C

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?

E = 6 N/C+

3 m

+

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

+

3 m

+

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

+

3 m+

45o

Solving this generically, a charge (q) in a uniform electric field (E) moved a distance (d) parallel with the field.

+E

+

E = Fq

W = F d

= q EF

Plugging in for F…..

Solving for F

And we all know work = the change in ….

W = q E d

UE = q E d

UE = qEd

The change in electric potential for a charge in a uniformElectric field. Uniform meaning that field strength is constantas is the case between parallel plates.

q = V

UE = qEd

UE

V = EdAnd of course by V we really mean V, a comparison between two states… One usually taken to be Zero.

V = E d

+ + + + + +

- - - - - -

batteryd E

The Field must be uniform for this to work

V = E d

+ + + + + +

- - - - - -

12 V battery

.11 m E

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 chargeand 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

+Q

Work = F dF =

qrb

ra= ∞

V =UE

qso

V =

k Q q r2

F dq

+Q

k Q q dq r2

qrb

ra= ∞

V =F d

q =

+Q

k Q d r2

qrb

ra= ∞

V =

The distance is really rso...

r

+Q

k Q r

qrb

ra= ∞

V =

The difference in voltage between the two locations

k Q rb

Vab = Vb - Va = - k Q ra

+Q

k Q r

qrb

ra= ∞

V =

The change in voltage of a particle brought from infinite distance (and zero force) to a distance r from the charge.

r

V =k Q

rThis 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

V =k Q

rAn 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?

V1 = 4 V

V2= 9 V

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?

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....

+ -

+

2C - 3 C

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?

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.

Common Misconceptions

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 roundor 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).

E=Fq

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?

Inside the conductor the electric field is zero

R

r

E =kQR2

(At the surface)

E =kQr2

(away from the surface)

This is an AP objective so copy this down

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

V = 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

Rr

V =kQR

(At the surface and inside)

V =kQr

Outside of the sphere

Also an AP objective

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….

The net force on a charge particle is___________

The electric field is ____________

The electric potential is___________

Zero

Zero

Constant

Explain why a conductor must be an equipotential, and apply this principle in analyzing what happens when conductors are connected by wires.

AP objective

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

capacitor animation

e-e-

- +- +- +- +

The Voltage across the plates will eventually be the same as the battery

1.5 V

1.5 V

The total charge that can be stored in a capacitor is

Q = CVStored Charge(Coulombs)

Capacitance (farads, F)a fudge factor based on the actual capacitor’s

size and materials

voltage of power source

The greater the voltage source and capacitancethe more charge can be stored

The capacitance depends on the:

C =K0A

d

d

A (area)

0 =8.85x10-12 C2/Nm2dielectric constant of material between the plates (page 514)

What will units on A and d be?

Table of dielectric constants

MaterialDielectric Constant

Vacuum 1Air(1 atm) 1.00059

Air(100 atm) 1.0548Teflon 2.1

Polyethylene 2.25Benzene 2.284

Mylar 3.1Polyvinyl chloride 3.18

Plexiglas 3.4Neoprene 6.7

Glass 7

Germanium 16

Liquid ammonia(-78°C 25

Glycerin 42.5Water 80.4

Strontiun titanate 310

Inserting a dielectric material between the

capacitor plates reduces the electric field there

C =K0A

dQ = 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”.

C =K0A

d

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?

Q = CV

Good animation for this

C =K0A

d

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)

Q = CV

For a given applied voltage.....

Typical Capacitance ranges from

F

pF

= 10-6 F

= 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

+ + + + + +

- - - - - -

batteryd E

What is the relationship between electric field inside a parallel plate capacitor, the voltage, and plate separation.

+ + + + + +

- - - - - -

batteryd EV

V = E d

V

Or…

+ + + + + +

- - - - - -

batteryd EV

E = dV

So as voltage___ electric field ____

distance___ electric field ____

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

UE =Energy (J)

Charge on capacitor (C)

Voltage between plates (V)

2QV

Since Q = CV

U = 2CQ2

plugging in for V

= 2CV2

plugging in for Q

2QV

=

How much energy was stored on our aluminum foil capacitor (C= 4.0 x 10-8 F) charged to 12 V?

Capacitance Problems

Honors PhysicsPage 524: 32, 33, 39