PHYS 1110 Lecture 5 Professor Stephen Thornton September 13, 2012

PHYS 1110

Lecture 5

Professor Stephen Thornton

September 13, 2012

sitting for a very long time. We bring up a negatively charged rod, close to, but not touching the conductor. Which of the following is most true about this diagram?A) The diagram is wrong, because charge is not conserved.B) The diagram looks okay.C) The diagram is wrong, because the charge configuration is unlikely.

metalconductor

Reading Quiz(rod and sphere are not touching)

A metal conductor has been

Answer: C

A is not correct, because charges do not have to be conserved. There was charge on the Teflon rod.

C is correct, because the negative charge on the conductor would be repelled by the negative charge on the rod and move away.

Rub a Teflon rod on fur.

See what happens. Try to pick up pieces of paper.

When we rub one item on another, electrons are rubbed off one item to the other.

Discuss atomic model.

Rabbit fur + + + + + +

Glass + + + + +

Human hair + + + +

Nylon + + +

Silk + +

Paper +

Cotton -

Wood - -

Amber - - -

Rubber - - - -

PVC - - - - -

Teflon - - - - - -

Electrical Polarization

Polar molecules (water H2O, ammonia NH3, hydrogen fluoride HF)

Look at demo:

2 x 4 on watch glass.

How does Teflon rod cause board to move?

Benjamin Franklin is the one who named the charges positive and negative. We now know the electrons (which are mobile and carry charge) are negative.

Law of conservation of charge: the net amount of charge is conserved in any process.

We are dealing with Electrostatics- charges at rest.

Conductors are materials that conduct charge easily. Examples are metals like aluminum, copper, iron, etc.

Insulators are materials that do not conduct charge easily. Examples are glass, plastics, ceramics (nonmetallic).

Semiconductors are materials that are between conductors and insulators and can conduct charge under special conditions like at high temperatures.

What about water and air?

Water is a polar molecule.

Air is mostly , noteasily polarized.

2 2N ,O

Look at this You Tube video for the dangers of electrostatics.

Let’s consider some experimentsand see what happens.

1) Like charges repel and unlike charges attract.2) If we vary the distance between point charges, we find the force becomes smaller as the separation distance increases.

3) If we vary the charge magnitude, we find F ~ q1q2 4) Put these results together and obtain the Coulomb force.

2

1F

r

9 2 21 22

0

8.99 10 N m / C1

where 4

kq qF k

r

Forces Between Point Charges

12 is force on 1 due to 2.F

1 212 2

erkq qF

r

Superposition of Forces

1 212 2

0

e4 r

q qF

r

We find the total force by adding the vector sum of the individual forces.

Conceptual Quiz

Which of the arrows best

represents the direction

of the net force on charge

+Q due to the other two

charges?

+2Q

+4Q

+Q

A BC

D

Ed

d

Conceptual QuizConceptual Quiz

The charge +2Q repels +Q toward the

right. The charge +4Q repels +Q

upward, but with a stronger force.

Therefore, the net force is up and to net force is up and to

the right, but mostly upthe right, but mostly up.

+2Q

+4Q

+Q

A BC

D

Ed

d

+2Q

+4Q

Conceptual QuizConceptual Quiz

Which of the arrows best

represents the direction

of the net force on charge

+Q due to the other two

charges?

Follow-up:Follow-up: What would happen if What would happen if the yellow charge were +3the yellow charge were +3QQ??

Electric field

What is a field? Why do we want to learn about them?

Discuss fields in general temperature (use thermometer) gravitation (use test mass) pressure (weather maps)

An Electrostatic Force Field

0q

Use a small test charge q0 to find force due to charge +q.

r20

The test charge is used to map out the electric field due to charge .

ˆ= e

q

F kqE

q r

02

qqF k r0

is force between charge and test charge (small).F q

q

Definition of Electric Field

0

Electric field due to a charge (not ). Unit: N/Cq q

Electric Field of a Point Charge

0

21

4k

qE kr

r2

0

ˆ= eF kq

Eq r

The Direction of the Electric Field for

Point Charges

Superposition of the Electric Field

22 2

qE k

d

11 2

qE k

d

Imagine the test charge could be placed here. The test charge is only useful to imagine the force field.

Relation between F and E1

1

1 1

If we put a charge in an electric field , then the charge feels a force of value

q Eq

F q E

This is the really useful part.

Don’t confuse this charge q1 with the test charge q0 or the original charges q that produced E. The test charge q0 was used to find the electric field. This is a real charge q1 placed in the electric field.

Determining electric fields

Rules and hints:

1) E lines start on + charges, end on – charges. Can start and stop at infinity.

2) Place test charge q0 at any point and find direction of force on q0 to determine E line.

3) E lines can never intersect!

4) E lines are more dense when magnitude is greater.

Electric Field Lines for a Point Charge

Electric Field Lines for Systems of Charges

We call this a dipole. It is a dipole field.

Conceptual QuizConceptual Quiz

Which of the charges

has the greater

magnitude?

A)

B)

C) both the same

Conceptual QuizConceptual Quiz

Which of the charges

has the greater

magnitude?

A)

B)

C) both the same

The field lines are denser around denser around

the red chargethe red charge, so the red one red one

has the greater magnitudehas the greater magnitude.

Follow-up:Follow-up: What is the red/green ratio What is the red/green ratio of magnitudes for the two charges?of magnitudes for the two charges?

The Electric Field of a Charged Plate

02E

is charge per unit area of plates

Parallel charged plates

Charge Distribution on a Conducting Sphere

If charges were inside thesphere, they would repeleach other. Also E must be zero inside conductor or free electrons would move.

Charges placed on ametal conductor must reside on the surface.

Wrong

Correct

The electric field near a conducting surface must be perpendicular to the surface when in equilibrium.

If we place conductor in electric field,the E lines must be to surface. If not,charges would move. must be zero inside.E

The charge q0 feels a force due to E.The electric field E does work on the charge.The charge has a higher potential energy on the left than it does on the right.The charge gains kinetic energy in the electric field.

0

work

F q E

W F s

U W qE s

Ignore gravity Where does this electric field come from?

Change in Electric Potential Energy

Who (or what) is doing work here?

Change in Electric Potential Energy

Who (or what) is doing work here?

Electric field Gravitational field

Electric Potential V

Electric potential, or potential, is one of the most useful concepts in electromagnetism. This is a biggie!!

(notice that it has its own unit!)

0 0

Unit: J/C = volt, VU W

Vq q

definition!!

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The electrostatic force is conservative – potential energy can be defined.

Change in electric potential energy is negative of work done by electric force:

Electrostatic Potential Energy and Potential Difference

b aU U W qEd- =- =-

The electric field does work to move the positive charge q from a to b.

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Electric potential can be thought of as potential energy per unit charge:

It is really only the change in electric potential that is important, and we define it that way.

Only changes in electric potential (or simply called potential) can be measured, allowing free assignment of V = 0. For example, we can let one of the voltages be zero at infinity.

aa

UV

q

UV

q

=

DD =

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Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured:

Energy conservationEnergy conservation relations are still valid.

If we look at definition of ,

we have , so

( )

A A B B

B A A B A B

K U K U

V

UV U q V

q

K K U U q V V

The change in kinetic energy is proportional to the change in electric potential!!

Notes on electric potential

Point charge

Scalar quantity, not vector like electric field.

For multiple charges, we simply add the potentials from each charge for simple superposition!

In practice, we use potential concept much more than electric field. We can measure potential easily, but not electric field.

kqV

r

Electric Potential Energy

Electric potential energy for two point charges, q and q0, separated by a distance r, is simply

00

q qU q V k

r

Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest kinetic energy when it reaches the other plate?

A) protonB) electronC) the kinetic energies are the same.

Answer: CThe particles experience the same electric field and have the same charge. The kinetic energy increase is equal to the work done by the electric field. W = Fd = qEd

Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest speed when it reaches the other plate?

A) protonB) electronC) the speeds are the same.

Answer: B

We just saw that the proton and electron will have the same kinetic energy increase. But K = mv2/2, and because the electron has such a smaller mass, its velocity must be much greater than that of the proton.

At which point At which point

does does VV = 0? = 0?

A

C

B

D

+Q –Q

E) all of them

Conceptual QuizConceptual Quiz

kqV

r

At which point At which point

does does VV = 0? = 0?

A

C

B

D

+Q –Q

E) all of them

All of the points are equidistant from both chargesAll of the points are equidistant from both charges. Since

the charges are equal and opposite, their contributions to

the potential cancel outcancel out everywhereeverywhere along the mid-plane

between the charges.

Conceptual QuizConceptual Quiz

Follow-up:Follow-up: What is the direction of the electric field at all 4 points? What is the direction of the electric field at all 4 points?

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An equipotential is a line or surface over which the potential is constant.

Electric field lines are perpendicular to equipotentials.

The surface of a conductor is an equipotential.

Equipotential Surfaces

kqV

r=

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Another case showing electric field lines are perpendicular to equipotentials.

The surface of a conductor is an equipotential.

Equipotential Surfaces

The electric field does no work by moving a charge perpendicular to the electric field, which is along the equipotential!

Electrostatic precipitators- demo

Capacitance

Simplest capacitor – two equal and oppositely charged conductors

Parallel-plate capacitor:

A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

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When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:

The quantity C is a constant called capacitance.

Q CV=

Capacitance

CUnit: = farad or F

V

C1F = 1

V

QCV

If Q = CV,

Parallel plate capacitor

0 0

0

0

So and

Q dV Ed d

AAQ

V d

AQC

V d

The capacitance value depends only on geometry!

Dielectric

Effect of a Dielectric on the Electric Field of a Capacitor

0E E 00 and /

where is the dielectric constant

/E E V V

The induced electric field reduces the overall field:

• Dielectric = insulator

• Molecules act as dipoles, permanent or induced

• This effectively reduces the electric field

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A dielectric is an insulator, and is characterized by a dielectric constant .

Capacitance of a parallel-plate capacitor filled with dielectric:

Using the dielectric constant, we define the permittivity:

0

0

0

for parallel-plate capacitorACd

C C

k

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Dielectric strength is the maximum electric field a dielectric can experience without breaking down.

Dielectrics

Energy Required to Charge a Capacitor

Move charge across plates. It takes work and increases U.

22

Sum over the

1 1

2 2 2

U W V QQ

QU QV CV

C

QD

W

Capacitor energy storage

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Electric Energy StorageEnergy stored in a capacitor.