Electrostatics Chapter 23 Week-1-2 What’s Happening Clicker use will start on Friday (maybe)....

Electrostatics Chapter 23

Week-1-2

What’s Happening• Clicker use will start on Friday

(maybe).• Today we begin the study of

charge with make-believe clickers.• There will NOTNOT be a quiz this week.• There WILLWILL be a quiz next Friday.• WebAssigns are now active.

Probable First Observation ElectricityElectricity

Idiot!

If lightening had actually traveled down the kite string, old Ben Franklin would have been toast!

Probably never happened, but good story!

A Quick Experiment

History

600 BC Thales of Miletos rubs amber (electron in

Greek) with cat fur and uses it to pick up feathers.

Important questions: Why was he doing this? Didn’t he have a job?? What happened to the skinned cat?

AmberMillion years ago large stands of forests in some parts of the world began to seep globs of sticky resin! This aromatic resin oozed down the sides of trees, as well as filling internal fissures, trapping debris, such as seeds, leaves, feathers and insects. As geologic time progressed the forests were buried and the resin hardened into a soft, warm, golden gem, known as amber. Amber is the fossilized resin of ancient trees which forms through a natural polymerization of the original organic compounds. Most of the world's amber is in the range of 30-90 million years old.

Demo – Lets make some observations

Rubber

Dead Cat or Rabbit

GlassWool

NOT Shown: Aluminum Rods

Experimental Procedure

Pivot

The sequence of Experiments1. Identify the two rods2. Treat each rod3. Bring one rod near to the other4. PREDICT WHAT WILL HAPPEN5. VOTE ON POSSIBILITIES6. Observe what happens7. Did we learn anything?

Predictions

1. Rods will attract each other

2. Rods will repel each other

3. Nothing will happen

4. Something not listed above will happen

Experiment #1

PivotRubber rod

Rubber rod





Experiment #2

PivotRubber rubbed withskin of dead rabbit

Rubber rubbed withskin of dead rabbit





Experiment #3

PivotGlass rubbed with wool





Glass rubbed with wool

What is the effect of

DISTANCE??

Experiment #4

Pivot





Glass rubbed with wool


What’s Going On?

All of these effects involve rubbing two surfaces together.

Or pulling two surfaces apart. Something has “happened “to each of these

objects. These objects have a new PROPERTY

Other properties are mass, color We call this NEW PROPERTY CHARGE.

From whence this charge???

-+

Pivot

Experiment #5


Metal Rod





Neutral Object

Positive charge attracts negative charges.Rod becomes “polarized.Negative end is closer to positive chargeDistance effect causes attraction.

Induction

Polarize

Ground

Remove Ground

Positive !

Balloon Physics

Same as before: Polarization

From WebAssign

Three are brought close to each other, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude which of the following? (Select all that apply.)

[_] Objects A and C possess charges of the same sign. [_] All three of the objects possess charges of the same sign. [_] One of the objects is neutral.[_] Objects A and C possess charges of opposite sign. [_] We need to perform additional tests to determine information about the charges on the object

Example

PITH BALLS

Another Example

Example - Tape

Effect of Charge

We have also observed that there must be TWO kinds of charge. Call these two types

positive (+) negative(-)

We “define” the charge that winds up on the rubber rod when rubbed by the dead cat to be NEGATIVE.

The charge on the glass rod or the dead cat is defined as POSITIVE.

What happens when two surfaces touch or rub?

Bonding!Bonding!

The Triboelectric Series

No! No!

When two of the following materials are rubbed together under ordinary circumstances, the top listed material becomes positively charged and the lower listed material becomes

negatively charged.

MORE POSITIVE rabbit's fur

glass mica nylon wool

cat's fur silk

paper cotton wood

acrylic cellophane tape

polystyrene polyethylene

rubber balloon saran wrap

MORE NEGATIVE

No! No!

Summary - Rubbings

What have we found?

There are TWO types of charge. Positive Negative

Like Charges Attract Un-Like charges repel The force between charges increases as they are

brought closer together. This charge separation results from chemical bonds

which are severe in the pocess.

Forces Between Charges

Q1 Q2 Attract Repel

+ + X

+ - X

- + X

- - X

Types of MaterialsTypes of Materials

Insulators“Holds” a charge

ConductorsAllows charge to easily move

(current)

This is WAR

You are fighting the enemy on the planet Mongo. The evil emperor Ming’s forces are behind a strange

green haze. You aim your blaster and fire … but ……

Ming themerciless

this guy is

MEAN!

Nothing Happens! The Green thing is a Force Field!

The Force may not be with you ….

Side View

TheFORCE FIELD

Force

Positiono

|Force| Big!

Properties of a FORCE FIELD

It is a property of the position in space. There is a cause but that cause may not be

known. The force on an object is usually proportional

to some property of an object which is placed into the field.

Fields Imagine an object is placed at a particular point in

space. When placed there, the object experiences a force F. We may not know WHY there is a force on the object,

although we usually will. Suppose further that if we double some property of

the object (mass, charge, …) then the force is found to double as well.

Then the object is said to be in a force field. The strength of the field (field strength) is defined as

the ratio of the force to the property that we are dealing with.

Example – Gravitational Field.

Property is MASS (m). Force is mg. Field strength is defined

as Force/Property

gg

gF

m

m

mass

m

Force nalGravitatio

Property

Force

Strength Field nalGravitatio

The Gravitational Field That We Live In.

m Mmg

Mg

Coulomb’s Law – Force between charges

The force between two charges is proportional to the product of the two charges and inversely proportional to the square of the distance between them.

0

221

221

02

21

4

1

4

1

k

r

qqk

r

qq

r

qqF

Remember

Coulomb’s Law

229

0

221

0

/1094

1

4

1

CNmxk

r

qqunit

rF

The Unit of Charge is calledTHE COULOMB

Smallest Charge: e ( a positive number) 1.6 x 10-19 Coul.

electron charge = -eProton charge = +e

Three point charges are located at the corners of an equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-μC charge.

Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. As shown in Figure P23.10, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?

The Electric Field

This is WAR

You are fighting the enemy on the planet Mongo. The evil emperor Ming’s forces are behind a strange

green haze. You aim your blaster and fire … but ……

Ming themerciless

this guy is

MEAN!

Nothing Happens! The Green thing is a Force Field!

The Force may not be with you ….

Side View

TheFORCE FIELD

Force

Positiono

|Force| Big!

Properties of a FORCE FIELD

It is a property of the position in space. There is a cause but that cause may not be

known. The force on an object is usually proportional

to some property of an object which is placed into the field.

Mysterious Force

F

Electric Field

If a charge Q is in an electric field E then it will experience a force F.

The Electric Field is defined as the force per unit charge at the point.

Electric fields are caused by charges and consequently we can use Coulombs law to calculate it.

For multiple charges, add the fields as VECTORS.

Two Charges

unitunit rrF

E22

0

00

1

r

qk

r

qqk

qq

Doing it

Q

r

q

A Charge

The spot where we wantto know the Electric Field

unit

unit

r

Qk

q

r

qQk

rF

E

rF

2

2

F

General-

unitjj

jjj

unit

unit

r

Qk

q

General

r

Qk

q

r

qQk

,2

2

2

rF

EE

rF

E

rF

Force Field

Two ChargesWhat is the Electric Field at Point P?

The two S’s

Superposition

Symmetry

What is the electric field at the center of the square array?

Kinds of continuously distributed charges Line of charge

or sometimes = the charge per unit length. dq=ds (ds= differential of length along the line)

Area = charge per unit area dq=dA dA = dxdy (rectangular coordinates) dA= 2rdr for elemental ring of charge

Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will look at later.

Continuous Charge Distribution

ymmetry

Let’s Do it Real Time

Concept – Charge perunit length

dq= ds

The math

)sin(2

)cos(2

)cos()2(

)cos()2(

0

0

0

02

02

0

0

0

r

kd

r

kE

r

rdkE

r

dqkE

E

rdds

x

x

x

y

Why?

A Harder Problem

A line of charge=charge/length

setupsetup

dx

L

r

x

dE dEy

2/

02/322

2/

02/322

22

2

2

22

)(2

)(2

)()cos(

)(

)cos(

L

x

L

x

L

Lx

xr

dxkrE

xr

dxrkE

xr

r

xr

dxkE

(standard integral)

Completing the Math

r

kL

r

kLE

Lr

L

Lrr

kLE

x

x

2

2

4

:line long VERY a oflimit In the

4

:nintegratio theDoing

22

22

1/r dependence

Dare we project this??

Point Charge goes as 1/r2

Infinite line of charge goes as 1/r1

Could it be possible that the field of an infinite plane of charge could go as 1/r0? A constant??

The Geometry

Define surface charge density=charge/unit-area

dq=dA

dA=2rdr

(z2+r2)1/2

dq= x dA = 2rdr

(z2+r2)1/2

R

z

z

rz

rdrzkE

rz

z

rz

drrk

rz

dqkdE

02/322

2/1222222

2

2)cos(

(z2+r2)1/2

Final Result

0z

220

2E

,R

12

When

Rz

zEz

Look at the “Field Lines”

What did we learn in this chapter??

We introduced the concept of the Electric FIELDFIELD. We may not know what causes the field. (The

evil Emperor Ming) If we know where all the charges are we can

CALCULATE E. E is a VECTOR. The equation for E is the same as for the force

on a charge from Coulomb’s Law but divided by the “q of the test charge”.

What else did we learn in this chapter? We introduced continuous distributions of

charge rather than individual discrete charges.

Instead of adding the individual charges we must INTEGRATE the (dq)s.

There are three kinds of continuously distributed charges.

Kinds of continuously distributed charges

Line of charge or sometimes = the charge per unit length. dq=ds (ds= differential of length along the line)

Area = charge per unit area dq=dA dA = dxdy (rectangular coordinates) dA= 2rdr for elemental ring of charge

Volume =charge per unit volume dq=dV dV=dxdydz or 4r2dr or some other expressions we will look at later.

The Sphere

thk=dr

dq=dV= x surface area x thickness= x 4r2 x dr

dq

Summary

222

,2

2

2

)()()(

r

rdsk

r

rdAk

r

rdVk

r

Qk

q

General

r

Qk

q

r

qQk

unitjj

jjj

unit

unit

E

rF

EE

rF

E

rF

(Note: I left off the unit vectors in the lastequation set, but be aware that they should

be there.)

To be remembered …

If the ELECTRIC FIELD at a point is E, then E=F/q (This is the definition!)

Using some advanced mathematics we can derive from this equation, the fact that:

EF q

Electrostatics Chapter 23 Week-1-2 What’s Happening Clicker use will start on Friday (maybe)....

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