Electrostatics Chapter 23

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Electrostatics Chapter 23

• Week-1-2

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Whats Happening

• Clicker use will start on Friday (maybe). We will
  use them today informally.
• There will NOT be a quiz this week.
• There WILL be a quiz a week from Friday.
• WebAssigns are now active. Get to work!!

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Probable First Observation Electricity
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Idiot!
If lightening had actually traveled down the kite
string, old Ben Franklin would have been
toast! Probably never happened, but good story!
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A Quick Experiment
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Experimental Procedure
Pivot

• The sequence of Experiments
• Identify the two rods
• Treat each rod
• Bring one rod near to the other
• PREDICT WHAT WILL HAPPEN
• VOTE ON POSSIBILITIES
• Observe what happens
• Did you learn anything? What?

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Allowable Predictions(Use your clicker if you
have one.)

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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Experiment 1

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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Experiment 2

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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The charges on the two rods are ..

1. Since we treated both rods in the same way, they
   should be of the same type
2. . different types
3. I have no idea what you are asking for.
4. Leave me alone Im napping!

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If you rubbed the rods longer and/or harder, do
you think the effect that you see would be

1. Stronger
2. Weaker
3. The same

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If the two rods are brought closer together, the
force acting between them will get

1. Stronger
2. Weaker
3. The same

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Definition of sorts
We DEFINE the stuff that we put on the rods by
the rubbing process as CHARGE. We will try to
understand what charge is and how it behaves. We
add to the properties of materials Mass Charge
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Experiment 3
Glass rubbed with wool
Glass rubbed with wool

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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Experiment 4
Rubber rubbed with skin of dead rabbit
Glass rubbed with wool

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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Whats 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.
• There seems to be two types of charge.

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We call these two types of charge

• Positive
• Negative

An object without either a () or (-) charge is
referred to as being NEUTRAL.
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Example - Tape
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Separation
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An Example
Volunteer Please
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Effect of Charge
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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
  consequently defined as POSITIVE.

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Old Ben screwed up more than once!!
--------- ------------
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From whence this charge???
Easily Removed
-
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Materials

• Two kinds of materials
• Insulators
• Electrons and Protons are tightly bound to their
  positions. Hard to move them around.
• Conductors
• Electrons are easily removed and moved around.
• Electrons are said to be MOBILE charges.
• There are other kinds of materials that we will
  not discuss semiconductors, semi-metals

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Experiment 5
Rubber rubbed with skin of dead rabbit
Metal Rod

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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What about a charged rod and a piece of wood??

1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen

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Ways to charge an object

• Rubbing or bond breaking (same thing)
• Transfer
• Direct transfer
• Polarization
• Induction

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Neutral Object - POLARIZATION
Positive charge attracts negative charges. Rod
becomes polarized. Negative end is closer to
positive charge Distance effect causes attraction.
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Induction
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Polarize
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Ground
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Remove Ground
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Positive !
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• Balloon Physics

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Same as before Polarization
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What happens when two surfaces touch or rub?

• Bonding!

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The Triboelectric Series
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!
No! No!
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So far we have 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 severed.

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Forces Between Charges
Q1 Q2 Attract Repel
X
- X
- X
- - X
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Coulombs 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.
• The force acts along the line connecting the two
  charges.

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Remember
Force is a VECTOR!!
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Coulombs Law
Force is a Vector !
The Unit of Charge is called THE COULOMB
Smallest Charge e ( a positive number)
1.6 x 10-19 Coul.
electron charge -e Proton charge e
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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.
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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?
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The Electric Field
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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.

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Example Gravitational Field.

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

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The Gravitational Field That We Live In.
M
m
mg
Mg
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This is WAR
Ming the merciless this guy is MEAN!

• You are fighting the enemy on the planet Mongo.
• The evil emperor Mings forces are behind a
  strange green haze.
• You aim your blaster and fire but

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Nothing Happens! The Green thing is a Force
Field!
The Force may not be with you .
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Side View
The FORCE FIELD
Force
Big!
Force
o
Position
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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.

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Mysterious Force
F
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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.

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Two Charges
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Doing it
Q
A Charge
r
F
q
The spot where we want to know the Electric Field
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General-
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Force ? Field
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Two ChargesWhat is the Electric Field at Point P?
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The two Ss

• Superposition
• Symmetry

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What is the electric field at the center of the
square array?
Superposition and Symmetry
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Kinds of continuously distributed charges

• Line of charge
• m or sometimes l the charge per unit length.
• dqmds (ds differential of length along the
  line)
• Area
• s charge per unit area
• dqsdA
• dA dxdy (rectangular coordinates)
• dA 2prdr for elemental ring of charge
• Volume
• rcharge per unit volume
• dqrdV
• dVdxdydz or 4pr2dr or some other expressions we
  will look at later.

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Continuous Charge Distribution
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ymmetry
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Lets Do it Real Time
Concept Charge per unit length m dq m ds
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The math
Why?
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A Harder Problem
setup
A line of charge mcharge/length
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(standard integral)
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Completing the Math
1/r dependence
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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??

Let's look at it...
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The Geometry
Define surface charge density scharge/unit-area
dqsdA
(z2r2)1/2
dA2prdr
dqs x dA 2psrdr
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q
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Final Result
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Look at the Field Lines
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What did we learn in this chapter??

• We introduced the concept of the Electric FIELD.
• 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 Coulombs Law but divided by the
  q of the test charge.

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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.

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Kinds of continuously distributed charges

• Line of charge
• m or sometimes l the charge per unit length.
• dqmds (ds differential of length along the
  line)
• Area
• s charge per unit area
• dqsdA
• dA dxdy (rectangular coordinates)
• dA 2prdr for elemental ring of charge
• Volume
• rcharge per unit volume
• dqrdV
• dVdxdydz or 4pr2dr or some other expressions we
  will look at later.

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The Sphere
dq
thkdr
dqrdVr x surface area x thickness r x 4pr2 x dr
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Summary
(Note I left off the unit vectors in the
last equation set, but be aware that they
should be there.)
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To be remembered

• If the ELECTRIC FIELD at a point is E, then
• EF/q (This is the definition!)
• Using some advanced mathematics we can derive
  from this equation, the fact that

REMEMBER THIS !