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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
1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen
Experiment #2
PivotRubber rubbed withskin of dead rabbit
Rubber rubbed withskin of dead rabbit
1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen
Experiment #3
PivotGlass 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
Glass rubbed with wool
What is the effect of
DISTANCE??
Experiment #4
Pivot
1. Rods will attract each other
2. Rods will repel each other
3. Nothing will happen
4. Something not listed above will happen
Glass rubbed with wool
Rubber rubbed withskin of dead rabbit
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
Rubber rubbed withskin 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
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
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
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
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