electrostatics chapter 23
DESCRIPTION
Electrostatics Chapter 23. Most classes will begin with a slide similar to the following. What’s 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. - PowerPoint PPT PresentationTRANSCRIPT
Electrostatics Chapter 23
Most classes will begin with a slide similar to the following.
What’s Happening• Clicker use will start on Friday (maybe).
We will use them today informally.• There will NOTNOT be a quiz this week.• There WILLWILL be a quiz a week from
Friday.• WebAssigns should be active shortly.
Keep an eye out for it.• It might be already there !!!
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
Experimental Procedure
PivotThe 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 you learn anything? What?
Allowable Predictions(Use your clicker if you have one.)
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
Experiment #1
Pivot
motion
Rubber rod
Rubber rod
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
Experiment #2
PivotRubber rubbed withskin of dead rabbit
Rubber rubbed withskin of dead rabbit
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
The charges on the two rods are ..
A. Since we treated both rods in the same way, they should be of the same type
B. ……. different typesC. I have no idea what you are asking for.D. Leave me alone … I’m napping!
If you rubbed the rods longer and/or harder, do you think the effect that you see would be
A. StrongerB. WeakerC. The same
If the two rods are brought closer together, the force acting between them will get …
A. StrongerB. WeakerC. The same
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
ChargeCharge
Experiment #3
PivotGlass rubbed with wool
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
Glass rubbed with wool
Experiment #4
Pivot
1. Rods will attract each other2. Rods will repel each other3. Nothing will happen4. 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. There seems to be two types of charge.
We call these two types of charge
PositiveNegative
An object without either a (+) or (-) charge is referred
to as being NEUTRAL.NEUTRAL.
Example - Tape
Separation
An Example
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.
Old Ben screwed up more than once!!
++++++++++-------------+++---++---+-++-
From whence this charge???
-+
Easily Removed
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
Pivot
Experiment #5
Rubber rubbed withskin of dead rabbit
Metal Rod
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
What about a charged rod and a piece of wood??
A. Rods will attract each otherB. Rods will repel each otherC. Nothing will happenD. Something not listed above will happen
Ways to charge an object
Rubbing or bond breaking (same thing) Transfer
Direct transfer Polarization Induction
Neutral Object - POLARIZATION
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
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!
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.
Forces Between Charges
Q1 Q2 Attract Repel
+ + X
+ - X
- + X
- - X
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.
The force acts along the line connecting the two charges.
0
221
221
02
21
41
41
k
rqqk
rqq
rqqF
Remember
Coulomb’s Law
229
0
221
0
/1094
14
1
CNmxk
rqq
unit
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
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
mm
mass
m
Force nalGravitatioProperty
ForceStrength Field nalGravitatio
The Gravitational Field That We Live In.
m Mmg
Mg
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 isMEAN!
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 rrFE 220
00
1rqk
rqqk
Doing itQ
r
q
A Charge
The spot where we wantto know the Electric Field
unit
unit
rQk
q
rqQk
rFE
rF
2
2
F
General-
unitjj
jjj
unit
unit
rQk
q
GeneralrQk
q
rqQk
,2
2
2
rF
EE
rFE
rF
Force Field
Two ChargesWhat is the Electric Field at Point P?
The two S’s
SuperpositionSymmetry
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
Let’s Do it Real Time
Concept – Charge perunit length
dq= ds
The math
)sin(2)cos(2
)cos()2(
)cos()2(
0
00
02
02
0
0
0
rkd
rkE
rrdkE
rdqkE
Erdds
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
xrdxkrE
xrdxrkE
xr
r
xrdxkE
(standard integral)
Completing the Math
rk
Lr
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
rzrdrzkE
rzz
rzdrrk
rzdqkdE
02/322
2/1222222
2
2)cos(
(z2+r2)1/2
Final Result
0z
220
2E
,R
12
WhenRz
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
)()()(rrdsk
rrdAk
rrdVk
rQk
q
GeneralrQk
q
rqQk
unitjj
jjj
unit
unit
E
rF
EE
rFE
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