Transcript Chapter 17 - UCF Physics

CHAPTER 17
Electric Charge & Stuff
A Slide Like This Every Day



Today we begin chapter 17 – Electric Charge,
Coulombs Law and the Electric Field
There will be NO QUIZ this week.
Clicker use will begin on Friday.
 Bring
your i-clicker to class every session
 Bring a scientific calculator ($13.00 – COSTCO)
 If you have your clicker with you, you may use it today.

There WILL be a Quiz next Friday
Probable First Observation Electricity
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
Allowable Predictions
(Use your clicker if you have one.)
A.
B.
C.
D.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
Experiment #1
motion
Rubber rod
Pivot
Rubber rod
A.
B.
C.
D.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
Experiment #2
Rubber rubbed with
skin of dead rabbit
Pivot
Rubber rubbed with
skin of dead rabbit
A.
B.
C.
D.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
The charges on the two rods are ..
A.
B.
C.
D.
Since we treated both rods in the same way, they should
be of the same type
……. different types
I have no idea what you are asking for.
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.
B.
C.
Stronger
Weaker
The same
If the two rods are brought closer together, the force
acting between them will get …
A.
B.
C.
Stronger
Weaker
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
Charge
Experiment #3
Glass rubbed with wool
Pivot
Glass rubbed with wool
A.
B.
C.
D.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
Experiment #4
Rubber rubbed with
skin of dead rabbit
Pivot
Glass rubbed with wool
1.
2.
3.
4.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
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
Positive
Negative

An object without either a (+) or (-) charge is referred to
as being
NEUTRAL.
Example - Tape
Separation
An Example
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
consequently defined as POSITIVE.
Old Ben screwed up more than once!!
++++++++++------------+++---++---+-++-
From whence this charge???
Easily Removed
+
AXON
Signal propagation in neurons. Neurons are components of the
nervous system of the body that transmit signals as electrical impulses
travel along their length. These impulses propagate when charge
suddenly rushes into and then out of a part of the neutron called an
axon. Measurements have shown that, during the inflow part of this
101111 Na
Na++ (sodium ions) per meter, each with charge +e
cycle, approximately 5.6 10
enter the axon. How many coulombs of charge enter a 1.5 cm length of
the axon during this process?
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
What about a charged rod and a
piece of wooden dowel??
A.
B.
C.
D.
Rods will attract each other
Rods will repel each other
Nothing will happen
Something not listed above will happen
Neutral (Conducting) Object POLARIZATION
Positive charge attracts negative charges.
Rod becomes “polarized.
Negative end is closer to positive charge
Distance effect causes attraction.
Contact Transfer
Q/2
Q/2
Q
A Question
Two iron spheres contain excess charge, one
positive and the other negative.
(a) Show how the charges are arranged on
these spheres if they are very far from each
other.
(b) If the spheres are now brought close to each
other, but do not touch, sketch how the charges
will be distributed on their surfaces.
(c) In part (b), show how the charges would be
distributed if both spheres were negative.
Ways to charge an object


Rubbing or bond breaking (same thing)
Transfer
 Direct
transfer
 Polarization
 Induction
Quickie: How many kinds of charge
are there?
A. Two: +,B. Three: +,-.neutral
Induction
Polarize
Ground
Remove Ground
Positive !
Balloon Physics
Same as before: Polarization
Bonding!
WHAT HAPPENS WHEN TWO
SURFACES TOUCH OR RUB?
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.
No! No!
No! No!
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
SUMMARY: 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.
Getting down to business:

We will discuss the inverse square law that
describes how electric charges interact via forces.
 This



is COULOMB’S LAW
We will discuss the FACT that Coulomb's law is a
VECTOR equation.
We will add forces acting on a charge from an
assembly of other charges.
We will discuss the concept of FLUX and use it to
“derive” a useful law for continuous distributions of
charge with high symmetry. This is Gauss’s LAW
Forces Between Charges


The force between charges is along the line
between them.
The direction depends on the type of charges Like
Charges Repel
 Unlike Charges Attract

The Magnitude of the force is proportional to the
inverse square of the distance between the charges.
Coulomb’s Law
The magnitude F of the force that each of two
point charges q1 and q2 a distance r apart
exerts on the other is directly proportional to
the product of charges (q1q2) and inversely
proportional to the square of the distance
between them (r2).
The relationship is
expressed symbolically as
F k
q1q2
r
2
.
This relationship is called Coulomb’s law.
Coulomb’s Law
Coulomb’s Law
The Unit of Charge is called
THE COULOMB
1 q1q2
F
runit
2
40 r
1
 k  9 x109 Nm2 / C 2
40
Smallest Charge: e ( a positive number)
1.6 x 10-19 Coul.
electron charge = -e
Proton charge = +e
EXAMPLE
Q = +12 nC. What is the magnitude of the force F on charge Q?
+12 nC
1.6 × 10-4 N
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
F  mg
Gravitatio nal Field Strength 
Force
Gravitatio nal Force mg


g
Property
mass
m
The Gravitational Field
That We Live In.
M
m
mg
Mg
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
F  q0 E
F  1  qq0
q
E    k 2  k 2
q0  q0  r
r
Doing it
qQ
F  k
runit
2
r
F
Q
E 
 k 2 runit
q
r
F
q
Q
A Charge
r
The spot where we want
to know the Electric Field
GeneralqQ
F  k 2 runit
r
Q
F
E   k 2 runit
r
q
General
E  E j  
Fj
q
 k
Qj
r
2
j
r j ,unit
Force  Field
The two S’s
Superposition
Symmetry

What is the electric field at the center
of the square array?
The FIELD DIAGRAM
NEW CONCEPT
What is so important about FLUX??
OUTWARD Pointing
Normal
CLOSED Surface
What is the TOTAL FLUX leaving a closed surface??
Gauss’s Law
    i   E (Ai )
  E  Ai  EA  E (4R 2 )

q
40 r
4R 
2
2
q
0
Gauss’s Law
 TOTAL FLUX 
Enclosed Charge


LEAVING A

  Total    i 
0
CLOSED VOLUME 
Conducting Materials

Conductors






Electrons are free to move.
In equilibrium, all charges are a rest.
If they are at rest, they aren’t moving!
If they aren’t moving, there is no net force on them.
If there is no net force on them, the electric field must be zero.
THE ELECTRIC FIELD INSIDE A CONDUCTOR IS
ZERO!
More on Conductors


Charge cannot reside in the volume of a conductor
because it would repel other charges in the volume
which would move and constitute a current. This is
not allowed.
Charge can’t “fall out” of a conductor.
Isolated Conductor
Electric Field is ZERO in
the interior of a conductor.
Gauss’ law on surface shown
Also says that the enclosed
Charge must be ZERO.
Again, all charge on a
Conductor must reside on
The SURFACE.
Charged Conductors
Charge Must reside on
the SURFACE
-
E=0
-
-
s
Very SMALL Gaussian Surface
E
sA
EA 
0
or
s
E
0
Isolated (Charged) Conductor with
a HOLE in it.
E=0 everywhere
inside the conductor.
So Q (total) =0 inside the hole
Including the surface.
A Spherical Conducting Shell with
A Charge Inside.
So much for Mr. Coulomb!