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Electrostatics Chapter 23. Week-1-2. 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. WebAssigns are now active. Get to work!!.

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Electrostatics chapter 23

Electrostatics Chapter 23

Week-1-2


What s happening
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.

  • WebAssigns are now active. Get to work!!



Idiot
Idiot!

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

Probably never happened, but good story!



Experimental procedure
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?


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

  • 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

Experiment #1

  • 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

Experiment #2

  • 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
The charges on the two rods are ..

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

  • Stronger

  • Weaker

  • The same


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

  • Stronger

  • Weaker

  • The same


Definition of sorts
Definition of sorts acting between them will get …

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

Pivot acting between them will get …

Experiment #3

Glass rubbed with wool

Glass rubbed with wool

  • Rods will attract each other

  • Rods will repel each other

  • Nothing will happen

  • Something not listed above will happen


Experiment 4

Pivot acting between them will get …

Experiment #4

Rubber rubbed with

skin of dead rabbit

Glass rubbed with wool

  • Rods will attract each other

  • Rods will repel each other

  • Nothing will happen

  • Something not listed above will happen


What s going on
What’s Going On? acting between them will get …

  • 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
We call these two types of charge acting between them will get …

  • Positive

  • Negative

An object without either a (+) or (-) charge is referred to as being NEUTRAL.


Example tape
Example - Tape acting between them will get …


Separation acting between them will get …


An example
An Example acting between them will get …

Volunteer Please


Effect of charge
Effect of Charge acting between them will get …


We have also observed that there must be two kinds 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
Old Ben screwed up more than once!! charge.

++++++++++---------

----+++---++---+-++-


From whence this charge
From whence this charge.charge???

Easily Removed

-

+


Materials
Materials charge.

  • 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


Experiment 5

Pivot charge.

Experiment #5

Rubber rubbed with

skin of dead rabbit

Metal Rod

  • Rods will attract each other

  • Rods will repel each other

  • Nothing will happen

  • Something not listed above will happen


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

  • Rods will attract each other

  • Rods will repel each other

  • Nothing will happen

  • Something not listed above will happen


Ways to charge an object
Ways to charge an object charge.

  • Rubbing or bond breaking (same thing)

  • Transfer

    • Direct transfer

    • Polarization

    • Induction


Neutral object polarization
Neutral Object - charge.POLARIZATION

Positive charge attracts negative charges.

Rod becomes “polarized.

Negative end is closer to positive charge

Distance effect causes attraction.


Induction
Induction charge.


Polarize
Polarize charge.


Ground
Ground charge.


Remove ground
Remove Ground charge.


Positive
Positive ! charge.





The Triboelectric Series charge.

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!


So far we have found
So far we have found? charge.

  • 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.



Coulomb s law force between charges
Coulomb’s Law – charge.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.


Remember
Remember charge.

Force is a VECTOR!!


Coulomb s law
Coulomb’s Law charge.

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


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 3 equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-q 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

The Electric Field equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-


Fields
Fields equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

  • 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
Example – Gravitational Field. equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

  • Property is MASS (m).

  • Force is mg.

  • Field strength is defined as Force/Property


The gravitational field that we live in
The Gravitational Field That We Live In. equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

M

m

mg

Mg


This is war
This is WAR equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

Ming the

merciless

this guy is

MEAN!

  • 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 ……


Nothing happens the green thing is a force field
Nothing Happens equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-! The Green thing is a Force Field!

The Force may not be with you ….


Side view
Side View equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

The

FORCE FIELD

Force

Big!

|Force|

o

Position


Properties of a force field
Properties of a equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-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
Mysterious Force equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

F


Electric field
Electric Field equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

  • 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
Two Charges equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-


Doing it
Doing it equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

Q

A Charge

r

F

q

The spot where we want

to know the Electric Field


General
General- equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-


Force field
Force equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00- Field


Two charges what is the electric field at point p
Two Charges equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-What is the Electric Field at Point P?


The two s s
The two S’s equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00-

  • Superposition

  • Symmetry



Kinds of continuously distributed charges
Kinds of continuously distributed charges array?

  • Line of charge

    • m or sometimes l = the charge per unit length.

    • dq=mds (ds= differential of length along the line)

  • Area

    • s = charge per unit area

    • dq=sdA

    • dA = dxdy (rectangular coordinates)

    • dA= 2prdr for elemental ring of charge

  • Volume

    • r=charge per unit volume

    • dq=rdV

    • dV=dxdydz or 4pr2dr or some other expressions we will look at later.



Ymmetry
ymmetry array?


Let s do it real time
Let’s Do it Real Time array?

Concept – Charge per

unit length m

dq= mds


The math
The math array?

Why?


A harder problem

q array?

dEy

dE

q

r

x

dx

L

A Harder Problem

setup

A line of charge

m=charge/length



Completing the math
Completing the Math array?

1/r dependence


Dare we project this
Dare we project this?? array?

  • 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...


The geometry
The Geometry array?

Define surface charge density

s=charge/unit-area

dq=sdA

(z2+r2)1/2

dA=2prdr

dq=s x dA = 2psrdr


(z array?2+r2)1/2

q


Final result

(z array?2+r2)1/2

Final Result



What did we learn in this chapter
What did we learn in this chapter?? array?

  • 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 Coulomb’s Law but divided by the “q of the test charge”.


What else did we learn in this chapter
What else did we learn in this chapter? array?

  • 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 charges1
Kinds of continuously distributed charges array?

  • Line of charge

    • m or sometimes l = the charge per unit length.

    • dq=mds (ds= differential of length along the line)

  • Area

    • s = charge per unit area

    • dq=sdA

    • dA = dxdy (rectangular coordinates)

    • dA= 2prdr for elemental ring of charge

  • Volume

    • r=charge per unit volume

    • dq=rdV

    • dV=dxdydz or 4pr2dr or some other expressions we will look at later.


The sphere
The Sphere array?

dq

thk=dr

dq=rdV=r x surface area x thickness

=r x 4pr2 x dr


Summary
Summary array?

(Note: I left off the unit vectors in the last

equation set, but be aware that they should

be there.)


To be remembered
To be remembered … array?

  • If the ELECTRIC FIELD at a point is E, then

  • E=F/q (This is the definition!)

  • Using some advancedmathematics we can derive from this equation, the fact that:

REMEMBER THIS !


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