Electrostatics chapter 23
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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

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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!!


Probable first observation electricity

Probable First Observation Electricity


Idiot

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

A Quick Experiment


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

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

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

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?

  • 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

  • Positive

  • Negative

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


Example tape

Example - Tape


Electrostatics chapter 23

Separation


An example

An Example

Volunteer Please


Effect of charge

Effect of Charge


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!!

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

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


From whence this charge

From whence this charge???

Easily Removed

-

+


Materials

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


Experiment 5

Pivot

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??

  • 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

  • Rubbing or bond breaking (same thing)

  • Transfer

    • Direct transfer

    • Polarization

    • Induction


Neutral object polarization

Neutral Object - POLARIZATION

Positive charge attracts negative charges.

Rod becomes “polarized.

Negative end is closer to positive charge

Distance effect causes attraction.


Induction

Induction


Polarize

Polarize


Ground

Ground


Remove ground

Remove Ground


Positive

Positive !


Balloon physics

Balloon Physics


Same as before polarization

Same as before: Polarization


What happens when two surfaces touch or rub

What happens when two surfaces touch or rub?

Bonding!


Electrostatics chapter 23

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!


So far we have found

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

Forces Between Charges


Coulomb s law force between charges

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.


Remember

Remember

Force is a VECTOR!!


Coulomb s law

Coulomb’s 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


Electrostatics chapter 23

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.


Electrostatics chapter 23

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

The Electric Field


Fields

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

Example – Gravitational Field.

  • 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.

M

m

mg

Mg


This is war

This is WAR

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! The Green thing is a Force Field!

The Force may not be with you ….


Side view

Side View

The

FORCE FIELD

Force

Big!

|Force|

o

Position


Properties of a force field

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

Mysterious Force

F


Electric field

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

Two Charges


Doing it

Doing it

Q

A Charge

r

F

q

The spot where we want

to know the Electric Field


General

General-


Force field

Force  Field


Two charges what is the electric field at point p

Two ChargesWhat is the Electric Field at Point P?


The two s s

The two S’s

  • Superposition

  • Symmetry


What is the electric field at the center of the square array

What is the electric field at the center of the square array?

Superposition and Symmetry


Kinds of continuously distributed charges

Kinds of continuously distributed charges

  • 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.


Continuous charge distribution

Continuous Charge Distribution


Ymmetry

ymmetry


Let s do it real time

Let’s Do it Real Time

Concept – Charge per

unit length m

dq= mds


The math

The math

Why?


A harder problem

q

dEy

dE

q

r

x

dx

L

A Harder Problem

setup

A line of charge

m=charge/length


Electrostatics chapter 23

(standard integral)


Completing the math

Completing the Math

1/r dependence


Dare we project this

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...


The geometry

The Geometry

Define surface charge density

s=charge/unit-area

dq=sdA

(z2+r2)1/2

dA=2prdr

dq=s x dA = 2psrdr


Electrostatics chapter 23

(z2+r2)1/2

q


Final result

(z2+r2)1/2

Final Result


Look at the field lines

Look at the “Field Lines”


What did we learn in this chapter

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 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?

  • 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

  • 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

dq

thk=dr

dq=rdV=r x surface area x thickness

=r x 4pr2 x dr


Summary

Summary

(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 …

  • 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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