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Electrostatics

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History

The word

electricity comes

from the Greek

elektron which

means “amber”.

The “amber effect”

is what we call

static electricity.

ELECTROSTATICS

the study of electric charges, forces and

fields

Static Electricity is “Stationary Electricity”

or Accumulation of charge

Two types of charges exists, arbitrarily named

POSITIVE and NEGATIVE

By Benjamin Franklin

So what is positive and what is negative?

History

We know that charged particles exist in atoms

Electrons are responsible for negative charge and Protons for positive charge

Benjamin Franklin did not know about the existence of these particles but, he did investigate the behavior of static discharge and lightning.

Ben knew that if certain electrically neutral objects are rubbed, they can become charged.

For example; when rubber is rubbed with a wool cloth, both become charged.

The rubber scrapes electrons

from fur atoms. So the rubber is

negatively charged and the cloth

is positively charged.

or a comb through hair

Ben also knew that a charge separation occurs when a glass rod is rubbed with a silk cloth

In the case of the glass and silk, the glass rod loses negative charge and becomes positively charged while the silk cloth gains negative charge and therefore becomes negatively charged.

Ben experimented with the interactions between the charge objects. He suspended one and brought other charged objects near…

Ben observed that like charged object repeland unlike charges attract

repelrepel

attract

Electrons:

Fundamental Rule

Opposites attract, Likes Repel

Things don’t like having a net charge

If objects don’t like having a net charge,

then how does it happen?

Silk on glass glass (+)

Who loses electrons?

The glass

Fur on rubber rubber (-)

Who loses electrons?

The fur

When objects get Charged:

Must obey Law of Conservation of Charge

Charges may be transferred among different atoms, materials, or objects but all charge is accounted for.

NO NEW charges are created nor are any charges destroyed.

Only electrons can move

Remember:

An excess of electrons results in:

A negative charge

A shortage of electrons results in:

A positive charge

ONLY ELECTRONS MOVE

How Do Charges Behave in

Materials?

Conductor:

Allows electrons to move easily

Metals, why?

Metals lose electrons, (not held tightly)

Insulator:

Does not allow electrons to move easily

Non metals. Glass, plastic, dry wood. Why?

Electrons held tightly

Semiconductors – charges only move

freely when certain conditions are met

(i.e., heat, sufficient voltage, etc.) ex

germanium, selenium, and silicon.

Superconductors – charges move

effortlessly and cannot be stopped once

they are moving

Objects become charged by…

Friction

Induction

Conduction

Electrons are rubbed off one insulator onto another insulator

Grounding

With a credit card

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FRICTION: e- rubbed off one

insulator to another

Objects become charged by…

Friction

Induction

Conduction Charging by CONTACT with a charged object

Grounding

Charging by Conduction

Some electrons leave rod

and spread over sphere.

Requires Contact Electrons transferred.Results in:Object with the same charge as original charged object.

Objects become charged by…

Friction

Induction

Conduction

Charging an object WITHOUT touching a charged object

Grounding

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Induction

no contact occurs between charged

object and neutral object..

Involves temporary rearrangement of

electrons on neutral object

Neutral Object becomes “polarized”

but net charge remains the same

If neutral polarized object is

grounded, charge will become

“opposite” of the charged object and

is no longer temporary

Neutral objects can be temporarily attracted to charged objects by a process called POLARIZATON.

Charging by Induction

A negatively charged balloon is brought near a

neutral conducting sphere as shown below. As it

approaches, charge within the sphere will

distribute itself in a very specific manner. Which one of the diagrams below properly depicts the

distribution of charge in the sphere?

What is grounding?

Involves Transfer of excess electrons to

and from the ground

Charging by Induction AND Grounding

The rod does not touch the sphere. It pushes electrons out

of the back side of the sphere and down the wire to

ground. The ground wire is disconnected to prevent the

return of the electrons from ground, then the rod is

removed.

The charge on the object is opposite if grounded

polarization grounding permanent charge

How can I tell if something is

charged?

Pith Ball Experiment

Pith Ball and a Charged Rod

Pith Ball Experiment

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In the beginning, the negative rod repels

the electrons in the neutral pith ball to

the ight. This causes the left side of the

pith ball to obtain a net positive charge.

Since opposite charges attract, the pith

ball is attracted to the rod. When they

touch, electrons are transferred to the

pith ball giving it a net negative charge.

Since the rod remains negative even

after the transfer, it repels the negatively

charged pith ball.27

Electroscope

-detects the

presence of

charge

When the leaves are charged, what will

happen?

When the leaves are not charged, what

will happen?

An electroscope is a devicethat detects static charge.

The metal leaves of the electroscope move apart if a charged object is brought near the knob. Benjamin Franklin used a similar device when he investigated charges.

Positively chargedNegatively charged

To review…

Induction results in an OPPOSITE CHARGEConduction results in the SAME CHARGE

Grounding is allowing charges to move freely along a connection between a conductor and the ground.

The Earth (the ground) is a practically infinite reservoir of electric charge.

Here a positively charge rod attracts electrons from the ground into the electroscope

Here a negatively charge rod repels electrons into the ground from the sphere

Static Electricity in our lives

Why are there more problems with static during the dry winter months?

The net charge of a water molecule is neutral, however it is a polar molecule. It can attract a build up of excess electrons

Some Static Electricity is due to friction

Clothes stick to each other in the dryer

How to solve this problem?

Dryer sheets. How do they work?

Dryer sheets contain lots of polar molecules to absorb the excess electrons and keep clothes neutral

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Lightning

Becomes

very

“negative.”

Becomes

very

“positive.”

WHO DETERMINED

POSITIVE AND

NEGATIVE?

How lightning forms – YouTube

how lightning works – YouTube

The Birth of a Lightning Bolt - YouTube

Four fundamental forces in nature

Gravity

Weak nuclear

Electromagnetic (electricity and

magnetism)

Strong nuclear

Electrical Forces

Why don’t we notice them?

The attractive and repulsive forces between the charges in Earth and the charges in your body balance out!!!!

Electromagnetic force is significant

at atomic level. Things you know:

Atom has positively charged nucleus surrounded by negatively charged electrons

All electrons are identical (same mass; same quantity of negative charge)

All protons are identical (same mass; same quantity of positive charge)

Nucleus composed of protons and neutrons. Neutrons are neutral

Neutral atoms have equal protons and electrons so zero net charge

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What exactly is CHARGE?

It is physical property of

matter.

It comes in two flavors:

“plus” and “minus.”

What is the unit for charge?

Coulombs (C)

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What is the smallest charge possible?

Millikan Oil Drop Experiment

In 1910, Millikan was able to measure

the charge of an electron.

The smallest charge possible is:

-1.602 x 10-19 Coulombs (C).

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Definition of Coulomb

Abbreviation: C

SI unit for charge

One coulomb is NOT equal to the charge of 1 electron!!!!

1C ~ the charge of 6.25 x 1018 electrons

It is the amount of charge to pass through a cross-section of wire in 1 second when 1 Ampere (A) of current is applied.

(We’ll cover the amp later.)

Likewise the + charge of protons is associated with 6.25 x 1018 protons

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Elementary Particles

Particle Charge,

(Coulombs

per particle)

# of particles

in a Coulomb

electron -1.6 x 10-19 6.25 x 1018

proton +1.6 x 10-19 6.25 x 1018

Ex 1

A strong lightning bolt transfers 35 C to

Earth. How many electrons were

transferred?

(35 C) (6.25 x 1018 electrons)

2.19 x 1020 electrons

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Coulomb’s Law

Charles-Augustin de Coulomb used a torsion pendulum to establish his law.

rd

qqkF ˆ

2

21

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Electric Force

q charge, C (coulombs)

d distance between charges, m

F electric force, N

k electrostatic constant 9.00 x 109 Nm2/C2

rd

qqkF ˆ

2

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What happens to F as charge increases?

Increase

What happens to F as r increases?

Decreases by inverse square

Look at kc. Is this a large or small value?

large

How is q described for a proton?

positive

For an electron?

negative

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The Product of q1and q2

If the product, q1q2 ,is

negative then the force is

attractive.

If the product, q1q2 ,is

positive then the force is

repulsive.

Ex 2: Two negatively charged balloons are 0.70m apart. If the charge of each is 2.0 x 10-6C, What is the electric force between the two balloons?

q1 = q2 = 2.0 x 10-6 Cd = r = 0.70 m

F kq q

r 1 2

2

F = 9.0 x 10 9 N m2/C2 (-2.0 x 10-6 C)2

(0.70m)2

F = 0.073 NAn attracting or repelling force?

Ex.3: Two equally charged balloons repel each other with a force of 4.0 x 10-3 N. If they are 0.015 m apart, what is the charge of the each balloon?

F = 4.0 x 10-3 Nd = 0.015 m F k

q q

r 1 2

2

q2 = (4x10-3N)(0.015m)2

(9x109Nm2/C2)

q2 = Fd2

k

q1 = q2 = 1.0 x 10-8C

Ex 4:

How many Coulombs are in a µC?

1 x 10-6

Two charges are separated by 3.0 cm.

Object A has a charge of +6.0 µC.

Object B has a charge of -6.0 µC. What

is the force on Object A? Is the force

attractive or repelling?

-360N, attractive

Ex 5

Two electrons exert an electrical force of

1.0 x 10-8 N on one another.

Is this an attractive or repelling force?

Repelling

Calculate the distance between them.

Rearrange formula to solve for d

Use known charge for an electron

1.5 x 10-10 m

Two charges create a

force on one another. If

the charge of one object

is doubled, how does

the resulting force

change?

F will double

What if charge of one

object is tripled?

F will triple

rd

qqkF ˆ

2

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Two charges create a force on one another. If the distance between the objects is increased by a factor of 2, the force changes by a factor of?

F will decrease by a factor of 4

What if distance between the objects is tripled?

F will decrease by a factor of 9

rd

qqkF ˆ

2

21

Review……….

How many electrons in one Coulomb?

6.25 x 1018 electrons

What is the charge of one electron

-1.6 x 10-19 Coulombs (C)

How many protons in one Coulomb?

6.25 x 1018 protons

What is the charge of one proton

+1.6 x 10-19 Coulombs (C).

Review……….

How many electrons in one Coulomb?

6.25 x 1018 electrons

Calculate the charge of one electron

-1.6 x 10-19 Coulombs (C)

How many protons in one Coulomb?

6.25 x 1018 protons

Calculate the charge of one proton

+1.6 x 10-19 Coulombs (C).

Force and Fields

Contact forces

What we mostly

deal with

Objects touch each

other directly

Ex. A tennis racket

hits a tennis ball

F=ma

www.CartoonStock.com.

Forces can occur without

contact!

Action at a distance

Can you think of anything that applies a

force without touching?

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Gravity demonstrates action at a

distance

What happens if you get too far away

from the mass exerting the force?

The effects are less

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What else applies an action at a

distance?

Magnets!

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60

What else applies an action at a

distance?

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Attracting and repelling forces of

charges

The space that surrounds these things is

altered

Examples:

Magnets

Sun

Planets

Electric charge

Action at a distance depends on

a field of influence An object within the field may be affected by it

Can be scalar or vector

Magnitude only

Ex. Heat

Can be vector

Magnitude and direction

Ex. Gravity (one direction only since only

attracts)

Ex. Electric (more than one direction; attracts

and repels

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Fields are NOT Force, they exert

the force

Ex. A person pushes a box.

The person is not the force, he exerts the

force!

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Electric field

A field that exerts force that surrounds

an electric charge or group of charges

Magnitude and direction (vector)

Electric field

How would you detect and measure an

electric field around a charge?

Place another one nearby and see what

happens!

Since all charges produce fields, come

up with a model

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Electric field model

Source charge: charge producing the

field. Usually designated with a capital

Q

Test charge: a mathematical creation

Always positive

Symbol: q’

Doesn’t exist

Infinitely small, thus produces no field of its

own

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What is the source charge if

The test charge q moves towards it?

Negative (attracts)

The test charge q moves away from it?

Positive (repels)

How would I draw these?

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Where do you think the field is

strongest?

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What if I had more than

one source charge?

What would the field lines

look like?

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Think: Where is the electrical potential energy of a

positive test charge (q+) higher, at the point A or B?

Why?

Point A. Because of it’s

location, it is not where

it “wants” to be. It took

work to get it there!

The electric field is strongest in regions where the lines are close together and weak when the lines are further apart.

Threads floating on oil bath become polarizedand align themselves with the electric field.

These fields can be detected in lab…

How do I measure the strength of the electrical field

around a source charge (Q)?

What factors do you think the

electrical field strength is dependent

on?1. Force (Push or Pull) of Source Charge

on Test Charge

2. Distance Between Source Charge

and Test Charge

First let’s consider effect of force

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Electric Field Intensity (Strength)

E - Electric Field Strength or Intensity (N/C)

F - Force experienced by a test charge at that

location (N)

q’ - magnitude of the test charge placed at that

location (C).

'q

FE

A test charge has a magnitude of 1 x 10-10C. It experiences a force of 2N in an electrical field. What is the Intensity of the field?

E = F/q’Variables:F = 2Nq’ = 1 x 10-10C

E = 2N/ 1 x 10-10C

E = 2 x 1010 N/C

Ex 6

A test charge of 6 x 10-26 uC is placed 200 mm from a proton (this is the source charge). What is the electrical force between them? What is the Field strength at this point? What is the direction of the field?

Variables:q’ = 6 x 10-26µCp+= 1.6 x 10-19Cd = 200 mm

Variables:q’ = 6 x 10-32Cp+= 1.6 x 10-19Cd = 0.2m

Now we can solve. This is a 2 step problem.

Step 1: Solve for force using Coulombs Law

Step 2: Use the calculated force and solve for Field Intensity

Ex 7

A test charge of 6 x 10-26 µC is placed 200 mm from a proton (this is the source charge). What is the electrical force between them? What is the Field strength at this point? What is the direction of the field?

Variables:q’ = 6 x 10-32Cp+= 1.6 x 10-19Cd = 0.2m

F = (9 x 109C)(6 x 10-32C)(1.6 x 10-19C)0.2m2

F = 2.16 x 10-39N

E = F/q’

F = kqq

d2

E = 2.16 x 10-39N / 6 x 10-32C

E = 3.6 x 10-8 N/C

Ex 7 cont

Remember: The direction of the electric field at a point in space is the same as the direction in which a positive charge would move if it were placed at that point. The electric field lines or lines of force indicate the direction.

Electric field line flow Out of positive charges and into Negative charges.

+ -Q

The electric field intensity E at a distance d from a source charge Q can be found without knowing the test charge!:

Units: N/C

EX 8: What is the electric field intensity at a distance of 2 m from a source charge of -12 μC? Include direction.

d = 2 mq = -12 μC

9 10 12 10

2

9 6

2

x x( ) = 2.7x104 N/C, towards q

or to the left

q = -12μC

To determine the direction of the field, ask

If the source charge is negative do the

field lines go out or in?

2d

kQE

How do I determine the field strength if

there are multiple charges?

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When more than one charge contributes to the field, the

resultant field is the vector sum of the contributions from

each charge.

Where k : 9x109Nm2/C2

Units: N/C

Note we will look at direction of the field to know whether fields add or subtract at a point.

2d

kQE

Remember this?

Electric field line flow Out of positive charges and into Negative charges.

+ -Q

Ex 9: Two charges q1=-8 μC and q2=+12 μC are placed 120 mm apart in the air. What is the electric field at the midpoint between them?

q1 = -8 μCq2 = +12 μCr = 0. 120m -

q1

+q2

E1 E2

ET

X

= kq1 + kq2

r2 r2

= (9 x 109)(8 x 10-6) + (9 x 109)(12 x 10-6)(0.06)2 (0.06)2

E= 2.0 x 107 + 3 x 107 = 5.0 x 107 N/Cto the left

2d

kQE

Ex.10: Two charges q1=+8 μC and q2=+12 μC are placed 120 mmapart in the air. What is the electric field at the midpoint between them?

q1 = + 8 μCq2 = +12 μCr = 0. 120m +

q1

+q2

E1E2

ET

X

Ekq

r

2

= kq1 - kq2

r2 r2

= (9 x 109)(8 x 10-6) - (9 x 109)(12 x 10-6)(0.06)2 (0.06)2

The fields are in opposite directions so they subtract

E= 2.0 x 107 - 3 x 107 = -1.0 x 107 N/C

E = 1.0 x 107 N/C to the left