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Electrostatics

ELECTROSTATICS

the study of electric charges, forces and

fields

Static Electricity is “Stationary Electricity”

or Accumulation of charge

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?

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 to neutralize it

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

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

Four fundamental forces in nature

Gravity

Weak nuclear

Electromagnetic (electricity and

magnetism)

Strong nuclear

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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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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

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Coulomb’s Law

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

rd

qqkF ˆ

2

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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

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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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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…

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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