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ELECTROSTATICS

Electrostatics

• electricity at rest.

• Involves electric charges, the forces between them and how they behave in materials SHOCKING STORY

Background

Static Electricity There are

Four Universal Forces

1. weak nuclear in nature: 2. strong nuclear 3.

gravitational - this one we've studied 4. electrical - this one is next Experiments show us that there are two kinds of charges. Ben Franklin named them positive and negative .

History of Electrostatics

Atomic Structure

Atoms

that have the same number of protons and electrons = electrically neutral . Net charge = zero

Ions

have lost or gained electrons = electrically charged .

 

Atoms

Proton as the has the same amount of positive charge electron has negative charge.

Why don't protons pull oppositely charged electrons into the nucleus?

Why don't the protons in a nucleus mutually repel and fly apart? [wave nature of e-] [strong nuclear force]

Conservation of Charge

In the whole universe:

•

number of + charges charges = number of So the universe is electrically neutral!

• Electric charge cannot be created destroyed .

Law of Charges

•

Likes repel and opposites attract.

Law of Charges Animated

Electric Charge

• the fundamental quantity that underlies all electrical phenomena.

• The attraction between positively charged protons and negatively charged electrons holds atoms (all matter) together.

• Charged particles have either: – gained – or lost extra electrons (

electrons (

charged) charged).

• This happens only when electrons from one object to another. • Protons are fixed in the nucleus move

Electric Charge

• Charged particles can only lose or gain whole electrons - so they can only have whole number multiples of the charge on an electron. – Fractions of the charge on an electron cannot exist alone. • Electric charge is

quantized

Electric Charge

The unit of charge is the • COULOMB ( C ) • 1 C = the charge ( q ) on 6.25 x 10 18 electrons • 1 electron has an

elementary charge

= 1.60 x 10 -19 C.

• The

Coulomb quantity

is a

fundamental

like grams and meters.

Insulators

:

A material whose electrons seldom move from atom to atom.

• Most insulators are non-metals .

– Electrons are tightly bound to one nucleus and cannot move around in the material. Example: • Electrons can be rubbed onto or off of glass and rubber but the electrons stay in one place and cannot move through the material.

Conductors

A material whose conduction electrons are free to move throughout the material.

• Most metals are conductors.

– In metals the outer shell electrons are not securely held by one particular nucleus.

If a conductor carries excess charge, the excess is distributed over the surface of the conductor.

Note: Electricity is just a flow of electrons!

Superconductors

• at very low temperatures (near absolute zero) some metals conduct with no

resistance

to flow of charge. Resistance causes current to "lose" energy because some of the energy is converted to heat - wires heat up when current flows through them.

Electric Charging Definitions

Electrification:

• process that produces electric charges

Electrostatic Charge:

• a charge that is confined to an object, remains still straight line.

and does not move in a

Electric Field:

The result of placing a static charge on an object is known as an electrostatic field around the charged end of the object. This is an invisible field of force much the same as that produced by gravity.

Electroscope

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Device used to detect the presence of an

electrostatic charge

• Rubber rod rubbed with fur =

negative

charge • Lucite rod rubbed with silk =

positive

charge Electroscope

Grounding

GROUNDING

reservoir of to the earth.

– The earth is a large electrons.

You are connected • When you touch something excess electrons can flow through you to the earth.

negative , • When you touch something that is positive , electrons flow from the earth through you to the object.

•

Grounding makes an object neutral!

Van de Graff Generator

Copywrited by Holt, Rinehart, & Winston

3 Methods of CHARGING

• Friction • Conduction • Induction

Charging by

Friction

• removing electrons by rubbing different materials together.

• When two different insulators are rubbed together, other.

electrons

can be transferred from one insulator to the – substance that negative ( gains rubber an electron rod) – substance that positive ( lucite loses rod) an electron Cutnell & Johnson,

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Charging by

Conduction

•

Conduction

(contact). is transfer by touching • the flow of electrons through a conductor. Charging by the flow of electrons.

• The only charges which can move freely through metals are carried by

negative electrons

charges Cutnell & Johnson,

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Conduction Example

• When a negatively charged rod [rubber is negative] touches a neutral conductor excess electrons flow from a negatively charged rod to the conductor.

• When a positively charged rod [acetate is positive] touches a neutral object excess electrons flow from the object to the positively charged rod.

neutral neutral • The object then becomes • The object then becomes negative .

positively charged. In conductors, the charge will spread out evenly over the object.

The neutral object (a conductor) will take the

same

charge as the charging rod. This transfer is

temporary

Conduction – Electroscope Example

Positive Rod  + Charge Negative Rod  - Charge

Charging by

Induction

Induction

is transfer without touching .

• the charging of an object without direct contact. • the process of " rearranging " the charges Cutnell & Johnson,

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Induction – Electroscope Example

Positive Rod Negative Rod Temporary Charge  Returns to

Neutral

after the Charged Rod is

Removed

Electroscope Grounding

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Induction

Induction with a Conductor Induction with an Insulator

Electrical

Polarization

occurs when an object’s attract a neutral one.

atoms rotate in response to an external charge. This is how a charged object can Copywrited by Holt, Rinehart, & Winston

Electrostatics Problem

Two metal spheres, one with a charge of 3C and the other with a charge of -1C are brought together and then removed. What is the resulting charge on the first sphere?

+3C -1C

Electrostatics Problem

Two metal spheres, one with a charge of 2µC and the other with a charge of 4µC are brought together and then removed. The first sphere is grounded and the second sphere then comes in contact with a -1µC sphere What are the resulting charges on these spheres?

+2 µ C +4 µ C

Electrostatics Problem

Three styrofoam balls are suspended from insulating threads. Several experiments are performed on the balls and the following observations are made: I. Ball A attracts B and repels C.

II. A negatively charged rod attracts A. What are the charges, if any , on each ball?

Clicker Understanding

• • • • Two spheres are touching each other. A charged rod is brought near. The spheres are then separated, and the rod is taken away. In the first case, the spheres are aligned with the rod, in the second case, they are perpendicular. After the charged rod is removed, which of the spheres is: i) Positive ii) Negative iii) Neutral Positive - B Negative - A Neutral - C, D

Calculating How Many Electrons

Since one electron has an elementary charge (1.6 x 10 -19 C), it is possible to determine how many extra electrons or how many missing electrons a charged particle carries:

N e



Q q e N e



M M e

= net charge .

charge of electron = mass of total electrons mass of one electron

Atomic Particles

Atomic Particle Charge (C) Mass (kg) Neutron 0

1.67 x 10 -27

Proton

1.6 x 10 -19 (positive) 1.67 x 10 -27

Electron

-1.6 x 10 -19 (negative) 9.11 x 10 -31

Electrons and Protons have the same magnitude of charge but opposite signs or direction.

Enlightning Question

A strong lightning bolt transfers about 25 C to Earth.

• How many electrons are transferred?

• If each water molecule donates one electron, what mass of water lost an electron to the lightning? Flm!

• (One mole of water has a mass of 18 g and 6.022 x 10 23 molecules = one mole.)

Coulomb’s Law

The force between charged particles depends on: • the charge on each particle –

directly proportional

magnitudes

F ~ Q 1 Q 2

to their • the distance between particles –

inversely proportional to the square of the distance between them

F ~ 1/r²

Clicker Understanding

• A small, positive charge is placed at the black dot. In which case is the force on the small, positive charge the largest?

Clicker Understanding

• A small, positive charge is placed at the black dot. In which case is the force on the small, positive charge the smallest?

Coulomb’s Law

The force between charged particles depends on: 1. the charge on each particle •

directly proportional magnitudes F ~ Q

1 Q 2

to their 2. the distance between particles •

inversely proportional

to the

square

of the

distance

between them.

F ~ 1/r²



Coulomb’s Law



2 • F = force in newtons (N) • k = 9.0 x 10 9 Nm 2 /C 2 : a constant whose value depends on the units used and on the medium (air) between the particles.

• q 1 = 1 st point charge • q 2 = 2 nd point charge • r (distance) in meters unit of Coulomb (C) (m)

Coulomb’s Law

If q 1 is and q 2 have opposite signs, the force attractive with a negative sign.

If q 1 and q 2 repulsive have same signs, the force is and has a positive sign.

Clicker Understanding

• All charges in the diagrams below are of equal magnitude. In each case, a small, positive charge is placed at the black dot. In which cases is the force on this charge to the left?

Clicker Understanding

• All charges in the diagrams below are of equal magnitude. In each case, a small, positive charge is placed at the black dot. In which cases is the force on this charge zero?

Coulomb’s Law

• The constant of proportionality depends on

the medium

K = 1/4πε • The constant ε is called the

permittivity

of the medium. • vacuum - the constant is written ε o . The units of ε are

N -1 C 2 m -2

, (this is usually written as

Farads per meter, F/m

• Air K = 1/4π ε where K = 9.0 x 10 9 Nm 2 /C 2

Comparing Gravity and Electricity

J.R. Zacharias, “Science”, March 8, 1957. • “ …. Coulomb’s law….in all of atomic and molecular physics, in all solids, liquids, and gases and in all things that involve our relationship with our environment, the only force besides gravity , is some manifestation of this simple law. Frictional forces, wind nothing but forces, chemical viscosity, magnetism.…all of these are Coulomb’s law bonds, ….”

Comparing Gravity and Electricity

Newton’s Law of Gravity Coulomb’s Law

F G



2 (1) Always is a very attractive small force, G number.

G = 6.67 x 10 -11 Nm 2 /kg 2

(2) Gravitational forces are very weak important.

, but very (3) Many large bodies have neutral charge therefore no net charge – only gravitational attraction.

F E



2 (1) Repulsive charge or attractive force replaces mass with , k is a very large number.

k= 9.0 x 10 9 Nm 2 /C 2

(2) Implies electrostatic charges are very strong .

Coulomb’s Law Practice

Find the magnitude of the force between two charges of 1.0 C each which are 1.0 m apart.

Coulomb’s Law Practice

Two small spheres are 20 cm apart. The left sphere has a charge of +10.8 µC and the right sphere has a charge of +12.2 µC • a. What force acts on each charge?

• b. What is the direction of the force?

+10.8 µ C + 12.2

µ C

Return of the 1’s Rule

• Used when a relative change not the actual size of the force is asked for • Example: : How is the force between two charges affected if the first charge is doubled, the second charge is tripled, and the distance between them is halved?



k q

~ ( 2 )( 3 )   2 2 F 2 =24F 1

Multiple Charges

Three point charges lie along the x axis in a vacuum as shown below. Calculate the net force acting on q 1 .

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Electrostatic Force Vectors

The electrostatic force is a • magnitude and direction When adding electrostatic forces: • Take into account the

vector

direction of all forces • Use vector components when needed Cutnell & Johnson,

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Electric Force Vectors

Find the magnitude and direction of the net electrostatic force on q shown below.

1 for three charges lying in the xy plane in a vacuum as Cutnell & Johnson,

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Electric Field

• Michael Faraday developed the concept of electric fields in the early 1800’s. The space around every electrically charged body is filled with an When another charge enters the field, an electric force

electric field

acts on it. . • Any electric field has both magnitude and direction. [What kind of quantity is this?]

Electric Field

• The magnitude of the field at any point is the force per unit charge .

• To find the magnitude of an electric field:



F q

E= magnitude of electric field F= force (on q) at that point q = size of test charge

Electric Field

• To normalize the electric field calculation, eliminating the arbitrary test charge we can substitute in Coulomb’s Law for F E



F E q

0 (1)

F E



kQq o r

2 (2) (2)  (1)

 1

kQq



kQ r

2 Where Q is the charge around which the electric field is being measured.

Electric Field Strength

• Electric Field ( E to as the electric field strength as it is similar in concept to gravitational field strength ( g )

 ) is sometimes referred

F E q



F G m

0 • Electric Field is a vector quantity so when calculating the net electric field, it must be summed per direction (like forces).

 

E tot

 

1  

2  

3 ...



E x





...



E y





...



E tot



x tot



y tot

  tan  1

E y tot E x tot

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Electric Field Strength Practice

Two positive charges with net charges of q 1 = 2C and q field equal zero.

2 = 4C respectively are separated by a distance of three meters. Calculate where on the line between them would the electric Cutnell & Johnson,

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Clicker Understanding

All charges in the diagram below are of equal magnitude. In each of the four cases below, two charges lie along a line, and we consider the electric field due to these two charges at a point along this line represented by the black dot. In which of the cases below is the field to the right?

Clicker Understanding

largest

Clicker Understanding

smallest

Electric Field Lines

• Imagine carrying a small positive test charge around and mapping the direction of the force on it.

• Lines representing the force vectors are ( drawn

away

toward

from a positive charge

a negative charge). The more crowded the lines of force, the stronger the electric field.

Electric Field Lines

• We draw arrows in the length is proportional to the the arrows to get charged sphere.

direction

field lines

of the force strength . Connect • Draw lines of force around a weak, positively • Draw lines of force around a strong, negatively charged sphere.

Single Charge Field

• Wherever the test charge is placed, the force will be directed away from the charge (or towards the charge if it is negative). Therefore, in this case, the shape of the field is

radial

Field due to two opposite point charges of equal magnitude

• a vector addition is needed to predict the direction of the line of force at the point considered.

• By considering a number of such additions, we obtain the following shape.

Field due to two opposite point charges of equal magnitude

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Field due to two opposite point charges of equal magnitude

Copywrited by Holt, Rinehart, & Winston

Field due to two similar point charges of equal magnitude

• Using vector addition to predict the direction of the line of force at various points produces a shape like this • At the center of this field is a place where the magnitude of the electric field strength is

zero

. This is called a

neutral point

Field due to two similar point charges of equal magnitude

Copywrited by Holt, Rinehart, & Winston

Electric Field between Parallel Plates

• In between the plates the field is

uniform

(constant magnitude and direction) except near the ends.

• The curving field at the end is known as an

edge effect

and is minimized by making the plates length much greater than the separation of the plates.

Clicker Understanding

Two parallel plates have charges of equal magnitude but opposite sign. What change could be made to decrease the field strength between the plates?

A. increase the magnitude of the charge on both plates B. decrease the magnitude of the charge on both plates C. increase the distance between the plates D. decrease the distance between the plates E. increase the area of the plates (while keeping the magnitude of the charges the same) F. decrease the area of the plates (while keeping the magnitude of the charges the same)

Electric Fields

• The electric fields around two charges interact with each other. Draw lines of force around the following pairs of charged spheres: – Two negatively charged spheres – Two positively charged spheres – One positive and one negative charged sphere

Clicker Understanding

• A set of electric field lines is directed as below. At which of the noted points is the magnitude of the field the

greatest

Clicker Understanding

• A set of electric field lines is directed as below. At which of the noted points is the magnitude of the field the

smallest

Clicker Understanding

A dipole is held motionless in a uniform electric field. For the situation below, when the dipole is released, which of the following describes the subsequent motion?

A. The dipole moves to the right.

B. The dipole moves to the left.

C. The dipole rotates clockwise.

D. The dipole rotates counterclockwise.

E. The dipole remains motionless.

Clicker Understanding

A dipole is held motionless in a uniform electric field. For the situation below, when the dipole is released, which of the following describes the subsequent motion?

A. The dipole moves to the right.

B. The dipole moves to the left.

C. The dipole rotates clockwise.

D. The dipole rotates counterclockwise.

E. The dipole remains motionless.

Clicker Understanding

A small sphere is suspended from a string in a uniform electric field. Several different cases of sphere mass and sphere charge are presented in the following table. In which case is the angle at which the sphere hangs the largest?

Sphere mass (g) A.

2.0

3.0

2.0

3.0

4.0

Sphere charge (nC) 4.0

4.0

6.0

8.0

9.0

Clicker Understanding

smallest

Sphere mass (g) A.

2.0

3.0

2.0

3.0

4.0

Sphere charge (nC) 4.0

4.0

6.0

8.0

9.0

Electric Fields of Conductors

• In a conductor excess charge on a conductor is free to move • So the charges will move until they are as far apart as possible. • This results in the excess charge on a conductor always being equally distributed on its surface.

Electric Fields of Conductors

• Since the charge is equally distributed on a conductor’s surface, the net electric field in a conductor is zero.

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Electric Fields of Conductors

• In addition the electric field lines are always perpendicular to the surface of a conductor.

• If not, the charge would move.

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Electric Fields of Conductors

• Since charge is equally distributed on the surface of a conductor.

• Charge is

concentrated

where the shape is more

sharply curved.

• Resulting in a curved areas.

larger

electric field at the more sharply

Lightning

Lightning Rod

• How do they work?

Electropotential Energy

• Work is required to push a small positive charge against the electric field around a positively charged sphere. • Since work is done on the little charge, its PE

increases

. • The closer it gets, the more strongly it is repelled the field ……. Therefore more work is required. by • If the charge were released, it would move away from the sphere and its PE would

decrease .

Its kinetic energy would increase .

Electropotential Energy

• When the little charge is added to the sphere, the charge on the sphere

increases

becomes and the field around it stronger . • Moving another positive charge toward the sphere will take even more work or energy and give the little charge

higher PE

Electropotential Energy

• Analogous to Mechanical Potential Energy Cutnell & Johnson,

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Voltage

• The amount of work done per unit charge as a charge is moved between two points in an electric field is called the

electric potential difference.

potential

• Because the unit for potential difference is the volt V , potential difference is often called

voltage

and uses the symbol V .

Voltage

• The equation for calculating voltage is:



EPE Q Q

symbols units V = W = Q = voltage Work (or electric PE) charge (V) (J) (C) • Since work done on a charge and the gain in potential energy voltage can also be thought of as charge . of the charge are the same, work per unit What theorem is this based on?

Electrical Potential

• Potential at a distance r Charge Q from a Point • It can be shown that the potential at p is given by



kQ r

Summing Up Electrical Potential

The electric potential of a group of point charges is the algebraic sum the potentials of each charge.

V tot



1 

2 

3 ...

Clicker Understanding

• Rank in order, from largest to smallest, the electric potentials at the numbered points.

a) 1 = 2,3 b) 3, 1 = 2 c) 3, 2, 1 d) 1 = 2, 3 = 4 e) 1, 2, 3

Electrical Potential Energy

• If the potential at point additional charge q p is V P and an is placed at P then

U E



qV p

• Where U E is the electrical potential energy of charge q .

• We can also define the electrical potential energy as the work required to move the charge from infinity to its current position.

Electrical Potential Energy

• When the positive charge q distance r is at some from Q , it experiences a repulsive force



kQq r

• So a force to the left would be required to move q closer to Q and the work dW done over a small distance, dr • Integrating (calculus) is

 

Fdr

 

kQq r

dr kQq W

 

 

kQq dr r

2 

kQq r R

 

kQq R U E



Electrical Potential Energy

• Both electrical potential energy electrical potential V are U E

scalars

and • So the change in either potential energy or potential is

path independent

Clicker Understanding

a) 0; b) negative; c) positive; d) negative; Is the change ∆

of the particle positive, f) negative; negative, or zero as it moves from i to f?

Electron Volt (eV)

• Unit of work (or energy) much smaller than the Joule. • If

1 electron

difference of done.

moves through a potential

then

1 eV

of work is •

W = Vq

and 1 eV is the work done moving one electron through a potential difference of 1 V.

• Therefore, 1eV = 1.6

×10 -19 J

Electrical Potential Energy

• Another form of Electrical Potential Energy is shown by (1)

U E



kQq r

(2)



kQ r

2 (2)  (1)

U E



kQ r



Eqr U E



Eqd

• From this a relationship between ( Electric Field ( V E ) and Electric Potential ) can be derived • Recall,

 

U E q



U E qd

 



Voltage & Electric Field

 



From calculus the relationship is

 

dV dr

• The electric field is related to how fast the potential is changing • If electrical potential is graphed versus distance, the electric field is the slope of the graph.

Voltage & Electric Field

• This relationship implies that when the potential is constant then the electric field is zero .

• So in a conductor where the electric field is zero, the voltage must be constant.

• All points on the surface of a charged conductor

are at the same potential

• A surface with the same potential is know as an equipotential .

 



Potential due to a Charged Hollow Metal Sphere

• Outside the sphere the charge can be considered to be a

point placed at the center

charge

• Inside the sphere, there is no electric field so all points are at the

same potential as the surface

Potential due to a Charged Hollow Metal Sphere

• Graphically, this is represented in a plot of Electric Potential V vs. distance from the center of a charged sphere r as: Physics for the IB Diploma 5th Edition (Tsokos) 2008 Physics for the IB Diploma 5th Edition (Tsokos) 2008 What would a graph of Electric Field E the center of a charged sphere look like?

vs distance from

Equipotentials

• An equipotential in a field is a line (or surface) joining all points which have the same potential. • An equipotential is therefore a line (or surface) along which a charge can be moved without work being done against (or by) the electric field. • This means that equipotentials must always be at

90°

to electric field lines so equipotentials near a single point charge are spherical.

Equipotentials

• Equipotential Lines • Moving along Equipotential Lines • Moving between Equipotential Lines

Voltage & Electric Field

 



• The relationship between voltage and electric field is shown graphically in electric field lines and equipotential lines • Electric field lines are always perpendicular to equipotential lines.

Equipotential Surfaces and the Electric Field •An ideal conductor is an equipotential surface.

• Therefore, if two conductors are at the same potential , the one that is more curved will have a larger electric field around it. This is also true for different parts of the same conductor as stated earlier.

Electric Field – Parallel Plates

• The field that exists between two charged parallel plates (like those on a bug zapper) is uniform EXCEPT near the plate edges , and depends upon the potential difference between the plates and the distance between the plates.

Electric Field = Potential Difference distance between plates



V d

Problems

If a conductor connected to the terminal of a battery has a potential difference (voltage) of 12 V, then each Coulomb of charge has a potential energy of _______J.

If a charge of 2 x 10 -5 C has a PE of 540 J, its voltage is ____________________V.

If a rubber balloon is charged to 5000 V, and the amount of charge on the balloon is 1 x 10 -7 C, then the potential energy of this charge is ___________J.

Problems

A force of .032 N is required to move a charge of 4.2 x 10 -6 C in an electric field between two points which are .25 m apart. What is the potential difference (voltage) between the points?

Electric Field Problems

• If an electron loses 1.4 x 10 -15 J of energy in traveling from the cathode to the screen of Andy’s computer screen, across what potential different must it travel?

• Chippy stands next to the Van De Graaff generator and gets a shock as she hold her knuckle 0.2 m from the machine. In order for a spark to jump, the electric field strength must be 3 x 10 6 V/m. At this distance, what is the potential difference between Chippy and the generator?

Similarities between Electric Fields and Gravitational Fields

Physics for the IB Diploma 5th Edition (Tsokos) 2008