Static Electricity - Chapter OutlineLesson 1: Basic Terminology and Concepts

The Structure of Matter Neutral vs. Charged Objects Charge Interactions Conductors and Insulators Polarization

Lesson 2: Methods of ChargingCharging by Friction Charging by Induction Charging by Conduction Grounding

Lesson 3: Electric ForceCharge Interactions Revisited Coulomb's Law Inverse Square Law Newton's Laws and the Electrical Force

Lesson 4: Electric FieldsAction-at-a-Distance Electric Field Intensity Electric Field Lines Electric Fields and Conductors Lightning

Lesson 5: Electric PotentialElectric Field and the Movement of ChargeElectric Potential Electric Potential Difference

objectives• Know:

– Charge is quantized. – Charge on an electron and proton. – Unit of charge.

• Understand: – Relationship between fundamental charge and

charge in coulombs. – Law of Conservation of Charge.

• Be able to: – Convert from fundamental charges to coulombs – Determine the charge on two or more objects after

they come in contact with one another.

The Structure of Matter• ATOMS- All material objects are composed of

atoms.

• Atoms contain a dense center called the nucleus and a larger surrounding of mostly empty space that contains the electrons.

Electrons• Electrons are present in the region of space

outside the nucleus. They are negatively charged and weakly bound to the atom. Electrons are often removed from and added to an atom by normal everyday occurrences. These occurrences are the focus of this Static Electricity unit.

Protons and Neutrons

• The nucleus of the atom contains positively charged protons and neutral neutrons. These protons and neutrons are not removable by usual everyday methods. It would require some form of high-energy nuclear occurrence to disturb the nucleus. Protons and neutrons will remain within the nucleus of the atom.

• Electrostatic phenomenon can never be explained by the movement of protons.

Summary of Subatomic Particles

Nucleus Electron

Proton Neutron Outside nucleusWeakly Bound

-ChargeNot very

massive(9.11X10-31kg)

Tightly Bound + Charge

Massive(1.67 X10-27 kg)

Tightly Bound No Charge

Massive(1.67X10-27kg)

Check Your Understanding• ____ are the charged parts of an atom.

a. Only electrons

b. Only protons

c. Neutrons only

d. Electrons and neutrons

e. Electrons and protons

f. Protons and neutrons

Charged versus Uncharged Objects• Electrically charged objects are formed when neutral

objects lose or gain electrons.• Note: protons and neutrons can not be removed, only

electrons can be removed or Added!

Positively-Charged

Negatively-Charged

Uncharged

Possesses more protons than

electrons

Possesses more electrons than

protons

Equal numbers of protons and

electrons

Charged objects contain unequal numbers of protons and electrons

Negatively charged Positively charged

Charged Objects as an Imbalance of Protons and Electrons

example

• Which part of an atom is most likely to be transferred as a body acquires a static electric charge?

1. proton

2. neutron

3. electron

4. positron

Charge as a Quantity• Like mass, the charge of an object is a measurable

quantity. The charge possessed by an object is often expressed using the scientific unit known as the Coulomb (C).

• One Coulomb of charge is an abnormally large quantity of charge.

– An object with -1 C of charge would need an excess of 6.25 x 1018 electrons,

– an object with a shortage of 6.25 x 1018 electrons would have a total charge of +1 C.

• The units of micro-Coulombs )1 µC = 10-6 C( or nano-Coulombs )nC = 10-9 C( are more commonly used as the unit of measurement of charge.

• +1.6 x 10 -19 Coulomb is called an elementary charge.

• The charge of one electron = -1e = -1.6 x 10 -19 C. • The charge on a single proton = + 1e = +1.6 x 10 -19C.

• If an object is charged, it possesses more or less ____________________________of electrons. It can not possess a fraction of an electron. An object can only have a charge that is multiple of the elementary charge – ______________of 1.6 x 10-19 C.

whole numbers

multiple

An object can not have a charge of

1. 3.2 × 10-19 C

2. 4.5 × 10-19 C

3. 8.0 × 10-19 C

4. 9.6 × 10-19 C

Example

example

• What is the smallest electric charge that can be put on an object?

1. 9.11 × 10-31 C

2. 1.60 × 10-19 C

3. 9.00 × 109 C

4. 6.25 × 1018 C

Determine the total charge of a charged object

• Determine the difference between the number of electrons and the number of protons to find the excess charge.

– if there are less electrons,

the total charge = the number of excess charge x )+1.6x10-19 C(– if there are more electrons,

the total charge = the number of excess charge x )-1.6x10-19 C(

• Similarly, if the net charge is given, one can divide the net charge by the elementary charge )1.6x10-19 C( to determine the excess number of electrons or protons.

example• An object possessing an excess of 6.0 ×

106 electrons has a net charge of

1. 2.7 × 10-26 C

2. 5.5 × 10-24 C

3. 3.8 × 10-13 C

4. 9.6 × 10-13 C

example

• Which quantity of excess electric charge could be found on an object?

1. 0.25 elementary charges

2. 5.25 × 10-19 C

3. 6.40 × 10-19 C

4. 1.60 elementary charges

• During a physics lab, a plastic strip was rubbed with cotton and became positively charged. The correct explanation for why the plastic strip becomes positively charged is that ...

a. the plastic strip acquired extra protons from the cotton.

b. the plastic strip acquired extra protons during the charging process.

c. protons were created as the result of the charging process.

d. the plastic strip lost electrons to the cotton during the charging process.

example

objectives• Know:

– Definition of insulator, conductor– Charge is transferred in solids by electron movement only.

• Understand: - How charges interact with each other- How to detect charges- How charges flow during polarization events.

• Be able to: - Explain how charged object attract neutral objects

Charge Interactions• The electric force is a non-contact force. Any

charged object can exert this force upon other objects - both charged and uncharged objects.

• The nature of the electric force:1. Opposites attract.

2. likes repel.

The Electric Force and Newton's Third Law

This electric force exerted between two charged objects is a force in the same sense that friction, tension, gravity and air resistance are forces. And being a force, the same laws and principles that describe any force describe the electrical force. One of those laws was Newton's law of action-reaction. )balloons(

Force of B upon A is the same in magnitude as Force of A upon B. they are action and reaction forces.

Force of D upon C is the same in magnitude as Force of C upon D. they are action and reaction forces.

Interaction Between Charged and Neutral Objects

• Any charged object - whether positively charged or negatively charged - will have an attractive interaction with a neutral object. – Positively charged objects and neutral objects

attract each other; – Negatively charged objects and neutral

objects attract each other.• Any charged object - plastic, rubber, or

aluminum - will exert an attractive force upon a neutral object. And in accordance with Newton's law of action-reaction, the neutral object attracts the charged object.

Charge detection• If two objects repel each other…

– one can conclude that both objects are charged and charged with the same type of charge. One could not conclude that the balloons are both positively charged or both negatively charged.

• If two objects attract each other…– one can conclude that at least one of the objects is

charged. The other object is either neutral or charged with the opposite type of charge. You cannot draw a conclusion about which one of the objects is charged or what type of charge )positive or negative( the charged object possesses.

example• A lightweight sphere hangs by an insulating

thread. A student wishes to determine if the sphere is neutral or electro statically charged. She has a negatively charged hard rubber rod and a positively charged glass rod. She does not touch the sphere with the rods, but runs tests by bringing them near the sphere one at a time. The student notes that the sphere is attracted to both rods. This test result shows that the charge on the sphere is

1. positive 2. negative 3. neutral

example• A negatively charged plastic comb is

brought close to, but does not touch, a small piece of paper. If the comb and the paper are attracted to each other, the charge on the paper

1. may be negative or neutral

2. may be positive or neutral

3. must be negative

4. must be positive

Conductors and Insulators• The behavior of an object that has been charged

is dependent upon whether the object is made of a conductive or a nonconductive material.

• Conductors are materials that permit electrons to flow freely from atom to atom and molecule to molecule.

• In contrast to conductors, insulators are materials that impede the free flow of electrons from atom to atom and molecule to molecule.

Examples of conductors and insulators• Examples of conductors include

– metals, – aqueous solutions of salts – graphite, – water– human body.

• Examples of insulators – plastics, – Styrofoam, – paper, – rubber, – glass – dry air.

The division of materials into the categories of conductors and insulators is a somewhat artificial division. It is more appropriate to think of materials as being placed somewhere along a continuum.

• Along the continuum of conductors and insulators, one might find the human body somewhere towards the conducting side of the middle. When the body acquires a static charge it has a tendency to distribute that charge throughout the surface of the body.

• phet

Human body is a conductor

• Water, being a conductor, has a tendency to gradually remove excess charge from objects. Since humidity levels tend to vary from day to day and season to season, it is expected that electrical affects )and even the success of electrostatic demonstrations( can vary from day to day.

Water is a conductor

Charge on an insulator will remain at the initial location of charging.

charge on a conductor is quickly distributed across the entire surface of the object. Why do think this happens?

The insulating cups are use to prevent charge from escaping to the surroundings as well as to provide for a convenient handle.

insulators vs. conductors

Distribution of Charge via Electron Movement

• Predicting the direction that electrons would move within a conducting material is a simple application of the two fundamental rules of charge interaction. Opposites attract and likes repel.

• The excess negative charge distributes itself throughout the surface of the conductor. This is because electrons wish to manipulate their surroundings in an effort to reduce repulsive affects.

Check your understanding• Suppose that a conducting sphere is charged

positively by some method. The charge is initially deposited on the left side of the sphere. Yet because the object is conductive, the charge spreads uniformly throughout the surface of the sphere. The uniform distribution of charge is explained by the fact that ____.

a. the charged atoms at the location of charge move throughout the surface of the sphere

b. the excess protons move from the location of charge to the rest of the sphere

c. excess electrons from the rest of the sphere are attracted towards the excess protons

• A conductor differs from an insulator in that a conductor ________.

a. has an excess of protons

b. has an excess of electrons

c. can become charged and an insulator cannot

d. has faster moving molecules

e. does not have any neutrons to get in the way of electron flow

f. none of these

objectives• Know:

– Definitions polarization and electroscope. – Charge is transferred in solids by electron movement only.

• Understand: - How charges flow during polarization events.

• Be able to: – Draw and interpret pith ball and electroscope diagrams.

Polarization - Why a charged object attract neutral object

• In an atom, the protons are tightly bound in a nucleus and incapable of movement. In conducting objects, electrons are so loosely bound that they may be induced into moving from one portion of the object to another portion of the object.

• By placing a charged object near a neutral conducting object you can create electron movement.

• No electrons have been added to or subtracted from the can yet there is a charge at either end of the can; overall the can is electrically neutral. This arrangement of charge is called polarization.

• Polarization is the process of separating opposite charges within an object.

• The polarization process always involves the use of a charged object to induce electron movement or electron rearrangement.

• By inducing the movement of electrons within an object, one side of the object is left with an excess of positive charge and the other side of the object is left with an excess of negative charge. Charge becomes separated into opposites.

• Polarization is not charging – the total charge in a polarized object is still zero just like before.

The Electroscope • An electroscope is a device which is capable of detecting

the presence of a charged object through polarization.

Polarization of an electroscope

How Can an Insulator be Polarized?• In an insulator, electrons merely redistribute

themselves within the atom or molecules nearest the outer surface of the object.

Polarization is Not Charging

• When an object becomes polarized, there is simply a __________________ of the centers of positive and negative charges within the object.

• While there is a separation of charge, there is NOT an imbalance of charge. When neutral objects become polarized, they are still ______________ objects.

redistribution

neutral

example• An inflated balloon which has been rubbed against a

person's hair is touched to a neutral wall and remains attracted to it.  Which diagram best represents the charge distribution on the balloon and the wall?

a b c d

example• The diagram below shows three neutral

metal spheres, x, y, and z, in contact and on insulating stands. Which diagram best represents the charge distribution on the spheres when a positively charged rod is brought near sphere x, but does not touch it?

A B

C

D

Lesson 2: Methods of Charging

1. Charging by Friction

2. Charging by Induction

3. Charging by Conduction

4. Grounding - the Removal of a Charge

objectives• Know:

– Definitions of conduction, induction, and grounding. – Charge is transferred in solids by electron movement only.

• Understand: - How charge is transferred by friction, conduction, and

induction.

• Be able to: - Draw and interpret pith ball and electroscope diagrams.

Charging by Friction

• When two objects are rubbed together electrons may be transferred from one object to another. One object gains electrons and the other object loses electrons, so both objects have a charge.

When wool is rubbed against a PVC pipe, the PVC steals electrons from the wool because it has higher electron affinity compared to wool. The PVC strip ends up with a negative charge while the woolends up with a positive charge

When wool is rubbed against a Nylon strip, the wool will steal electrons from the Nylon because wool has higher electron affinity than Nylon.  As a result, the Nylon ends up positively charged and the wool ends up negative.

How do we know which object will gain electrons and which will lose electrons?

• electron affinity determines which object will gain electrons.

• The property of electron affinity refers to the relative amount of love that a material has for electrons. High affinity means the material has more pull to electrons.

• The more love of electrons a material has the more likely it is to steal electrons from the other object during charging by friction

Triboelectric series • A triboelectric series is an

ordering of substances with high affinities on top.

• When any two materials in the table are rubbed together, the one which is higher can be expected to pull electrons from the material which is lower.

Law of Conservation of Charge• The total amount of charge in a closed

system remains constant – charge is not created or destroyed, it only moves from one object to another

• The frictional charging process )as well as any charging process( involves a transfer of electrons between two objects.

• During all charging processes, the net charge of the system is conserved.

Charging by Induction• the charging by induction method is to charge

an object without actually touching the charged object.

• An understanding of charging by induction requires an understanding of the nature of a conductor and an understanding of the polarization process.

• What is a conductor?• What is polarization?

Charging by induction - Using a Negatively Charged Object

Two metal spheres are mounted on insulating

stands

The presence of a – charge

induces e- to move from

sphere A to B. the two-sphere

system is polarized.

Sphere B is separated from

sphere A using the insulating stand. The

two spheres have opposite charges.

The excess charge

distributes itself

uniformly over the

surface of the

spheres.

Charging by induction - Using a Positively Charged Object

Two metal spheres are mounted on insulating

stands

The presence of a + charge

induces e- to move from

sphere A to B. The two-sphere

system is polarized.

Sphere B is separated from

sphere A using the insulating stand. The

two spheres have opposite charges.

The excess charge

distributes itself

uniformly over the

surface of the

spheres.

Charging a single sphere by induction

A metal sphere is mounted

on insulating

stand

A – balloon induces e- to

move from left side to the

right side. The sphere is polarized.

When touched, the e- leave the sphere through the hand

and enter “the ground.” The person has replaced the

second sphere )Sphere B( and

serves the role of the ground.

The positive charge evenly

distributes itself over

the sphere.

The sphere is now charged

positively, with the excess

charge attracted to the

balloon.

The Importance of a Ground in Induction Charging

• In the charging by induction cases, charge is never transferred from the charged object to the neutral object… They do not touch! The charged object causes the neutral object to become polarized.

• The neutral object got charged through a ground.

• A ground can serve as a supplier or receiver of electrons.

Examples of ground

Grounding is also a way of uncharging an object.

The Need for a Conducting Pathway• Any object can be grounded provided that the charged

atoms of that object have a conducting pathway between the atoms and the ground.

Electrons will travel along that pathway.

Charging an electroscope by induction

1. Bring a charged object near the electroscope

2. The electroscope is being polarized.

3. Touch the part of the electroscope that is away from the charged object.

4. Remove your hand.

5. Remove the charged object.

fundamental principles regarding induction charging

1. The charged object is never touched to the object being charged by induction.

2. The charged object does not transfer electrons to or receive electrons from the object being charged. The charged object serves to polarize the object being charged.

3. The object being charged is touched by a ground; electrons are transferred between the ground and the object being charged )either into the object or out of it(.

4. The object being charged ultimately receives a charge that is opposite that of the charged object which is used to polarize it.

example

• A charged body may cause the temporary redistribution of charge on another body without coming in contact with it. This process is called

1. conduction

2. potential

3. Charging by friction

4. induction

Charging by Conduction • Charging by conduction involves the contact of a

charged object to a neutral object.

Upon contact, e- move from the sphere to the electroscope and spread about uniformly.

The metal sphere now has less excess – charge and the electroscope now has a - charge

A metal sphere with an excess of – charge is brought near to a neutral electroscope.

• When charging by conduction both object have the same type of charge when separated. – If A negatively charged object touches a

neutral object the neutral object gains electrons and becomes negatively charged as well.

– If a positively charged object touches a neutral object then the neutral object loses electrons and when separated it is positively charged as well.

• To charge by conduction successfully your charged and neutral object must be conductors!

Law of Conservation of Charge • In a closed system, charge is always

conserved. The total amount of charge among the objects is the same before the charging process starts as it is after the process ends.

example• Two metal spheres having charges of

+4.0 × 10-6 coulomb and +2.0 × 10-5 coulomb, respectively, are brought into contact and then separated.  After separation, the charge on each sphere is

1. 8.0 × 10-11 C

2. 8.0 × 10-6 C

3. 2.1 × 10-6 C

4. 1.2 × 10-5 C

• A physics student, standing on the ground, touches an uncharged plastic baseball bat to a negatively charged electroscope. This will cause ___.

a. the electroscope to be grounded as electrons flow out of the electroscope.

b. the electroscope to be grounded as electrons flow into the electroscope.

c. the electroscope to be grounded as protons flow out of the electroscope.

d. the electroscope to be grounded as protons flow into the electroscope.

e. the baseball bat to acquire an excess of protons.f. absolutely nothing )or very little( to happen since the

plastic bat does not conduct.

Lesson 3: Electric Force

1. Charge Interactions Revisited

2. Coulomb's Law

3. Inverse Square Law

4. Newton's Laws and the Electrical Force

objectives Know:

– Definition of electrostatic force. – Electrostatic force equation – Inverse square relationship between Fe and r

Understand: – Relationship between electrostatic force, charge, and

separation distance. Be able to:

– Use the electrostatic force equation to solve for unknown variables.

– Sketch or recognize a graph of Fe vs. r – Predict changes to force based on changes to:

One or both charges Separation distance

• The two fundamental charge interactions are: – oppositely charged objects attract – like charged objects repel.

• These mutual interactions resulted in an electrical force between the two charged objects.

Charge Interactions are Forces

A charged PVC pipe and a paper bit interact. The electrical force on the paper bit from PVC pipe balances the weight on the paper bit. The paper remains in equilibrium.

Electric force is a non-contact force• The electrical force is a non-contact force - it exists despite

the fact that the interacting objects are not in physical contact with each other.

Two like-charged objects exert equal and opposite repulsive electrical force on each other without contact with each other.

Free body diagrams for objects A and B shown that there are three forces on each of the two objects. Both Felect and Fgrav are non-contact forces.

Force as a Vector Quantity • Being a force, the strength of the electrical interaction is

a __________________ which has both magnitude and direction.

vector quantity

• The best way to determine the direction of it is to apply the fundamental rules of charge interaction – opposites ____________.– likes ____________.

attract repel

example• An electron is located 1.0 meter from a +2.0-coulomb charge, as shown in the diagram. The electrostatic force acting on the electron is directed toward point1.  A 2.  B 3.  C 4.  D

A

B

C

D

example• Two plastic rods, A and

B, each possess a net negative charge of 1.0 × 10-3 coulomb.  The rods and a positively charged sphere are positioned as shown in the diagram.  Which vector below best represents the resultant electrostatic force on the sphere?

a b c d

Coulomb's Law

charge

distance

charge

•k is a proportionality constant known as the Coulomb's law constant. k = 8.99 x 109 N • m2 / C2. •F: force between two charges, (in Newtons)

rQ2Q1

• The interaction between charged objects is a non-contact force that acts over some distance of separation. The force between two charged objects depends on three variables:– The ______________on object 1, – The ______________ on object 2, – The _________________ between them.

• Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.

• The force value is positive )repulsive( when q1 and q2 are of like charge - either both "+" or both "-".

• The force value is negative )attractive( when q1 and q2 are of opposite charge - one is "+" and the other is "-".

• Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them.

Example

• Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of 0.0626 Newtons. Determine the separation distance between the two balloons.

Example

Comparing Electrical and Gravitational Forces

• Both electrical force and gravitational force are non-contact forces.

•The two equations have a very similar form. –Both equations show an _________________ relationship between force and separation distance. –both equations show that the force is proportional to the product of the quantity that causes the force.

inverse square

• Coulomb's law constant )k( is significantly greater than Newton's universal gravitation constant )G(. Subsequently the force between charges – electric force - are significantly stronger than the force between masses – gravitational force.

• Gravitational forces are only attractive; electrical forces can be either attractive or repulsive.

example

• The diagram below shows two identical metal spheres, A and B, separated by distance d. Each sphere has mass m and possesses charge q.

•                                                   

• Which diagram best represents the electrostatic force Fe and the gravitational force Fg acting on sphere B due to sphere A?

A B C D

example

• Two protons are located one meter apart. Compared to the gravitational force of attraction between the two protons, the electrostatic force between the protons is

1.stronger and repulsive

2.weaker and repulsive

3.stronger and attractive

4.weaker and attractive

• That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed.

• If the separation distance is doubled )increased by a factor of 2(, then the electrostatic force is decreased by a factor of four (22)

• If the separation distance is tripled )increased by a factor of 3(, then the electrostatic force is decreased by a factor of nine (32).

F

d

Coulomb’s Law – force and distance is inverse squared

example• Two charges that are 2 meters apart

repel each other with a force of 2x10-5 newton. If the distance between the charges is decreased to 1 meter, the force of repulsion will be

1. 1 x 10-5 N 2. 5 x 10-6 N 3. 8 x10-5 N 4. 4 x 10-5 N

• Electrostatic force is directly proportional to the charge of each object. So if the charge of one object is doubled, then the force will become two times greater. If the charge of each of the object is doubled, then the force will become four times greater.

Coulomb’s law – force and charge has direct relationship

example

• A repulsive electrostatic force of magnitude F exists between two metal spheres having identical charge q.  The distance between their two centers is r.  Which combination of changes would produce no change in the electrostatic force between the two spheres?

1.doubling q on one sphere while doubling r 2.doubling q on both spheres while doubling r 3.doubling q on one sphere while halving r 4.doubling q on both spheres while halving r

Newton's Laws and the Electrical Force

• Electric force, like any force, is analyzed by Newton's laws of motion. The analysis usually begins with the construction of a free-body diagram. The magnitudes of the forces are then added as vectors in order to determine the resultant sum, also known as the net force. The net force can then be used to determine the acceleration of the object.

• In some instances, the goal of the analysis is not to determine the acceleration of the object. Instead, the free-body diagram is used to determine the spatial separation or charge of two objects that are at static equilibrium. In this case, the free-body diagram is combined with an understanding of vector principles in order to determine some unknown quantity.

example• A 0.90x10-4 kg balloon with a charge of -7.5 x 10-10 C is

located a distance of 0.12 m above a plastic golf tube which has a charge of -8.3 x 10-10 C. Determine the acceleration of the balloon at this instant?

example• Balloon A and Balloon B are charged in a like manner by

rubbing with animal fur. Each acquires 4.0 x 10-6 C. If the mass of the balloons is 1 gram, then how far below Balloon B must Balloon A be held in order to levitate Balloon B at rest? Assume the balloons act as point charges.

Felec

Fg

Lesson 4: Electric Fields1. Action-at-a-Distance

2. Electric Field Intensity

3. Electric Field Lines

4. Electric Fields and Conductors

5. Lightning

objectives Know:

– Electric fields: Exist near charges, originate on positives and end on negatives, never cross

– Electric field intensity equations. Understand:

– Relationship between field strength, distance, force and charge

– Behavior of charges between charged plates Be able to:

– Use the electric field equation to solve for unknown variables. – Draw and recognize electric field diagrams for:

Point charges Systems of charges Parallel plates

Action-at-a-distance force

• There are two categories of forces - contact forces and action-at-a-distance forces.

• Electrical force and gravitational force were both action-at-a-distance forces.

• Gravitational force - – the mass of the Earth exerted an influence,

affecting other masses which were in the surrounding neighborhood.

• electrical force – – The charges exerts an influence over a

distance affecting other charges which were in the surrounding neighborhood

The Electric Field and Gravitational Field Concept

• How can a balloon reach across space and pull a second balloon towards it or push it away?

• A charged object creates an electric field. Other charges in that field would feel its effect in the space. Whether a charged object enters that space or not, the electric field exists.

• How can an apple reach across space and falls toward Earth?

• The massive Earth creates a Gravitational field. Other masses in that field would feel its effect in the space. Whether a mass object enters that space or not, the gravitational field exists.

g = Fg / m

Electric Field strength

• Electric field strength is a vector quantity. it has both magnitude and direction.

• E is The electric field strength.

• q is the test charge – in Coulombs

• Fe is the force on the test charge q – in Newton

• Electric field strength is the force per charge ratio. The unit for electric field is N/C

e

• Note that there are two charges here - the source charge and the test charge. Electric field is the force per quantity of charge on the test charge.

• The electric field strength is not dependent upon the quantity of charge on the test charge.

• According to Coulomb's law, Felect = kQq/d2, increasing the quantity of charge on the test charge - say, by a factor of 2 - would increase the electric force )F( by a factor of 2 also, so the ratio of Fe/q still stays the same,

• So regardless of what test charge is used, the electric field strength at any given location around the source charge Q will be measured to be the same.

e

Another Electric Field Strength Formula

• The electric field strength is dependent upon the quantity

of charge on the source charge )______( and the

distance of separation )______( from the source charge.

Q

d

By applying Coulomb’s Law equation, we can deduce that

2d

GMg E

An Inverse Square Law• Electric field strength is location dependent, and its

magnitude decreases as the distance from a location to

the source increases. And by whatever factor the

distance is changed, the electric field strength will

change inversely by the square of that factor.

E

d

E = d2

k∙Q

example• What is the magnitude of the electric force

acting on an electron located in an electric field with an intensity of 5.0 x 103 N/C?

example• What is the magnitude of an electrostatic

force experienced by one elementary charge at a point in an electric field where the electric field intensity is 3.0 × 103 N/C?

example

• The diagram above represents a uniformly charged rod.  Which graph below best represents the relationship between the magnitude of the electric field intensity )E( and the distance from the rod as measured along line AB?

A B C D

The Direction of the Electric Field Vector

• Electric field strength is a _______quantity.

• the direction of the electric field vector is defined as the

direction that a ______________________________ is

pushed or pulled when in the presence of the electric

field.

• the electric field vector would always be directed

_______ from positively-charged objects.

• electric field vectors are always directed ____________

negatively-charged objects

vector

positive test charge

away

towards

Electric Field Lines

• Lines are directed away from positively charged source charges and toward negatively charged source charges.

• The closer lines near the charge indicating stronger field.

Rules for Drawing Electric Field Patterns

1. Surround more charged objects by _____________________.more lines.

• The electric field is ___________________ at locations closest to the surface of the charge and least at locations further from the surface of the charge.

greatest

2. draw the lines of force ___________________ to the

surfaces of objects at the locations where the lines

connect to object's surfaces.

• The electric force, and thus the electric field, is always

directed perpendicular to the surface of an object.

There are never any component of force parallel to the

surface.

perpendicular

3. Electric field lines should _____________________.

• Every single location in space has its own electric field

strength and direction associated with it; consequently,

the lines representing the field cannot cross each other

at any given location in space.

never cross

Electric Field Lines for Configurations

• two same charges• At what point is E = 0

0

Two Opposite charges

• Two Unequal amount of charges

example• The diagram shows the electric field in the vicinity of

two charged conducting spheres, A and B. What is the static electric charge on each of the conducting spheres?

1. A is negative and B is positive. 2. A is positive and B is negative. 3. Both A and B are positive. 4. Both A and B are negative.

example• Two small metallic spheres, A and B, are separated by a

distance of 4.0 × 10-1 meter, as shown. The charge on each sphere is +1.0 × 10-6 coulomb. Point P is located near the spheres. Which arrow best represents the direction of the resultant electric field at point P due to the charges on spheres A and B?

1 2 3 4

Fields between two oppositely charged parallel plates

• If the distance separating

two oppositely charged

parallel plates is small

compared to their area, the

electric field between the

plates is ____________.

• The field lines are from

positive plate to the

negative plate.

uniform

• Since E=F/q, the __________________________ on a

charged particle everywhere inside the plates.

• A charged particle will accelerate toward the plate with the

opposite charge.

• Ex: negative charge accelerates to positive plate, and

positive charge accelerate to negative plate.

force is the same

─

++++++++++++++++++++++++++++++++++++++++++++++

┼

example• As an electron moves

between two charged parallel plates from point B to point A, as shown in the diagram, the force of the electric field on the electron

1. decreases

2. increases

3. remains the same

example• In the diagram, proton p, neutron n, and electron e are

located as shown between two oppositely charged plates. The magnitude of acceleration will be greatest for the

1. neutron, because it has the greatest mass 2. neutron, because it is neutral 3. electron, because it has the smallest mass 4. proton, because it is farthest from the negative plate

Electric field and conductors• A _______________ is material which allows electrons

to move relatively freely from atom to atom.

• Electrostatic equilibrium is the condition established

by charged conductors in which the excess charge has

optimally distanced itself so as to reduce the total

amount of repulsive forces. Once a charged conductor

has reached the state of electrostatic equilibrium, there

is no further motion of charge about the surface.

conductor

+

+

+

+ -

-

-

-

Four properties of conductor in electric equilibrium

1. the electric field anywhere beneath the surface of a

charged conductor is zero.

• This principle of shielding is commonly utilized today

as we protect delicate electrical equipment by

enclosing them in metal cases.

2. Any excess charge on an isolated conductor resides

entirely on the conductor’s outer surface.

3. the electric field on the surface of the conductor is

directed entirely perpendicular to the surface.

4. A forth characteristic of conducting objects at

electrostatic equilibrium is that the electric fields are

strongest at locations along the surface where the

object is most curved.

example• A metallic sphere is positively charged.

The field at the center of the sphere due to this positive charge is

1. positive

2. negative

3. zero

4. dependent on the magnitude of the charge

Millikan’s oil-drop experiment

• In 1909, Robert Millikan performed the oil-drop experiment to measure the elementary electric charge. The experiment entailed balancing the downward gravitational force with the upward electric forces on tiny charged droplets of oil suspended between two metal plates..

Fg = Fe

m∙g = E∙q

q = mg / EFg

Fe

• Milliken measured the forces on charged oil drops in a

uniform electric field.

• He found no drop with a charge less than 1.60 x 10-19

coulomb. The charges on other drops were integral

multiples of this value.

• This finding demonstrated that there is a ______________

unit of charge. This elementary charge of 1.60 x 10-19

coulomb is called the charge on a single electron.

fundamental

example• What did Milliken conclude after performing his

oil-drop experiment?

1. The charge on an electron is 1.0 C. 2. The mass of an electron is 1.7 × 10-27 kg. 3. The charge on any oil drop is an integral

multiple of the charge on an electron. 4. The charge on an oil drop may have any value

larger than 1.6 × 10-19 C.

example• The diagram, which illustrates the Milliken oil drop

experiment, shows a 3.2 × 10-14-kilogram oil drop with a charge of -1.6 × 10-18 coulomb.  The oil drop was in equilibrium when the upward electrical force on the drop was equal in magnitude to the gravitational force on the drop.  What was the magnitude of the electric field intensity when this oil drop was in equilibrium?

example• An object with a net charge of 4.80 × 10-6 coulomb

experiences an electrostatic force having a magnitude of 6.00 × 10-2 newtons when placed near a negatively charged metal sphere. What is the magnitude and direction of electric field strength at this location? [show all work including substitution with units]

lightning• Perhaps the most

known and powerful displays of electrostatics in nature is a lightning storm.

• What is the cause and mechanism associated with lightning strikes?

• How do lightning rods serve to protect buildings from the devastating affects of a lightning strike?

Static Charge Buildup in the Clouds

• The precursor of any lightning strike is the polarization of positive and negative charges within a storm cloud. The tops of the storm clouds are known to acquire an excess of positive charge and the bottom of the storm clouds acquire an excess of negative charge.

• When a thunderhead passes over the ground, electrons on Earth's outer surface are repelled by the negatively charged cloud's bottom surface. This creates an opposite charge on the Earth's surface. Buildings, trees and even people can experience a buildup of static charge as electrons are repelled by the cloud's bottom.

• The electric field between the cloud and the Earth is similar to the electric field between two oppositely charged plates.

• When the difference in negative and positive charges between ground and cloud gets large enough, a lightning bolt begins. The excess electrons on the bottom of the cloud start a journey through the conducting air to the ground at speeds up to 60 miles per second.

• As electrons travel close to the Earth, it encounters the positive charges traveling upward, when the two types of charges meet, lightning begins.

• The enormous and rapid flow of charge along this pathway between the cloud and Earth heats the surrounding air, causing it to expand violently. The expansion of the air creates a shockwave which we observe as thunder

Lightning Rods and Other Protective Measures

• Tall buildings, farm houses and other structures susceptible to lightning strikes are often equipped with lightning rods.

• the lightning rod serves to safely divert the lightning to the ground in event that the cloud discharge its lightning via a bolt.

Check Your Understanding1. TRUE or FALSE:

The presence of lightning rods on top of buildings prevents a cloud with a static charge buildup from releasing its charge to the building.

 

 

2. TRUE or FALSE:

If you place a lightning rod on top of your home but failed to ground it, then it is unlikely that your home would be struck by lightning.

Lesson 5 - Electric Potential Difference

Electric Field and the Movement of Charge

Electric Potential

Electric Potential Difference

objectives Know:

- Definition of electrical potential; electron-volt - Unit of electrical potential - Electrical potential equation

Understand: - How energy is stored in electric fields. - Relationship between electrical potential, work, and charge. - Appropriateness of using electron-volts vs. joules.

Be able to: - Use the electrical potential equation to:

• Solve for unknown variables. • Find kinetic energy

- Determine methods for maximizing or minimizing electrical potential.

- Convert from electron-volts to joules.

• A charged object creates an electric field. Electric field is a vector quantity. As another charged object enters into the field, its movement is affected by the field.

+e

+e

-e -e

Electric Field and the Movement of Charge

Electric Field, Work, and Potential Energy • Electric fields are similar to gravitational fields - both involve

action-at-a-distance forces.

• In the case of gravitational fields, when gravity does work upon an object to move it in the direction of the gravitational field, then the object loses potential energy. However, when work is done to move an object against gravity, the object gains potential energy.

• In a similar manner, when a charge is moved by the electric field, it loses energy. To move a charge in an electric field against its natural direction of motion would require work. The exertion of work by an external force would in turn add potential energy to the object.

Moving the + test charge against the E field from A to B will require work and increase the potential energy of the charge. This is similar to an object going uphill.

The + test charge will naturally move in the direction of the E field from B to A; work is not required. The potential energy of the charge will decrease. This is similar to an object going downhill.

One can conclude that the high energy location for a positive test charge is a location nearest the positive source charge; and the low energy location is furthest away.

Now consider the motion of the same positive test charge within the electric field created by a negative source charge. The same principle regarding work and potential energy will be used to identify the locations of high and low energy.

Moving the + test charge against the E field from B to A will require work and increase the potential energy of the charge.

The + test charge will naturally move in the direction of the E field from A to B; work is not required. The potential energy of the charge will decrease.

One can conclude that the low energy location for a positive test charge is a location nearest the negative source charge; and the high energy location is furthest away.

example

B

A

+e

++++++++++++++++++++++++++++++

As a positive charge moves for B to A, it potential energy is _____.

a. increased b. decreased c. stays the same

• The concept of electric potential is related to the potential energy of a positive test charge at various locations within an electric field.

Electric potential

+

BA

B: high energy location

A: low energy location

The Gravitational Analogy Revisited• Gravitational potential energy was defined as the energy

stored in an object due to its vertical position above the Earth.

GPE = mgh

The height, h, is a quantity that could be used to rate various locations about the surface of the Earth in terms of how much potential energy each kilogram of mass would possess when placed there. The height, h, is known as gravitational potential. It is defined as the PE/mass. It is mass independent. Gravitational potential describes the affects of a gravitational field upon objects that are placed at various locations within it.

• The concept of electric potential must have a similar meaning.

• Electric potential is purely location dependent. Electric potential is the potential energy per charge.

• Electric potential is a property of the location within an electric field.

The electric potential is the same for all charges at a given location. A test charge with twice the quantity of charge would possess twice the potential energy at that location;Suppose that the electric potential at a given location is 12 Joules per coulomb, a 2 coulomb object would possess 24 Joules of potential energy at that location and a 0.5 coulomb object would experience 6 Joules of potential energy at the location.

Equipotential lines• Equipotential lines connect positions of equipotential

energy. As a charge moves on an equipotential line, there is _________________in potential energy. As the charge crosses equipotential lines, the potential energy changes.

+e

no change

+e

++++++++++++++++++++++++++++++

------------------------------------------------------

Check Your Understanding

• The quantity electric potential is defined as the amount of _____.

a. electric potential energy

b. force acting upon a charge

c. potential energy per charge

d. force per charge

• The following diagrams show an electric field )represented by arrows( and two points - labeled A and B - located within the electric field. A positive test charge is shown at point A. For each diagram, indicate

• a( whether work must be done upon the charge to move it from point A to point B.

• b( indicate the point )A or B( with the greatest electric potential energy and the greatest electric potential. 

1

3

2

4

• Electric potential is a location-dependent quantity that expresses the amount of potential energy per unit of charge at a specified location. – When a given amount of charge possesses a

relatively large quantity of potential energy at a given location, then that location is said to be a location of high electric potential.

– And similarly, if the same charge possesses a relatively small quantity of potential energy at a given location, then that location is said to be a location of low electric potential.

• As we begin to apply our concepts of potential energy and electric potential to circuits, we will begin to refer to the difference in electric potential between two points.

Electric Potential Difference

• Consider the task of moving a positive test charge within a uniform electric field from location A to location B as shown in the diagram.

As a result of this change in potential energy, there is also a difference in electric potential between locations A and B. This difference in electric potential is represented by the symbol ∆V. By definition, the electric potential difference is the difference in electric potential )V( between the final and the initial location when work is done upon a charge to change its potential energy. In equation form, the electric potential difference is

In moving the charge against the electric field from location A to location B, work will have to be done on the charge by an external force. The amount of work that is done is equal to the increase in the potential energy.

• The standard metric unit on electric potential difference is the volt, abbreviated V and named in honor of Alessandro Volta.

• 1 Volt = 1 Joule / Coulomb.

If the electric potential difference between two locations is 1 volt, then one Coulomb of charge will gain/lose 1 joule of potential energy when moved between those two locations. If the electric potential difference between two locations is 3 volts, then one coulomb of charge will gain/lose 3 joules of potential energy when moved between those two locations. Because electric potential difference is expressed in units of volts, it is sometimes referred to as the voltage.

Alessandro Giuseppe Antonio Anastasio Volta

)2/18/1745 – 3/5/1827( Italian physicist known for the development of the first electric cell in 1800.

Electron volt )eV(

• If an elementary charge is moved against an electric field through a potential difference of one volt, the work done on the charge is:

• W = Vq = )1 volt()1 e( = 1 eV • 1 eV aka electron volt is a quantity of energy

needed to move 1 electron )elementary charge( through a 1 volt of potential difference of one volt.

• W = Vq = )1 volt()1.6 x 10-19 C( = 1.6 x 10-19 J• 1 eV = 1.6 x 10-19 J

Check Your Understanding

• Moving an electron within an electric field would change the ____ the electron.

a. mass of

b. amount of charge on

c. potential energy of   

example• Moving a point charge of 3.2 ×10-19 C between

points A and B in an electric field requires 4.8 ×10-19 J of energy.  What is the potential difference between these two points?

example• How many eV is required to move 3.2 x 10-19 C

of charge through a potential difference of 5.0 volts?

example• A helium ion with +2 elementary charges is

accelerated by a potential difference of 5.0x103 volts.  What is the kinetic energy acquired in eV by the ion?

example• Moving +2.0 coulombs of charge from infinity

to point P in an electric field requires 8.0 joules of work.  What is the electric field potential at point P?

example

• How much energy in eV is needed to move one electron through a potential difference of 1.0x102 volts?

example• The graph shows the relationship between

the work done on a charged body in an electric field and the net charge on the body.   What does the slope of this graph represent?