ELECTROSTATICS Electrostatics electricity at rest. Involves electric charges, the forces between them and how they behave in materials SHOCKING STORY

ELECTROSTATICS

Electrostatics

• electricity at rest.• Involves electric charges,

the forces between them and how they behave in materials

SHOCKING STORY

Background

There are Four Universal Forces in nature:1. weak nuclear 2. strong nuclear3. 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 ofElectrostatics

Static Electricity

Copywrited by Holt, Rinehart, & Winston

Atomic Structure

Atoms that have the same number of protons and electrons = electrically neutral.

Net charge = zeroIons have lost or gained

electrons = electrically charged.

AtomsProton has the same amount of positive charge as the 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?

[strong nuclear force]

[wave nature of e-]

Conservation of Charge

In the whole universe:number of + charges = number of - charges

• So the universe is electrically neutral!

• Electric charge cannot be created or destroyed.

Law of Charges

• Likes repel and opposites attract.

Law of ChargesAnimated

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 extra electrons ( - charged) – or lost electrons ( + charged).

• This happens only when electrons move from one object to another.

• Protons are fixed in the nucleus

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

1018 electrons• 1 electron has an elementary

charge = 1.60 x 10-19 C.• The Coulomb is a

fundamental quantity 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.

ConductorsA 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!h

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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

chargesElectrostatic Charge: • a charge that is confined to an

object, remains still and does not move in a straight line.

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

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

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

Grounding

GROUNDING – The earth is a large reservoir of electrons. You are connected to the earth.

• When you touch something negative, excess electrons can flow through you to the earth.

• 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


3 Methods of CHARGING

• Friction• Conduction• Induction

Charging by Friction• removing electrons by rubbing

different materials together.• When two different insulators

are rubbed together, electrons can be transferred from one insulator to the other. – substance that gains an electron

- negative (rubber rod)– substance that loses an electron

- positive (lucite rod)


Charging by Conduction

• Conduction is transfer by touching (contact).

• the flow of electrons through a conductor. Charging by the flow of electrons.

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


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

• The object then becomes 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 Example• When a negatively

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

• The object then becomes negative.

neutral

neutral

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Conduction – Electroscope Example

Positive Rod Negative Rod

+ Charge

- Charge


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Charging by Induction

Induction is transfer without touching.

• the charging of an object without direct contact.

• the process of "rearranging" the charges


Induction – Electroscope ExamplePositive Rod Negative Rod

Temporary Charge Returns to Neutral after the Charged Rod is Removed

Electroscope Grounding


InductionInduction with a Conductor

Induction with an Insulator

Electrical Polarization

occurs when an object’s atoms rotate in response to an external charge. This is how a charged object can attract a neutral one.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 ProblemTwo 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?

+2µC

+4µC

Electrostatics ProblemThree 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 - BNegative - ANeutral - 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:

= net charge .

charge of electron

= mass of total electrons

mass of one electron

ee q

QN

ee M

MN

Atomic Particles

Atomic

Particle

Neutron Proton Electron

Charge

(C)

0 1.6 x 10-19

(positive)-1.6 x 10-19 (negative)

Mass(kg)

1.67 x 10-

27

1.67 x 10-27 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 1023 molecules = one mole.)

Coulomb’s Law

The force between charged particles depends on:

• the charge on each particle– directly proportional to their

magnitudes • the distance between

particles– inversely proportional to the

square of the distance between them.

F ~ Q1Q2

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?


• 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 LawThe force between charged particles

depends on:1. the charge on each particle• directly proportional to their

magnitudes 2. the distance between particles• inversely proportional to the

square of the distance between them.

F ~ Q1Q2

F ~ 1/r²

221

r

qkqF

Coulomb’s Law

• F = force in newtons (N)• k = 9.0 x 109 Nm2/C2 : a constant

whose value depends on the units used and on the medium (air) between the particles.

• q1 = 1st point charge

• q2 = 2nd point charge • r (distance) in meters (m)

221

r

qkqF

unit of Coulomb (C)

Coulomb’s Law

If q1 and q2 have opposite signs, the force is attractive with a negative sign.

If q1 and q2 have same signs, the force is repulsive and has a positive sign.


• 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?


• 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.

• The constant ε is called the permittivity of the medium.

• vacuum - the constant is written εo. The units of ε are N-1C2m-2, (this is usually written as Farads per meter, F/m).

• Air K = 1/4πε where K = 9.0 x 109 Nm2/C2

K = 1/4πε

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 forces, chemical bonds, viscosity, magnetism.…all of these are nothing but Coulomb’s law….”

Comparing Gravity and Electricity

Newton’s Law of Gravity

(1) Always attractive force, G is a very small number.G = 6.67 x 10-11 Nm2/kg2

(2) Gravitational forces are very weak, but very important.

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

Coulomb’s Law

(1) Repulsive or attractive force replaces mass with charge, k is a very large number. k= 9.0 x 109 Nm2/C2

(2) Implies electrostatic charges are very strong.

221

r

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QkQFE

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 µC + 12.2 µC

Return of the 1’s Rule

• Used when a relative change is asked for not the actual size of the force

• 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?

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Multiple ChargesThree point charges lie along the x

axis in a vacuum as shown below. Calculate the net force acting on q1.


Electrostatic Force VectorsThe electrostatic

force is a vector

• magnitude and direction

When adding electrostatic forces:

• Take into account the direction of all forces

• Use vector components when needed


Electric Force Vectors

Find the magnitude and direction of the net electrostatic force on q1 for three charges lying in the xy plane in a vacuum as shown below.


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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 electric field. When another charge enters the field, an electric force 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:

E= magnitude of electric fieldF= force (on q) at that pointq = size of test charge

q

FE

Electric Field

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

(1) (2) (2)(1)

0q

FE E

2r

kQqF oE

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kQq

qE

2r

kQE

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

Electric Field Strength

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

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

0q

FE E

0m

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Electric Field Strength Practice

Two positive charges with net charges of q1= 2C and q2 = 4C respectively are separated by a distance of three meters. Calculate where on the line between them would the electric field equal zero.



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?


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 case is the magnitude of the field at the black dot the largest?


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 case is the magnitude of the field at the black dot the 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 from a positive charge (toward a negative charge). The more crowded the lines of force, the stronger the electric field.

Electric Field Lines

• We draw arrows in the direction of the force - length is proportional to the strength. Connect the arrows to get field lines.

• Draw lines of force around a weak, positively charged sphere.

• 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.

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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 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.





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 UnderstandingTwo 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 platesB. decrease the magnitude of the charge on both platesC. increase the distance between the platesD. decrease the distance between the platesE. 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


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


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


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.


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 UnderstandingA 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) Sphere charge (nC)

A. 2.0 4.0

B. 3.0 4.0

C. 2.0 6.0

D. 3.0 8.0

E. 4.0 9.0

Clicker UnderstandingA 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 smallest?

Sphere mass (g) Sphere charge (nC)

A. 2.0 4.0

B. 3.0 4.0

C. 2.0 6.0

D. 3.0 8.0

E. 4.0 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.

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

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



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

• If not, the charge would move.



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

• Charge is concentrated where the shape is more sharply curved.

• Resulting in a larger electric field at the more sharply curved areas.

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 by the field ……. Therefore more work is required.

• If the charge were released, it would move away from the sphere and its PE would decrease. Its kinetic energy would increase.

• When the little charge is added to the sphere, the charge on the sphere increases and the field around it becomes stronger.

• Moving another positive charge toward the sphere will take even more work or energy and give the little charge higher PE.

Electropotential Energy

Electropotential Energy

• Analogous to Mechanical Potential Energy

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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 or potential difference.

• 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:

symbols units V = voltage (V) W = Work (or electric PE) (J) Q = charge (C)

• Since work done on a charge and the gain in potential energy of the charge are the same, voltage can also be thought of as work per unit charge.

What theorem is this based on?

Q

EPE

Q

WV

Electrical Potential

• Potential at a distance r from a Point Charge Q

• It can be shown that the potential at p is given by

or

r

kQV

Copyright ©2007 Pearson Prentice Hall, Inc.

Summing Up Electrical Potential

The electric potential of a group of point charges is the algebraic sum of the potentials of each charge....321 VVVVtot


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

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

Electrical Potential Energy

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

• Where UE 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.

pE qVU q


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

• 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 is

• Integrating (calculus)

q2r

kQqF

drr

kQqFdrdW

2

R

kQq

r

kQqdr

r

kQqW

RR

2 r

kQqU E


• Both electrical potential energy UE and electrical potential V are scalars.

• So the change in either potential energy or potential is path independent.

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Is the change ∆U of the particle positive, negative, or zero as it moves from i to f?

a)0; b)negative;

c)positive;

d)negative;

e)zero; f)negative;

g)zero

Electron Volt (eV)

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

• If 1 electron moves through a potential difference of 1V then 1 eV of work is done.

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

• Therefore,1eV = 1.6×10-19J


• Another form of Electrical Potential Energy is shown by

(1) (2) (2)(1)

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

• Recall, so

r

kQqU E

2r

kQE Eqrqr

r

kQU E

2

EqdU E

q

UV E

d

V

qd

UE E

Voltage & Electric Field

• 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.

d

VE

dr

dVE

From calculus the relationship is

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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.

d

VE

Potential due to a Charged Hollow Metal Sphere

• Outside the sphere the charge can be considered to be a point charge placed at the center.

• Inside the sphere, there is no electric field so all points are at the same potential as the surface.

• Graphically, this is represented in a plot of Electric Potential V vs. distance from the center of a charged sphere r as:



Potential due to a Charged Hollow Metal Sphere

What would a graph of Electric Field E vs distance from the center of a charged sphere look like?

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.

d

VE

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

d

VE

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 10-15J 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 106 V/m. At this distance, what is the potential difference between Chippy and the generator?

Similarities between Electric Fields and Gravitational

Fields


Documents

ELECTROSTATICS Electrostatics electricity at rest. Involves electric charges, the forces between them and how they behave in materials SHOCKING STORY