Energy, Environment, and Industrial Development

Energy, Environment, and Industrial Development

Michael B. McElroyMichael B. McElroyFrederick H. AbernathyFrederick H. Abernathy

Lecture 16Lecture 16April 10, 2006April 10, 2006

© Science A 52 FHA + MBM2

An atom in its normal state is An atom in its normal state is electrically neutral. If it loses an electrically neutral. If it loses an electron, it assumes a electron, it assumes a positivepositive charge and is known as a charge and is known as a positivepositive ion. ion.

The fundamental unit of negative The fundamental unit of negative charge is that carried by an charge is that carried by an electron electron


Charge in the SI system of units is Charge in the SI system of units is expressed in units of coulombs (C): expressed in units of coulombs (C): French physicist Charles-Augustin French physicist Charles-Augustin de Coulomb (1736-1806). The de Coulomb (1736-1806). The charge on an electron = -1.602x10charge on an electron = -1.602x10--

1919 C. C. How many electrons do you need to How many electrons do you need to

provide a charge of -1 C?provide a charge of -1 C?

1819

19102.6

602.1

10

10602.1

1x

x


Consider the electrostatic force Consider the electrostatic force between particles of charge qbetween particles of charge q11 and and qq22. The force on q. The force on q11 due to the due to the presence of qpresence of q22 is given by is given by

This is known as Coulomb’s LawThis is known as Coulomb’s Law

221

ˆ1 r

rqkqFq

rq1

q2rrr ˆ


Suppose the charges qSuppose the charges q11 and q and q22 have have

opposite signs. For example, suppose qopposite signs. For example, suppose q22

represents the charge on a proton and qrepresents the charge on a proton and q11

the charge on an electron as in a the charge on an electron as in a hydrogen atom.hydrogen atom.

The force is now directed opposite to The force is now directed opposite to : it acts to attract particles of opposite : it acts to attract particles of opposite sign.sign.

Particles of the same sign are repelledParticles of the same sign are repelled

221

ˆ1 r

rqqkFq

r̂


Coulomb’s Law: Coulomb’s Law:

With charges expressed in units of With charges expressed in units of Coulombs (C) and distance in m, Coulombs (C) and distance in m, FF is in Newtons (N), with k = is in Newtons (N), with k = 8.99x108.99x1099NmNm22CC-2-2

Check units:Check units:

221

ˆ

r

rqkqF

221

ˆ

r

rqqkF

N Nm2C-2 C2 m-2


Example A1.14 The charge passing position P in the The charge passing position P in the

conductor in unit time defines what is conductor in unit time defines what is known as currentknown as current

If charge If charge ΔΔq passes P in time q passes P in time ΔΔt, then t, then I = I = ΔΔq/ q/ ΔΔtt defines current defines current

I has dimensions of charge per unit time, I has dimensions of charge per unit time, Coulomb secCoulomb sec-1-1

The unit of current is the ampere (A) The unit of current is the ampere (A) honoring Andre-Marie Ampere (1775-honoring Andre-Marie Ampere (1775-1836)1836)

P


The electrostatic force on a particle of The electrostatic force on a particle of charge q is given by qcharge q is given by qEE

Here Here EE is a vector known as the is a vector known as the electric electric fieldfield

The gravitational force on a particle of The gravitational force on a particle of mass m is given by mmass m is given by mgg, where , where gg is the is the acceleration of gravityacceleration of gravity

EE, the electric field, is analogous to the , the electric field, is analogous to the field defining the gravitational force field defining the gravitational force experienced by a particle of unit massexperienced by a particle of unit mass


To move a particle of charge q through a To move a particle of charge q through a displacement displacement ΔΔrr in the presence of an in the presence of an electric field electric field EE requires an input of work requires an input of work

If we wish to move q in a direction If we wish to move q in a direction opposite to E, thenopposite to E, then is negative. is negative. Hence Hence ΔΔW is positive. Work must be W is positive. Work must be done to move a (positive) charge q done to move a (positive) charge q against the direction of the electric field. against the direction of the electric field.

Work must be done to move a mass m Work must be done to move a mass m up against the gravitational field. up against the gravitational field.

rEqW

rE


Work done to move unit charge from Work done to move unit charge from aab in the presence of an electric b in the presence of an electric field field EE: :

V is known as the V is known as the electric potentialelectric potential or simply as the potential. The or simply as the potential. The potential is expressed in units of potential is expressed in units of Volts (V)Volts (V)

rEVVWb

a

ab


It follows that the electric field has It follows that the electric field has dimensions of Vmdimensions of Vm-1-1

A positive charge placed in the electric A positive charge placed in the electric field E will accelerate in the direction of field E will accelerate in the direction of the field:the field:ΔΔW < 0 W < 0 V Vbb – V – Vaa < 0 < 0

VVbb < V < Vaa

The motion proceeds from high to low The motion proceeds from high to low voltagevoltage

Gravitational analogue: If mass falls from Gravitational analogue: If mass falls from aab, its kinetic energy increases, its b, its kinetic energy increases, its potential energy decreasespotential energy decreases


A material with the property that it can A material with the property that it can maintain a net flow of charge is known maintain a net flow of charge is known as a as a conductorconductor. Examples: copper or . Examples: copper or aluminum wire.aluminum wire.

In the presence of an electric field, or In the presence of an electric field, or equivalently a voltage differential, equivalently a voltage differential, electrons will moveelectrons will move

Electrons move from low to high voltage: Electrons move from low to high voltage: current flows from high to low as though current flows from high to low as though charge was transferred by positively charge was transferred by positively charged particles.charged particles.

1A is equivalent to a flow of charge equal 1A is equivalent to a flow of charge equal to 1C secto 1C sec-1-1


Ohm’s Law, named for Bavarian Ohm’s Law, named for Bavarian George Simon Ohm (1789-1854) George Simon Ohm (1789-1854) defines a relation between current defines a relation between current and voltage: and voltage: ΔΔV = RIV = RI

R is known as the R is known as the resistanceresistance. R . R has dimensions of V Ahas dimensions of V A-1-1

The unit of R in the SI system is The unit of R in the SI system is know as the ohm (know as the ohm (ΩΩ))


For a wire of length L and cross For a wire of length L and cross section A,section A,

R = r L/AR = r L/A

where r, known as the resistivity, is a where r, known as the resistivity, is a property of the mediumproperty of the medium

r has dimensions of ohm metersr has dimensions of ohm meters


The loss of electrical energy per unit time The loss of electrical energy per unit time due to movement of charge from adue to movement of charge from ab b through a voltage drop V is given by through a voltage drop V is given by multiplying the charge transferred per multiplying the charge transferred per unit time by the work exerted by the unit time by the work exerted by the electric field on unit chargeelectric field on unit charge

Using Ohm’s LawUsing Ohm’s Law

P = IV = I (RI) = IP = IV = I (RI) = I22RR Or, P = IOr, P = I2 2 r (L/A)r (L/A)

IVVt

qP

)(


Figure A1.8


To maintain a steady current I a To maintain a steady current I a conductor requires a continuous conductor requires a continuous input of energy. This is referred to input of energy. This is referred to as a as a seat of electromotive forceseat of electromotive force or or simply a source of emf.simply a source of emf.

The seat of emf maintains the The seat of emf maintains the voltage differential required to drive voltage differential required to drive the currentthe current


Figure A1.9


Charged particles experienced a force Charged particles experienced a force due not only to the electric field but also due not only to the electric field but also due to the magnetic field due to the magnetic field FF = q = q vv x x BB

With F in N, q in C, With F in N, q in C, vv in m/s, B has in m/s, B has dimensions of NCdimensions of NC-1-1mm-1-1s or N As or N A-1-1 m m-1-1

The unit of magnetic field in the SI The unit of magnetic field in the SI system is the tesla (T) – Serbian-system is the tesla (T) – Serbian-American Nikola Tesla (1856-1943).American Nikola Tesla (1856-1943).

Strength of the Earth’s magnetic field at Strength of the Earth’s magnetic field at mid latitudes is about 7x10mid latitudes is about 7x10-5-5T = 0.7 T = 0.7 Gauss (G)Gauss (G)


A current can produce a magnetic A current can produce a magnetic fieldfield

Intensity of the magnetic field Intensity of the magnetic field defined by the Biot-Savart Law.defined by the Biot-Savart Law.

To find the direction of the magnetic To find the direction of the magnetic field at pt. P, place your thumb field at pt. P, place your thumb along direction of current flow at Q along direction of current flow at Q extend hand towards P extend hand towards P curl of curl of fingers with indicate direction of Bfingers with indicate direction of B


Figure A1.10

27

2

10

ˆ

NAk

r

rlIkB

m

m


For a current flowing in a long For a current flowing in a long straight wirestraight wire

R

IIkB m2

Figure A1.11


Consider currents flowing in 2 Consider currents flowing in 2 contiguous wires, 1 and 2. Assume wires contiguous wires, 1 and 2. Assume wires are long, straight, and parallelare long, straight, and parallel

The force on a length l of 2 due to wire 1 The force on a length l of 2 due to wire 1 is given by is given by

Here R defines the separation of the wiresHere R defines the separation of the wires If the currents are flowing in the same If the currents are flowing in the same

direction, the wires are drawn together. If direction, the wires are drawn together. If currents are flowing in opposite currents are flowing in opposite directions, wires are driven apartdirections, wires are driven apart

R

IIlkF m

212 2


Ampere’s Law allows for an Ampere’s Law allows for an alternative way to calculate the alternative way to calculate the strength of the magnetic field strength of the magnetic field produced by a currentproduced by a current

IklB m 4

Figure A1.12


For a circular path For a circular path IklB m 4

Figure A1.12

R

IkB

IkRB

m

m

2

42


A strong magnetic field can be formed inside A strong magnetic field can be formed inside the solenoidthe solenoid

where n is the number of loops of wire per unit where n is the number of loops of wire per unit length of the solenoidlength of the solenoid

Figure A1.12

nIkB m4


Concept of magnetic flux Concept of magnetic flux Фm = B.n ∆A

If B is constant over the area and If B is constant over the area and perpendicular to the area, then perpendicular to the area, then Фm = B A

Figure A1.14


Faraday’s Law, named for English Faraday’s Law, named for English physicist Michael Faraday (1791-1841) physicist Michael Faraday (1791-1841) states that states that

Figure A1.14

dt

d mdt

d m

dt

d m

Electromotive force


Consider coil rotating at a uniform rate Consider coil rotating at a uniform rate ωω θθ= = ωωtt

At orientation At orientation θθ, , Фm = = BAcosωt BAcosωt ε(t) = BAωsinωt ε(t) = BAωsinωt ε oscillates in timeε oscillates in time Since, by Ohm’s Law, ε = IR Since, by Ohm’s Law, ε = IR

Example of an Example of an alternating currentalternating current

dt

d m

tBA sindt

d m

tR

BAt

RtI sin)(

1)(


dt

d m

R

ABP

tR

ABRtItP

av

222

2222

2

2

1

sin)()(


Figure A1.16

11

22

1

122

22

11

)(

)(

VN

NV

N

VNV

dt

dNV

dt

dNV

m

m


If number of turns in secondary circuit is If number of turns in secondary circuit is larger than in primary, voltage is larger than in primary, voltage is increased. increased.

If smaller, voltage is decreased.If smaller, voltage is decreased.

Step-upStep-up or or step-downstep-down transformer transformer

dt

d m

11

22 )( V

N

NV


Development of the US electric power system

Beginning of modern electric industry, 1882Beginning of modern electric industry, 1882 Edison’s Pearl Street generating station Edison’s Pearl Street generating station

operational on Sep. 4, 1882operational on Sep. 4, 1882 Consumed 10 pounds of coal per kilowatt-hourConsumed 10 pounds of coal per kilowatt-hour Served 59 customers charging 24 cents/ Served 59 customers charging 24 cents/

kilowatt-hourkilowatt-hour By end of 1880’s small central stations in By end of 1880’s small central stations in

many US citiesmany US cities Development of hydroelectric plant at Niagara Development of hydroelectric plant at Niagara

Falls by George Westinghouse in 1896. Falls by George Westinghouse in 1896. Delivered power to Buffalo, 20 miles awayDelivered power to Buffalo, 20 miles away


Development of the US electric power system Municipally owned utilities supplied street Municipally owned utilities supplied street

lighting and trolley services. Accounted for 8% lighting and trolley services. Accounted for 8% of total power generation in 1900of total power generation in 1900

Residential rate fall to <17 cents a kilowatt-Residential rate fall to <17 cents a kilowatt-hourhour

Consolidation in generating industry. By late Consolidation in generating industry. By late 1920s, 16 companies controlled >75% of total 1920s, 16 companies controlled >75% of total US generating capacityUS generating capacity

State regulation of utilities. Later federal State regulation of utilities. Later federal involvement with creation of Federal Power involvement with creation of Federal Power Commission in 1920Commission in 1920

Electric power capacity grew at ~12% per year Electric power capacity grew at ~12% per year from 1901-1932from 1901-1932


Development of the US electric power system Electricity prices dropped to 5.6 cents per Electricity prices dropped to 5.6 cents per

kilowatt-hour in 1932kilowatt-hour in 1932 By 1932, 67% of residences supplied with By 1932, 67% of residences supplied with

electricity –80% of urban dwellings. But, only electricity –80% of urban dwellings. But, only 11% of farms had electricity11% of farms had electricity

Rural Electrification Act of 1936 established Rural Electrification Act of 1936 established the Rural Electrification Administrationthe Rural Electrification Administration

By 1941, 35% of farms were electrified.By 1941, 35% of farms were electrified. Hoover Dam, 1936; Grand Coulee 1941Hoover Dam, 1936; Grand Coulee 1941 Electricity prices in 1941, 3.73 cents a kilowatt-Electricity prices in 1941, 3.73 cents a kilowatt-

hour. Half of all farms electrified by 1945hour. Half of all farms electrified by 1945


Development of the US electric power system

From 1945-1950, electricity use grew at From 1945-1950, electricity use grew at >8% per year. Prices continued to >8% per year. Prices continued to decline. 80% of farms electrified by 1950decline. 80% of farms electrified by 1950

Generation increased by >8.5% per year Generation increased by >8.5% per year from 1950-1960. Commercial nuclear from 1950-1960. Commercial nuclear power introduced. power introduced.

During 1960’s environmental concerns During 1960’s environmental concerns with power generation begin to have with power generation begin to have influenceinfluence

Energy, Environment, and Industrial Development

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