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Energy, Environment, and Industrial Development. Michael B. McElroy Frederick H. Abernathy Lecture 16 April 10, 2006. An atom in its normal state is electrically neutral. If it loses an electron, it assumes a positive charge and is known as a positive ion.

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Energy environment and industrial development

Energy, Environment, and Industrial Development

Michael B. McElroy

Frederick H. Abernathy

Lecture 16

April 10, 2006




q1

r

q2


  • Suppose the charges q q1 and q2 have opposite signs. For example, suppose q2 represents the charge on a proton and q1 the charge on an electron as in a hydrogen atom.

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

  • Particles of the same sign are repelled


  • Coulomb’s Law: q

  • With charges expressed in units of Coulombs (C) and distance in m, F is in Newtons (N), with k = 8.99x109Nm2C-2

  • Check units:

N Nm2C-2 C2 m-2


Example a1 14
Example A1.14 q

  • The charge passing position P in the conductor in unit time defines what is known as current

  • If charge Δq passes P in time Δt, then I = Δq/ Δt defines current

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

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

P


  • The electrostatic force on a particle of charge q is given by qE

  • Here E is a vector known as the electric field

  • The gravitational force on a particle of mass m is given by mg, where g is the acceleration of gravity

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


  • To move a particle of charge q through a displacement by qΔr in the presence of an electric field E requires an input of work

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

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


  • Work done to move unit charge from a by qb in the presence of an electric field E:

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


  • It follows that the electric field has dimensions of Vm by q-1

  • A positive charge placed in the electric field E will accelerate in the direction of the field:

    ΔW < 0  Vb – Va < 0

     Vb < Va

  • The motion proceeds from high to low voltage

  • Gravitational analogue: If mass falls from ab, its kinetic energy increases, its potential energy decreases


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

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

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

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





Figure A1.8 of charge from a



Figure A1.9 continuous input of energy. This is referred to as a


  • Charged particles experienced a force due not only to the electric field but also due to the magnetic field F = q v x B

  • With F in N, q in C, v in m/s, B has dimensions of NC-1m-1s or N A-1 m-1

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

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


  • A current can produce a magnetic field electric field but also due to the magnetic field

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

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


Figure A1.10 electric field but also due to the magnetic field


Figure A1.11


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

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

    Here R defines the separation of the wires

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


Figure A1.12


For a circular path the strength of the magnetic field produced by a current

Figure A1.12


Figure A1.12


  • Concept of magnetic flux the strength of the magnetic field produced by a currentФm = B.n ∆A

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

Figure A1.14


Electromotive force

Figure A1.14


  • Consider coil rotating at a uniform rate (1791-1841) states that ω θ= ωt

  • At orientation θ, Фm = BAcosωt

  • ε(t) = BAωsinωt

  • ε oscillates in time

  • Since, by Ohm’s Law, ε = IR 

  • Example of an alternating current


Figure A1.16 (1791-1841) states that


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

If smaller, voltage is decreased.

Step-up or step-down transformer


Development of the us electric power system
Development of the US electric power system primary, voltage is increased.

  • Beginning of modern electric industry, 1882

  • Edison’s Pearl Street generating station operational on Sep. 4, 1882

  • Consumed 10 pounds of coal per kilowatt-hour

  • Served 59 customers charging 24 cents/ kilowatt-hour

  • By end of 1880’s small central stations in many US cities

  • Development of hydroelectric plant at Niagara Falls by George Westinghouse in 1896. Delivered power to Buffalo, 20 miles away


Development of the us electric power system1
Development of the US electric power system primary, voltage is increased.

  • Municipally owned utilities supplied street lighting and trolley services. Accounted for 8% of total power generation in 1900

  • Residential rate fall to <17 cents a kilowatt-hour

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

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

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


Development of the us electric power system2
Development of the US electric power system primary, voltage is increased.

  • Electricity prices dropped to 5.6 cents per kilowatt-hour in 1932

  • By 1932, 67% of residences supplied with electricity –80% of urban dwellings. But, only 11% of farms had electricity

  • Rural Electrification Act of 1936 established the Rural Electrification Administration

  • By 1941, 35% of farms were electrified.

  • Hoover Dam, 1936; Grand Coulee 1941

  • Electricity prices in 1941, 3.73 cents a kilowatt-hour. Half of all farms electrified by 1945


Development of the us electric power system3
Development of the US electric power system primary, voltage is increased.

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

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

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


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