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Energy, Environment, and Industrial Development

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

- Charge in the SI system of units is expressed in units of coulombs (C): French physicist Charles-Augustin de Coulomb (1736-1806). The charge on an electron = -1.602x10-19 C.
- How many electrons do you need to provide a charge of -1 C?

- Consider the electrostatic force between particles of charge q1 and q2. The force on q1 due to the presence of q2 is given by
- This is known as Coulomb’s Law

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 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 qb 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 ab, 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

- Ohm’s Law, named for Bavarian George Simon Ohm (1789-1854) defines a relation between current and voltage: ΔV = RI
- R is known as the resistance. R has dimensions of V A-1
- The unit of R in the SI system is know as the ohm (Ω)

- For a wire of length L and cross section A, defines a relation between current and voltage:
R = r L/A

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

- r has dimensions of ohm meters

- The loss of electrical energy per unit time due to movement of charge from ab through a voltage drop V is given by multiplying the charge transferred per unit time by the work exerted by the electric field on unit charge
- Using Ohm’s Law
P = IV = I (RI) = I2R

- Or, P = I2 r (L/A)

Figure A1.8 of charge from a

- To maintain a steady current I a conductor requires a continuous input of energy. This is referred to as a seat of electromotive force or simply a source of emf.
- The seat of emf maintains the voltage differential required to drive the current

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

- For a current flowing in a long straight wire 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

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

Figure A1.12

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

Figure A1.12

- A strong magnetic field can be formed inside the solenoid the strength of the magnetic field produced by a current
where n is the number of loops of wire per unit length of the solenoid

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

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

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 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 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 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 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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