Assessing of Magnetic Field Pollution

8/10/2019 Assessing of Magnetic Field Pollution

1/51

Prof.: Dr. Hussein Anis

And

Dr.: Abdel-Bari Mahdy

2011

H3

[ASSESSING MAGNETIC FIELD POLLUTION IN EGYPT]


2/51

H3 | Assessing Magnetic Field Pollution in Egypt 2

Special thanks to

Prof.: Dr. Hussein Anis

And

Dr.: Abdel-Bari Mahdy

And

Eng.: Ayman

And

Eng.: Hatem

To their efforts in helping us in this project

Our words cannot express how grateful we are


3/51


By: Ahmed Wahid Abass


4/51


List of contents Page 4

Chapter 1:

Abstract ----Page 6

Introduction----Page6

Background----Page 7

Medical Effects ----Page 8

Environmental Effects----Page 9

Factors That affect magnetic Field----Page 11

Mitigation----Page 13

Recommendations----Page 16

Chapter 2:

Equations----Page 18

How to Calculate----Page 21

66 KV Tower----Page 22

How to Calculate Sag----Page 27

Usage of Literal Curve----Page 31

Contour Curve----Page 32

Chapter 3:

Measurements----Page 35 Comment----Page 43

Contour Curve----Page 44

Appendix----Page 46


5/51



6/51

H3 Chapter 1

|M a g n e t i c F i e l d E f f e c t s


The potential hazard due to exposure to extremely low frequency (ELF) magnetic fields emitted by electricpower systems and installations still represents a public and environmental concern. To obtain accurateinformation on the possible biological effects of electric power systems and installations, analytical studiesand measurement are used in residential areas, workplaces and close to power lines. Computational effortsare made to evaluate magnetic fields in the vicinity of different power lines and apparatus. A complexmagnetic field environment exists near a power line, where a number of factors are known to affect the fieldintensity in a direct or indirect manner. For a certain power line configuration, the magnetic field intensity at agiven position in the line vicinity, and at the standard height of one meter above the ground, is affected bythe conductor sag which, in turn, determines the conductor height above the ground.

One of the most important sources of magnetic field are Transmission lines as it carries high voltage so it hasa wide environmental effect in addition to its effect on humans.We are going to discuss about its effect andhow we mitigate it by reducing value of magnetic field as it cost us a lot of money spend on diseases and also

the lands that reserved as a right of way.Also, we are going to calculate the magnetic field produced by transmission lines and compare it with realvalues that we will measure to estimate Error in method used to calculate magnetic field, also we discussabout values we find and factors affect it to be able to reduce it.Through our research we will:

Collect transmission line data for any tower type and any power line.

Compute the magnetic field in the vicinity of selected power lines.

Examine the factors that affects magnetic field.

Calculate magnetic at any point near transmission line.Covering these points, we will be aware of value of magnetic field around transmission line and could toestimate limits of safety near any transmission line.

Let's refresh our minds with some information that helps us through our research.


7/51

H3 Chapter 1



Before we start our discussion about magnetic field, let's fresh our mind about different types of Transmission

Lines and towers used in Egypt to be able to determine configuration of each tower.

Different types of transmission lines:

We will define type of transmission lines by value of voltage it transmits.

In Egypt we have five types of Transmission Lines:

500 KV

220 KV

132 KV

66 KV

22 KV

Different Types of Towers:

According to its configuration:

One Circuit ( as 500 KV and 22 KV)

Double Circuit ( as 220 , 132 , 66 KV)

According to its Insulation Type:

Tension Type

Suspension Type

In our research we will care about 66 KV double circuit Transmission Line.

Also we need to define magnetic field Produced by Transmission Line.

Magnetic Field:

Magnetic Field is produced around any conductor carrying a current and independent of voltage present on

this conductor, and its value decreases with Distance from the Conductor, So magnetic Field is a Function of

both current passes through conductor and these conductor Configurations.


8/51

H3 Chapter 1



Transmission Lines are very dangerous because they carry high voltage and they also not insulated, so it

could cause a disaster if they fall on ground if there any people beside them. Also it may affect people with

such step and touch potentials which may cause people death.

Also the current passes through these transmission lines will produce a magnetic field

This Magnetic field has a very dangerous effect on humans rather than electric Field as it causes circulating

current in human body causing very dangerous diseases such as:

Cardiovascular disorders

Immunological modification

Alzheimer's disease

Sleep Disturbance

Cancers in adults

Headaches

And there are a lot of researches and experiments about diseases that affect people lived nears transmission

lines.


9/51

H3 Chapter 1



Besides Noise and corona effect comes from transmission lines which have a environmental pollution,

Magnetic fields produced by these transmission lines has a bad effect on Environment such as:

Environmental impactas we reserve an area which may worth too much as a ROW

If Transmission Lines passes through woodland, we may need to cut a lot of trees to clean

Transmissions Lines path and ROW to avoid Fires that may happen.

Potential Aesthetic impactsas transmission lines and towers have a negative impression on People

Potential impacts to Agricultural Land as it may cause difficulty to farmers to move there tools

(irrigation equipment) through the land, and it also cause soil damage.

Problems to Airports and Airplanes as it make it difficult during takeoff and landing

Problems in Archeological and Historical Sites

So, it is found that it is not safe to live near transmission lines as magnetic field produces by it causes these

bad effect on human been and Environment.

Thus, in all countries in the world there are limits of distance that should not exceed it to keep their people

safe, these limits are called Right of Wayor ROW

These ROWs are not the same in all countries as each country decide what its suitable ROW is.

In some Arab countries it is estimated depending on Voltage on it such that

From To Distance1 KV 11 KV 1.2 M

11 KV 66 KV 1.5 M

66 KV 132 KV 2 M

132 KV 220 KV 3 M

220 KV 330KV 3.5 M

330 KV 4.5 M


10/51

H3 Chapter 1



International Standards:

Standard 500 KV 220 KV 66 KV 22 KVInternational 6 m 4 m 3 m 3 m

Finland 7m 5 m 3.7 m 3.12 m

German 5.25 m 3.75 m 3 m 3 mRussian 10 m 6 m 4 m 4 mFrom previous tables its found that in Egypt standards lower than national standards.

But despite all these bad effects on Humans, in Egypt we have a big problem as people doesn't believe in all

these bad effects that are very harmful to them.

Let's examine some cases:


11/51

H3 Chapter 1



These pictures show how our problem is big and we all should increase our effort to convince people with this

dangerous around them and the government should put a sharp laws and rough punishment on people

breaks these laws.

There are many factors affect magnetic fields; we will concern about two factors:

Line Design

Loading Condition

Temperature

There are certain line design details which are required as inputs for magnetic field calculations.These are:

structure, conductor and earth wire geometry

conductor type and parameters

earth wire type and parameters conductor and earth wire stringing data

minimum design ground clearance

actual and equivalent span

soil resistivity


12/51

H3 Chapter 1



Loading Conditions:

A Short Time Emergency:- Could be short time thermal limit - may in practice never be reached on a lineB Infrequent High Load:- For example yearly peak with the system substantially normalC Typical Daily Maximum:- The peak value reached for the line on a typical dayD Typical Daily Minimum:- The value reached for the minimum daily load on a line


13/51

H3 Chapter 1



There are a lot of researches about mitigation which aim to mitigate effect of Magnetic Field to reduce bad

effects of it.Lets examine some techniques used to mitigate effect of magnetic field.

Replacing or Upgrading Existing LinesOne way to mitigate impacts during project design is replacing or double-circuiting an existing line ratherthan building a new line. The environmental advantages of double-circuiting an existing line are:

Little or no additional ROW clearing, if the new line can be placed in the center of the existing ROW

Land use patterns may have already adapted to the existing ROW

Electric and magnetic fields (EMF) may be reduced because new structure designs place lineconductors closer together resulting in lower EMF

Corridor SharingAnother common method for mitigating impacts is corridor sharing. Transmission line ROW can be sharedwith town or county roads, highways, railroads, or natural gas pipelines. Corridor sharing with existingfacilities is usually encouraged because it minimizes impacts by:

Reducing the amount of new ROW required

Concentrating linear land uses and reducing the number of new corridors

Creating an incremental, rather than a new impact

Underground Electric Transmission LinesIt is a common practice in residential areas to place low-voltage distribution lines underground. However,placing high-voltage transmission lines underground is less common and can cost two to ten times more thanbuilding an overhead line. While this practice may reduce aesthetic and other impacts, it may increase others.Underground transmission lines can be a reasonable alternative:

In urban areas where an overhead line can NOT be installed with appropriate clearances

When it allows for a shorter route than overhead

When aesthetic impacts would be significant

Underground transmission lines can have the following disadvantages:

An increase in soil disturbance

A complete removal of small trees and brush along the transmission ROW

Increased construction and repair costs

Oil-filled underground lines can leak, contaminating surrounding soils


14/51

H3 Chapter 1



Mitigation of Aesthetic ImpactsElectric transmission lines can be routed to avoid areas considered scenic. Routes can be chosen that pass throughcommercial/industrial areas or along land use boundaries.

The form, color, or texture of a line can be modified to minimize aesthetic impacts. The color and constructionmaterial of poles can be chosen to blend with or complement the landscape around them. Lines constructed usingH-frame poles or on wood rather than steel structures may blend in better with natural surroundings. Strongerconductors can minimize line sag.

ROW management can mitigate aesthetic impacts by planting vegetative screens to block views of the line, leavingthe ROW in a natural state at road crossings, creating curved or wavy ROW boundaries, pruning trees to create afeathered effect, and screening and piling brush from the cleared ROW so that it provides wildlife habitat.

Mitigation of Agricultural ImpactsThe utility should work with agricultural landowners to determine optimal pole heights, pole locations, and

other significant land use issues. Problems with pole placement can be addressed by using single-polestructures and placing the line along fence lines or adjacent to roads. If a field must be crossed, largerstructures with longer spans can be used to span them. If the structure is not single-pole, it should beoriented with the plowing pattern. Guy wires can be kept outside crop or hay land and have highly visibleshield guards.

Reducing EMF Levels of Transmission LinesMagnetic fields can be measured with a gauss meter. The size of the magnetic field cannot be predicted fromthe line voltage but is related to the current flow. A 69 kV line can have a higher magnetic field than a 115 kV

line. Magnetic fields quickly dissipate with distance from the transmission line.

A common method to reduce EMF is to bring the lines closer together. This causes the fields created by each

of the three conductors to interfere with each other and produce a reduced total magnetic field. Magnetic

fields generated by double-circuit lines are less than those generated by single-circuit lines because the

magnetic fields interact and produce a lower total magnetic field. In addition, double circuit poles are often

taller resulting in less of a magnetic field at ground level.


15/51

H3 Chapter 1



One of techniques used today to mitigate effect of magnetic field is to transmit power as a dc instead of dc

due to dc transmission advantages.

Advantages DC Transmission over AC Transmission Systems

AC system is used in the transmission of bulk power, instead of DC (Direct Current), because of its ability to

transform voltage to various levels by using a transformer. The voltage transformation follows the faradays

Law which states

The EMF induced in a circuit is directly proportional to the time rate of change of magnetic flux through the

circuit

Note that, at higher voltage, the current was reduced thus line losses was also reduced.

Ability to transform voltage and to flow power in two opposite directions (bidirectional) are the only

advantages of AC system over DC system

DC transmission system on the other hand has more advantages over AC transmission system:

1. Reactance.

DC system does not introduce a reactance in the line.

2. ResistanceDC system reduces the amount of resistance in the line.

3. Power

In DC system, the power is just the real component.

4. Frequency

In DC system, the frequency is zero, thus no frequency variation to monitor. Connection will not also require

synchronization.

All previous techniques are used to mitigate effect of magnetic field.


16/51

H3 Chapter 1



In prior decades, electric transmission lines were constructed from point A to point B in the most directmanner possible without too much regard for communities, crops, natural resources, or private property

issues. As these older lines require improvements, they may now be rerouted to share corridors with roads,and to avoid, where possible, community and natural resource impacts. At the same time, a continued growthin energy usage will require new electric substations and transmission lines to be sited and constructed. Newand upgraded electric facilities will impact many communities and many property owners.

To meet future growth, communities often draft plans for sewers, roads, and development districts, but fewcities, towns, or counties include transmission lines in their plans. Transmission lines are costly to build anddifficult to site. Cities, towns, and counties can help reduce land use conflicts by:

dedicating a strip of land along existing transmission corridors for potential future ROW expansions

identifying future potential transmission corridors and substation sites in new developments

defining set-backs or lot sizes for properties adjacent to transmission lines so that buildings dontconstrain future use of the ROW

Being an active participant in the decision-making process will improve the ability of communities to manage

future growth and protect their resources.


17/51

H3 Chapter 2

|C a l c u l a t i o n s



18/51

H3 Chapter 2



We need to calculate magnetic field (Flux density as an Indicator of magnetic field) to determine Safe

Distances around transmission lines, so firstly let's examine the equations used in calculations

Calculations of magnetic fields are based on two-dimensional space, which assumes parallel line segments

and a flat earth. All line conductors are represented by their line currents and their line images.

For the nth overhead single conductor segment located at (Xcn, Ycn), which carries a phase current In, themagnetic field components at an observation point at (X, Y)can be expressed as :

We consider the following


19/51

H3 Chapter 2



These equations are valid for field observation points above the earth's surface, whose distance away from the

conductors Rcnis less than / 20, where is the free space wavelength.


20/51

H3 Chapter 2



The total magnetic field of N parallel conductors is simply the superposition of the fields from N conductors.

The RMS value of magnetic field at the point under study can be expressed as follows:

Use MATLAB to write a code used to calculate B rms at any Point in the domain around transmission Line,

Saved as M.File named CalulateMagField.m

LOOK AT APPENDIX A TO SEE CODE.

After we could calculate Magnetic field at a point we could draw the literal curve in the X axis by calculating

Brmsat number of points in X axis then connect them to construct the literal curve.


21/51

H3 Chapter 2



Before we start Calculating Brms we need to collect Data About our transmission Line

Required Data:

Number of Conductors

Soil Resistivity

Conductors Configuration (From Tower Configurations)

Current through Conductors

(X, Y) of point needs to Calculate B rmsat it

Number of Conductors: 6Conductor as 66 KV T.L. is a Double circuit

Soil Resistivity:near to 800ohm.m

Current through Conductors: current depend on Loading of line and type of conductor material andif it is bundled or not so the value of current is not constant so we will choose an average value

represent a 80 % of Full load equals 800Amp.

Coordinates of Required Point: will be different from point to another.

Tower Configurations: look at Figure at next page to discover tower configuration

And it is found that:

Xn = [-2.93 -2.93 -2.93 2.93 2.93 2.93]

Yn= [16.664 20.084 23.504 16.664 20.084 23.504]


22/51

H3 Chapter 2



From tower Configuration:

We have double circuit one on the right and the other on the left, we extract dimension from this

figure as:Xn = [-2.93 -2.93 -2.93 2.93 2.93 2.93]

And Yn= [16.664 20.084 23.504 16.664 20.084 23.504]


23/51

H3 Chapter 2



After collecting data for 66 KV transmission line, let's start using MATLAB files

Firstly: Calculate Brms

Using CalculateMagField.m (Look at Appendix A)

For point (0, 1):

For point (1, 1):

For point (2, 1):


24/51

H3 Chapter 2



For point (3, 1):

For point (4, 1):

And so on, Calculate for number of points then plot them on X versus Brmsto get out literal Curve.

So we could use MATLAB code to automatically calculate Brms for a certain distance and then Plot the output

versus Distance.

Secondly: Draw Literal Curve

Using PlotFieldXaxis.m (Look at Appendix A)

Where X will be a vector represent distance over x Axis such as X = [0: 1: 30]

This means that program will calculate Brms from point zero to point 30 every 1 meter. (Program will be

repeated for 30 times).


25/51

H3 Chapter 2



Draw Literal Curve from 0 to 30 with step 0.5 m.

If we look carefully at the curve for the first 4 meters we will find that values of Brms is the same we

calculated previously.


26/51

H3 Chapter 2



There are many factors that affect the position of conductor as transmission line won't be fully tension

causing phenomena called SAG: the difference in levels between the points of supports and the lowest point

of the conductor, These Sag comes when erecting the lie, if conductors are stretched too much betweensupports then there prevails an excessive tension on the line which may break the conductor so to have a safe

tension in the conductor a sag in the line is allowed.

These factors such as:

Weight of the Conductor

Length of the Span

Working tensile strength

Temperature

All these factors affects the sag, it's found that max sag for transmission lines as follows:

Voltage Insulator Length Max. Sag500 7.6 m 12.5 m

220 4.2 m 10.5 m

132 3.4 m 8 m

66 1.9 m 8 m

22 0.5 m 3 m

For 66 KV: Max sag was 8 m.

Image indicate Sag in 220 KV Lines


27/51

H3 Chapter 2



We need a method to find the Sag at any point between two supports:

We consider transmission line as a parabola curve, where:

Span: Distance between two towers

As we know Max sag and Span and From These Equation:

Y = m * X 2

As Span about 300 m and Max Sag = 8 m then

8 = m * 150 2

So m = 0.00035556 Then for any point under transmission lines (from -150 to 150 m) we could estimate sag from

Y = 0.00035556 * X 2


28/51

H3 Chapter 2



Draw Literal Curve at Mid Span:

Sag = 8 m

So,

Xn = [-2.93 -2.93 -2.93 2.93 2.93 2.93]

Yn = [16.664-8 20.084-8 23.504-8

16.664-8 20.084-8 23.504-8]

Yn = [8.664 12.084 15.504 8.664 12.084 15.504]


29/51

H3 Chapter 2



Draw Literal Curve at 10 m from Mid Span:

Firstly Sag from 10m from mid span equals:

Y = 0.00035556 * X 2

Y = 0.00035556 * 10 2= 0.0356

Sag = 8 - 0.0356 = 7.9644 m

So,

Yn = [16.664-7.9644 20.084-7.9644 23.504-7.9644 16.664-7.9644 20.084-7.9644 23.504-7.9644]

Yn = [8.6996 12.1195 15.5396 8.6996 12.1196 15.5396]


30/51

H3 Chapter 2



Draw Literal Curve at 80 m from Mid Span:

Firstly Sag from 80m from mid span equals:

Y = 0.00035556 * X 2

Y = 0.00035556 * 80 2= 2.2756

Sag = 8 2.2756 = 5.7244 m

So,

Yn = [16.664-5.7244 20.084-5.7244 23.504-5.7244 16.664-5.7244 20.084-5.7244 23.504-5.7244]

Yn = [10.9396 14.3596 17.7796 10.9396 14.3596 17.7796]


31/51

H3 Chapter 2



From the previous curves it's found that worst case was at Mid Span, which is logical as at mid span the Sag

has its Max Value.

We will include both curves of Mid Span and Tower together:

We will use literal curve to estimate ROW by make medical researches for required country then get max

allowable Magnetic Field.

If in A country it was determined that max allowable mag. Field is 8 micro tesla then ROW will be 11 m


32/51

H3 Chapter 2



We could draw a lot of curves between two towers to have a background about the magnetic field

in this Area.

But we could compound all these literal curves in one Contour Curve, We just need to determine

the next:

Number of steps required between two towers

Max Sag allowed

Distance required to be covered


33/51



34/51

H3 Chapter 3

|M e a s u r e m e n t s


In a great day with our project teammates and with one of the best engineers in Cairo University we went to Bahtim location near Shobra alkhima near to 220 KV T.L. to study the magnetic field by this T.L.

Firstly, special thanks for our Supervisors for supporting us with device used in measuring magnetic field, also special

thanks to Eng.: Ayman for his effort in this day and all his answers on our Questions.

After reaching our location we start measuring distance between two towers using meter of 30 m., we found that

distance near to 330 m., also we determine the mid Span point.

Max Sag wasnt exactly at mid Span as two towers we chose were of 2 different types one of them was a

Suspension type and the other was of tension type.


35/51

H3 Chapter 3



Device used in Measurement

We chose number of points under T.L.:

Mid Span

10 m. from Mid Span

20 m. from Mid Span

130 m. from Mid Span

At each point we start to measure Magnetic Field over X axis each 5 m., so we take 8 readings of magnetic field. The

value was as followed:

0 5 10 15 20 25 30 350 10 10.3125 7.5 2.8125 2.5 2.1875 1.875 1.25

10 10 10.125 8.125 5 3.75 2.125 1.75 1.625

20 9.0625 10 8.125 4.375 1.875 1.75 1.625 1.375130 5 4.625 3.75 1.875 1.25 0.625 0.25 0.1875


36/51

H3 Chapter 3



How we determine Sag at each Point:

We use a branch have a certain length

Stand in front of T.L.

One of us carries this branch in a vertical state between observer and T.L.

Another one (observer) look to the top of branch to have two points on one line:

o T.L.

o

First Point of the branch

A line between observer eyes and First point of branch and T.L. completes a triangle to estimate Sag Value

It was found that minimum clearance to ground:

15.2 at mid Span

18.5 at 20 m. from mid Span


37/51

H3 Chapter 3



0 5 10 15 20 25 30 350 10 10.3125 7.5 2.8125 2.5 2.1875 1.875 1.25

Using Curve Fitting to estimate any Value on X axis:


38/51

H3 Chapter 3



0 5 10 15 20 25 30 3510 10 10.125 8.125 5 3.75 2.125 1.75 1.625



39/51

H3 Chapter 3



0 5 10 15 20 25 30 3520 9.0625 10 8.125 4.375 1.875 1.75 1.625 1.375



40/51

H3 Chapter 3



0 5 10 15 20 25 30 35130 5 4.625 3.75 1.875 1.25 0.625 0.25 0.1875



41/51

H3 Chapter 3



Let's examine theoretical Values of 220 KV Transmission Lines to could compare them with measured Values.


42/51

H3 Chapter 3




43/51

H3 Chapter 3



From all previous curves we will discover the next:

All measured values are smaller than theoretical values and this is sound of logic as measured values affected by a lot offactors as:

Temperature:temperature wasn't high as we take our measurements in 26 march.

Loading:the line was lightly loaded

But in our calculations we used the data as maximum load and normal temperature.

If we decrease load:

As min. clearance at mid span equals 15.2 assume sag at this loading condition equals 0.5 and current will be

changes to reach magnetic field similar to what we measured.

Current was near to 900 Amp.


44/51

H3 Chapter 3




45/51



46/51

H3 Appendix A

|M A T L A B C o d e


This M File Used to Calculate RMS Value of Magnetic Field @ any Point under Study depending on the following

Parameters:

In: Phase Current carried by each T.L. (Ex. 1000 Amp).

X: Coordinate X of Observation Point. (Ex. 4 m).

Y: Coordinate Y of Observation Point. (Ex. 1 m).

Xn: Coordinate X of nth overhead T.L. (Ex. [-13.5 0 13.5]).

Yn: Coordinate Y of nth

overhead T.L. (Ex. [20.5 20.5 20.5]).

Ro: Earth Resistivity (Ex. 800 ohm.m).

N: no. of T.L. Conductors (Ex. 3 in case of 1 circuit).

its just a kind of GUI of M File, Just Recall File named CalculateMagField.m in Command Window In Matlab

then enter Parameters required then press enter to find out the Brms Value at required Point.


47/51

H3 Appendix A



This M File Used to Literal Curve of Magnetic Field @ versus Certain Distance depending on the following Parameters:


X: Distance Required to Plot Literal Curve over it. (Ex. [0: 1: 30]).


Xn: Coordinate X of nth

overhead T.L. (Ex. [-13.5 0 13.5]).

Yn: Coordinate Y of nth overhead T.L. (Ex. [20.5 20.5 20.5]).



This Code is basically depend on the previous code of calculating Brms at a certain point as we repeat it

number of times depend on the distance required to be covered.

its just a kind of GUI of M File, Just Recall File named PlotFieldXaxis.m in Command Window In Matlab then

enter Parameters required then press enter to find out the Lateral Curve at required Distance.


48/51

H3 Appendix A



This M File Used to Contour Lines of Magnetic Field @ versus certain area depending on the following Parameters:


X: Distance Required to Plot Literal Curve over it. (Ex. [0: 1: 30]).


Xn: Coordinate X of nth

overhead T.L. (Ex. [-13.5 0 13.5]).

Yn: Coordinate Y of nth overhead T.L. (Ex. [20.5 20.5 20.5]).



Span: Distance between two towers (Ex. 360 m) Sag: Max sag - at mid Span - (Ex. 12.5 m).

Steps: No. of steps between two towers (Ex. 200 step).


49/51

H3 Appendix A



its just a kind of GUI of M File, Just Recall File named PlotContour.m in Command Window In Matlab then

enter Parameters required then press enter to find out the Contour graph at required area.

This Code is basically depend on the previous code of calculating Brms at a certain point as we repeat it

number of times depend on the distance required to be covered over X axis then make a step, determine sag

value after this step so we could estimate Yn new of the T.l then recalculate Brms at each point along X axis

then repeats again and again for all steps then draw contour lines

We consider the T.L. as Parabola Curve to determine Sag at each Point


50/51

H3

|R e f e r e n c e s


Websites:

http://www.wikipedia.org/

http://www.ieee.org/index.html

http://www.google.com.eg/

http://www.pollutionissues.com/Ec-Fi/Electromagnetic-Fields.html

http://www.hydroquebec.com/sustainable-development/champs/faune-flore.html

Files that Prof. Dr. Hussein Anis and Dr. Abdel-Bari Mahdygives us

Thanks for your help in this research

I hope that it could reach what you expected from me

Ahmed Wahid Abass

Cairo University

Faculty of Engineering
http://www.wikipedia.org/http://www.wikipedia.org/http://www.ieee.org/index.htmlhttp://www.ieee.org/index.htmlhttp://www.google.com.eg/http://www.google.com.eg/http://www.pollutionissues.com/Ec-Fi/Electromagnetic-Fields.?htmlhttp://www.pollutionissues.com/Ec-Fi/Electromagnetic-Fields.?htmlhttp://www.hydroquebec.com/sus?tainable-development/champs/fa?une-flore.htmlhttp://www.hydroquebec.com/sus?tainable-development/champs/fa?une-flore.htmlhttp://www.hydroquebec.com/sus?tainable-development/champs/fa?une-flore.htmlhttp://www.pollutionissues.com/Ec-Fi/Electromagnetic-Fields.?htmlhttp://www.google.com.eg/http://www.ieee.org/index.htmlhttp://www.wikipedia.org/


51/51

H3

|R e f e r e n c e s

Special Thanks to my friends to all their help

I want to thank you very much

You taught me a lot of things, and the most important thing is what a brother means

Your brother

Ahmed Wahid Abass

Documents

Assessing of Magnetic Field Pollution