Magnetic Field Measurement In Residential Areas Biology Essay

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All conductors carrying electricity produce a field of force around them called magnetic field therefore increasing use of electrical equipments means there is increased exposure to magnetic field and concerns regarding health hazards due to exposure to low frequency magnetic fields arise due to this reason it is of great importance to know about the distribution of the magnetic field in residential area. In Sweden Strålsäkerhetsmyndigheten (Swedish Radiation Safety Authority) asked Chalmers University of Technology in Gothenburg to perform a study in Gothenburg, Borås and Mark in order to provide the Authorities with magnetic field distribution in the houses in these areas, for this purpose a total number of 97 houses were chosen randomly in Gothenburg, Borås and Mark to measure the magnetic field in them.

Mainly two types of measurements were performed in each house first a single point measurements in the living room, bedroom and kitchen in 15 different points in 3 different height levels in each of the mentioned rooms, then 24 hours measurements in the master bedroom .Finally the readings from both measurements were combined and a net value for the average magnetic field in each home was calculated based on the results of this study 90% of these houses had an average magnetic field in the range 0-0.2 µT. Beside this results it was also aimed in this study to include some information regarding harmonics forming the magnetic field in each house and include some information about the total harmonic distortion (THD). It was seen that most of the houses have high values of THD. It was also seen that the largest component of the magnetic field comes for the harmonics at the 50 Hz frequency. Finally it was observed that the magnetic field has its highest value at the bottom of each room.

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This thesis work is aimed to give a distribution of the magnetic field of houses in Gothenburg, Borås and Mark in Sweden.

In chapter1 magnetic field and different sources of magnetic field are introduced then electromagnetic spectrum is analyzed and health hazard associated with non ionizing part of the spectrum are reviewed.

In chapter2 methods used in this study for measuring the magnetic field are described as well as the instruments used for the measurement purpose then at the end different measurement metrics used in study to express the results are explained

In chapter 3 results of this study are presented. As the final goal of this study a Comulative distribution function (CDF) is represented which shows how much percent of the houses are below a certain magnetic field level.

In chapter 4: a discussion on the final results is held

Chapter 1

1. Introduction

In this chapter it is aimed to provide the reader with the definition of the main concepts used in this study and beside explain the importance of conducting this study.

1.1 Magnetic Field

Magnetic field is defined as "a field of force produced by moving electric charges or by elementary particles that possess their own 'intrinsic' magnetic field, a relativistic effect which is usually modeled as a spin of the particle"[1].

Among different sources indicated in former definition of the magnetic fields in this study we are interested in the magnetic fields produced by conductors carrying electricity.

Magnetic fields caused by electrical currents as depicted in figure 1.1 occur in continuous closed paths around the currents producing them therefore a conductor carrying electrical current gives rise to a magnetic field, the strength of this magnetic field is always proportional to the current in the conductor and the distance from the conductor. To show the Magnetic fields usually field lines are used and the magnetic field strength is constant along the conductor in closed paths around the conductor. In the case of other sources, magnetic fields tend to have a complicated appearance which usually cannot be calculated but have to be measured instead. The unit used to measure the magnetic flux density is called the tesla [T]. Based on the earlier definitions magnetic fields can be caused by electrical devices and installation cables. In certain cases, stray currents can give rise to magnetic fields. In Sweden, since the electricity system often contains four conductors leading to each building, stray currents can result in major problems.[2] "The decay current can pass through the neutral conductor as intended, but it can also pass through the earth conductor and into the plumbing pipe work to the transformer's earth point. This increases the magnetic field both along the path of the stray current and along the supply cable.

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Figure 1.1.Magnetic field around a wire carrying electrical current.

Power lines are also considered as a major external source of magnetic field. The phase current is producing the magnetic field caused by power lines. "Close to power lines magnetic flux can reach to a maximum of 10 to 30 μT but at a distance of 50 to 200 meter it decreases to less than 1 μT" [3].

Magnetic field at homes and working environments come from both external and internal sources, typical external sources are power lines, power distribution substations close to residential sections and even water pipes carrying unbalanced neutrals current while internal sources are the households appliances.

As it was mentioned earlier It comes from the definition of the magnetic field that electrical current is capable of producing magnetic field therefore increasing use of electrical equipments means there is increased exposure to magnetic field and concerns regarding health hazards due to exposure to low frequency magnetic fields arises therefore International Commission on Non-Ionizing Radiation Protection (ICNIRP) [10] was established to investigate the hazards associated with exposure to non ionizing radiation (NIR) and develop guidelines on NIR exposure. ICNIRP is considering acute health effects that may for example lead to the stimulation of the nerves. Among all guidelines introduced by ICNIRP there are guidelines for limiting time varying electric and magnetic fields (EMF) exposure. ICNIRP guidelines in this regard come in two in two major categories [10].

Occupational exposure [10].

General public exposure [10].

Occupational guidelies consider the expousure of the workers to time varying electric and magnetic fields at their workplace while general public guidlines consider all people of the society in all ages exposed to time varying electric and magnetic fields even in cases they are no aware of being exposed to magnetic fields [10].

reference levels for general public exposure and occupational exposure by ICNIRP are summerized in table 1 and table 2 [10].

Frequency range magnetic flux density B(T)

1 Hz-8 Hz 4Ã-10-2 /f2

8 Hz-25 Hz 5Ã-10-3 /f

25 Hz-50 Hz 2Ã-10-4

50 Hz-400 Hz 2Ã-10-3

400 Hz-3KHz 8Ã-10-3 /f

3 KHz-10M Hz 2.7Ã-10-5

Table 1.General public exposure guidelines by ICNIRP.

Frequency range magnetic flux density B(T)

1 Hz-8 Hz 0.2/f

8 Hz-25 Hz 2. 5Ã-10-3 /f

25 Hz-300 Hz 1Ã-10-3

300 Hz-3 KHz 0.3 /f

3 KHz-10M Hz 1Ã-10-5

Table 1.Occupational exposure guidelines by ICNIRP.

1.2. Health Hazards Associated with Exposure to Low Frequency Magnetic Field

The electromagnetic spectrum includes ionizing, optical and non-ionizing radiation. The non-ionizing radiation is in the frequency range from 0 Hz up to 300 GHz. The energy of the non-ionizing radiation is not strong enough to break the chemical bonds of genetic molecules however there are some biophysical mechanisms that can lead to adverse health effects. For low frequencies the mechanism is stimulation of nerves and cell due to induction of current. For higher frequency ranges the mechanism will be tissue heating [4].

"Extremely low frequency magnetic fields are also classified possible carcinogenic. Epidemiological studies consistently are showing an association between long-term average exposure to magnetic fields above 0.3/04 μT and childhood leukemia cancer"[4].

In the upcoming section some health hazards related to exposure to low frequency magnetic fields are reviewed based on some major studies.

Childhood Leukemia and Magnetic field Exposure in Ontario, Canada.

In a case control study including 88 cases comprising incident leukemia at 0-14 years of age and 133 controls an association between magnetic field exposure and increased risk of leukemia was observed [5].

Childhood Leukemia and Magnetic field Exposure in Japan

Power frequency magnetic field is labeled as a possible carcinogen by the International Agency for Research on cancer panel. In Japan one of the high exposure areas of the world a population-based case-control study was performed. This study covered areas with 54% of the Japanese children. 312 case children between 0-15 years old with acute leukemia and 603 controls matched for gender, age and residential area were analyzed. magnetic field mean was measured in each child house the study showed that most of the leukemia cases were exposed to magnetic field levels far above 0.4 μT.[6]

Exposure to Magnetic Fields during Pregnancy and the Risk of Miscarriage.

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In a study performed in San Francisco 969 pregnant women all with a positive pregnancy test at less than 10 weeks of gestation and all the women were residing in San Francisco. The outcome results were tested using the health maintenance organization databases. Although no association was observed between miscarriage risk and the average magnetic field level, miscarriage increases with an increasing level of maximum magnetic field exposure with a threshold around 1.6 µT [7].

This all shows it is of great importance to know about the distribution of the magnetic field in the residential areas. The methods used to provide such a graph showing this distribution are explained in the next chapter.

Chapter 2

2. Methods

In the previous chapter the health hazards associated with exposure to low frequency magnetic fields were discussed and based on several studies mentioned in the same chapter. Magnetic fields above a certain level might be considered as a possible threat to dwellers overall health in residential areas therefore it is of great importance to know about the distribution of magnetic fields in residential areas.

In Sweden Strålsäkerhetsmyndigheten (Swedish Radiation Safety Authority) asked Chalmers University of Technology in Gothenburg to perform a study in Gothenburg, Borås and Mark in order to provide the Authorities with magnetic field distribution in the houses of these area.

In this chapter methods for providing such a distribution are described as well as instruments used for measurement purpose. Totally 97 houses in Gothenburg, Borås and Mark in Västergötland were subject of this study. All the houses were chosen randomly to cover all the residential areas in the mentioned areas.

2.1. Instruments

It was explained in the first chapter that magnetic fields tend to have a complicated appearance which usually cannot be calculated, but have to be measured. Five different instruments were used in this study, a short description of each one beside its application in this study is given in this section.

2.1.1. Envirometor ML-1

Figure 2.1. Enviromentoir ML-1 magnetic field logger.

This instrument is capable of measuring RMS value of the magnetic fields in X, Y and Z direction irrespective of the direction in which the instrument is pointing in relation to the magnetic field. This instrument is able to store the measurement data in a logging basis with logging intervals ranging from 1 second to 150 seconds and totally the instrument can store up to 8,192 readings. The stored data can be transferred to a computer using the Rs232 connection then the PC software accompanying the instrument will provide the user with mean of stored readings

Maximum and minimum of stored data, standard deviation, median and finally high and low quarter.

A number of reports and graphs can also be generated using this PC software. Ml-1 frequency range is 30Hz-2kHz. In this study we used ML-1 for 24 hours logging in the bedrooms with logging intervals equal to 40 seconds. However in the houses near the railways this instrument could not be used for 24 hours logging since trains in Sweden are producing a dominant magnetic field in 16 Hz and ML-1 due to its internal band pass filter starting at 30 Hz cannot measure this major component therefore due to this hardware limitation for houses near the railways this instrument was not suitable and another instrument Combinova MFM10 was used. In the next page an example of a report generated by ML-1 PC software is shown.

Figure 2.2.Intensity distribution of magnetic field from Enviromentor ML-1.

In this report as well as the intensity distribution of the logging data some other statistical information like Min, Max, Mean, Median, Standard deviation, Low quart and High Quart are given.

2.1.2. Combinova MFM10

Figure 2.3. Combinova MFM10 magnetic field logger.MFM10 is capable of single point measurements of the magnetic field. It can as well be used for logging measurements. The frequency range MFM10 covers is between 5-2000 Hz. Since this frequency range covers the 16 Hz frequency it was used for 24 hours logging of the houses in the vicinity of railways instead of Enviromentor ML-1. The 16 Hz magnetic field component generated by trains which is a major component that Enviromentor ML-1 is unable to measure due to its hardware limitations will be taken into account using this instrument. Stored readings From CombinovaMFM10 are transferred to computer using RS232 cable as a text file. The logging interval used for MFM10 is 60 seconds. A typical image of this instrument is show in figure 2.3.

2.1.3. MFM 3000

Figure 2.4. Combinova MFM 3000 magnetic field loggerThis instrument, as depicted in figure 2.4 is used for single point measurements. MFM 3000 is an advanced instrument that besides giving the total RMS value for the magnetic field it also provides user with the largest and second largest frequency components of the total RMS value. The frequency coverage of this instrument is from 5 Hz up to 400 KHz. However this instrument gives the user the possibility to narrow this frequency range. In the case of these study frequencies up to 10 Hz were filtered to reduce the signals due tomeasurments in the earth magnetic field.

2.2. Calibration:

Before performing any measurements all the instruments used in this study were calibrated. A calibration test was performed in Strålsäkerhetsmyndigheten's laboratory to see if they were all fully functional and measure true values for the magnetic field. For this purpose a set up including a Helmholtz coil producing magnetic field was used The magnetic field created in the center of coil was calculated then all the instruments were placed in the center of the coil to see if they were measuring the expected value or not. This set up includes four main parts

Signal generator (SPN) (1Hz -1.3MHz)

Amplifier (gain 16.1 for load of 5 ohm)

Resistor to measure the current (3.3 ohm, 1 ohm)

Helmhotz coil (dimension of the box is 56x79)

Voltmeter

These five parts were conected based on the schem dipicted in figure 2.5.

Resistor

Figure 2.6. Calibration Setup

Signal generator was connected to the Amplifier and then to the resistance. Finally the coil was conected to the other parts to the coil. .

The formula µT was used to calculate the magnetic field produced by the coil at its center; therefore the voltage was set to 0.581883v then based the former equation all the instruments were supposed to measure a magnetic field of 1 µT (RMS) at the center of the coil.

2.3. Measurement Metrics

It was mentioned earlier that the purpose of this study is mainly to have the distribution of the magnetic field in houses in Gothenburg, Borås and Mark and a total number of 97 houses were randomly chosen for this goal and a number of metrics have been defined to be express the measurement results from each of these house. In this part a short description of each of these metrics is given then procedures for data acquisition are given in the following section.

2.3.1. Adjusted Average:

Two types of measurements are performed in this study one is single point measurement and the other one is the 24 hours logging. For single point measurements Combinova MFM 3000 is used and the single point measurements are performed in the living room, kitchen and bedroom according to the scheme depicted in figure 2.7 in which for each room the magnetic field is measured in the four corners of the room and the center in three different height levels. For 24 hour logging either Enviromentor ML-1 or Combinova MFM10 are used therefore we need a unique formula to calculated the average magnetic field of the house based on the reading of both instruments. In order to give such a formula two concepts are taken into consideration, first one is the average exposure of the people in house that requires a weighted average formula based on the average time people spend in each room, second is the average magnetic field of the house that is a normal average. The formula for calculating the average magnetic field that people in each house are exposed to is called Badjust and it is calculated from the following values. It is assumed that people on average spend 9 hours in the bedroom 2 hours in the kitchen and 4 hours in the living room so the weighted average formula can be calculated as follow

Bbed = 24 h average from the measurement point at the bed.

BsleepR = Room average for sleeping room.

Bkitchen = Room average for kitchen

BlivingR = Room average for living room

3 rooms: Badjust =

2 rooms: Badjust =

1 room: Badjust = Bbed.

Figure(2.7): single point measurements scheme

2.3.2. Total Harmonic Distortion (THD)

To have a better underestanding of the THD we refre to Wikipedia

"To understand a system with an input and an output, such as an audio amplifier, we start with an ideal system where the transfer function is linear and time-invariant. When a signal passes through a non-ideal, non-linear device, additional content is added at the harmonics of the original frequencies. THD is a measurement of the extent of that distortion.

When the input is a pure sine wave, the measurement is most commonly the ratio of the sum of the powers of all higher harmonic frequencies to the power at the first harmonic, or fundamental, frequency:

Which can equivalently be written as

Measurements based on amplitudes (e.g. voltage or current) must be converted to powers to make addition of harmonics distortion meaningful. For a voltage signal, for example, the ratio of the squares of the RMS voltages is equivalent to the power ratio:

where Vn is the RMS voltage of nth harmonic and n=1 is the fundamental frequency.

THD is also commonly defined as an amplitude ratio rather than a power ratio,[1] resulting in a definition of THD which is the square root of that given above:

This latter definition is commonly used in audio distortion (percentage THD) specifications. It is unfortunate that these two conflicting definitions of THD (one as a power ratio and the other as an amplitude ratio) are both in common usage. The power THD can be higher than 100% and is known as IEEE, but for audio measurements 100% is preferred as maximum, thus the IEC version is used (used by Rohde & Schwartz, Brüel and Kjær).

Measurements for calculating the THD are made at the output of a device under specified conditions. The THD is usually expressed in percent as distortion factor or in dB as distortion attenuation.".[8]

Based on the former section from Wikipedia there are two different definitions, however in this study the power definition (IEEE) is used

Measuring the amplitudes of the B-field from MFM 3000 we get

Figure 2.7. A typical measurment on Combinova MFM 3000 display.

Here Ptotal is proportional to

P1 is proportional to (the square of the largest signal)

Therefore the THD = %

Frequency of the 2nd largest signal:

At each house there are 15 measurement values in each room and up to 3 rooms (Bed room, living room and kitchen) are measured.

The THD for each measurement point (up to 45 values) is calculated and then the average THD is calculated

THD Average =

Where THD1 = is the THD for the first measurement point in that house …and THDn is the last measurement point in that house.

For the frequency of the 2nd largest signal the most frequent value of the n measurements is chosen however Due to FFT some inexact frequencies can appear, values from 149 to 151 Hz are rounded to 150 Hz and values around 16 - 18 Hz are rounded to 16.7 Hz (train frequency).

However in some cases some conflicts may arise so some rules are set for calculation of the THD. These rules are listed below.

If L.S. > RMS put THD = 0. (If L.S. is considerable > RMS then in data must be wrong, try to correct indata, if data can't be corrected then don't use this data for any calculations (THD and B adjust, levels etc))

If L.S. = 0 then do not calculate THD and don't consider it in the average THD.

If L.S. is not 50 Hz do not calculate THD and don't consider it in the average THD.

If 2nd L.S. is not 0 or 150 Hz do not calculate THD and don't consider it in the average THD.

If L.S. < 30 nT do not calculate THD and don't consider it in the average THD.

2.3.3. Fields Highest on Level

The RMS readings for the 3 levels (floor, middle or top) measured in the house are compared therefore there will be up to 15 results for the different positions. In each position the highest field can be at level: floor, middle, top or none (if the measurement values are the same for the two or three highest values). Numbers of highest level at "floor", "middle", "top" or "none" are calculated then the most frequent one is chosen. If the numbers of the most frequent level is shared with more than one level, then "none" is chosen. However for floor numbering two methods are used based on Wikipedia

"Floor numbering is the numbering scheme used for a building's floors. There are two major schemes in use across the world. In one system, used for instance in the British Isles, the floor just above the ground floor is assigned the number 1 (or "first"); in the other system, used in the United States, that same floor is number 2 (or "second"). In both systems, the numbering of higher floors continues sequentially as one goes up, as shown in the following table:

Displacement from ground level

British convention

American convention

3 story heights above ground

"3rd floor"

"4th floor"

2 story heights above ground

"2nd floor"

"3rd floor"

1 story height above ground

"1st floor"

"2nd floor"

at ground level

"Ground floor"

"Ground floor" or "1st floor"

In this study the British Scheme is used." [9]

2.4. Data Acquisition Procedures:

In this section procedures for data acquisition and also data documentation are described. All the instruments are capable of storing readings and through their PC software they transfer data to a PC. Beside these computerized stored data a check list was used as well for manual documentation of data. Besides readings from the instruments some additional information regarding each house like house type (if it is a villa or an apartment) and its location (if it is near railways or not) were documented on a hardcopy. An example of list for manual documentation of the data is shown in figures 2.8 and 2.9. beside addresses and contact info a unique code was also assigned to each house therefore the hard copies and softcopies were match easily with an anonymous cod and after sharing the measurement data between group members over internet participants privacy was reserved since there is nothing regarding the identity of the participants over internet and they are all called with a unique dummy cod. Due to privacy reasons the method for generation of unique cods is not explained here.

Figure 2.9. Typical checklist Used in this study.

In the first page of this check list as it is shown in figure 2.9 basic information like the house type, number of floors and its location if it is near railways or not are filled out then information regarding the 24 hours logging are filled out finally a small plot of the bedroom is given with major magnetic field sources if there is any in the room. In the next pages of the checklist as depicted in figure 2.10 single point measurements from MFM 3000 are filed out and a simple plot of that room with the major magnetic field sources is included.

Figure 2.9. Checklist used for single point measurements.

Chapter 3

In the previous chapter methods for measuring the magnetic field were described in details then a number of metrics introduced to represent the magnetic field measurments corresponding to each house. The final goal of this chapter is to show how much percent of the houses are below a certain value for the magnetic field, meanwhile some individual graphs and values for some houses with certain properties are given.

3.1.24 Hours Measurements Using Combinova ML-1

As it was explained earlier for 24 hours measurements of the magnetic field in the houses not in the vicinity of the railways ML-1 was used in the master bedroom. Here two examples for the distribution of the magnetic field in the bedroom for 24 hours logging are given. Figure 3.1 belongs to a villa house in Boras and figure 3.2 belongs to an apartment in Boras.

Figure 3.1. Magnetic field distribution of a typical house in Boras after 24 hours logging in the master bedroom.

Figure 3.2. Magnetic field distribution of a typical house in Boras after 24 hours logging in the master bedroom.

3.2. 24 Hours Measurements Using MFM10

AverageHouses in the vicinity of the railways are exposed to magnetic field at 16.7 Hz since Enviromentor ML-1 rejects the magnetic components below 30 Hz another instrument Combinova MFM10 for 24 hours measurements in the master bedroom was used. This instrument creates a text file including the logging data, in figure 3.3 part of such a file for a house in Mark is given. The logging interval is set to 60 seconds and the instrument automatically calculates the average value of the logging data for every 30 minutes, however it rejects data that are too far from the range of other data during each 30 minutes.

Figure 3.3. Part of a text file from MFM10 containing 24 logging data.

An example of a house near railways having high values over 24 hours is given in figure 3.4. This house comprises the average magnetic field of 0.003 μT in the bedroom over 24 hours logging and the adjusted magnetic field average of 0.08 μT from both 24 hours logging in the bedroom and single point measurements in other rooms. THD is also 3.6. In contrast to figure 3.4 an example of a house near railways having high values over 24 hours is present in figure 3.5. This second house comprises the average value of 0.51 μT for 24 hours logging in the bedroom and 0.39 for the adjusted average as explained earlier. THD for this second house is 257.2%. Reviewing these two examples and observing their relevant distribution figures for 24 hours logging in the bedroom in the next page, reader can have a visual understanding of the difference with the mentioned values.

Figure 3.4.A house near railways having typical values for magnetic field over 24 hours logging.

Figure 3.5. A house near railways having high values for magnetic field over 24 hours logging.

3.3. Single Point Measurements Using MFM 3000

Single point measurements are all performed using MFM 3000 instrument in 15 different points at three different heights in up to three rooms for each house. Distribution values of magnetic field for all these 15are shown in figure 3.6 and figure 3.7 these graphs are coming from the same house for which the 24 hours logging graph from ML-1 were represented in figure 3.1 and 3.2.

Figure 3.6.Single point measurements for a villa in 45 different single points of living room, kitchen and master bedroom.

Figure 3.7. Single point measurements for an apartment in 45 different single points of living room, kitchen and master bedroom.

3.4. Final Results:

Final results are given in five different parts the first section includes a Cumulative Distribution Function (CDF) that shows how much percent of the houses are below a certain magnetic field for the entire house( adjusted average from both 24 hours logging in bedroom and single point measurements in all room). In figure 3.7 this graph is represented.

Figure (3.8): Cumulative distribution function showing how much percent of houses are below a certain value for the magnetic field coming from both single point measurements and 24 hours logging

This graph shows that 90% of the houses have the adjusted average magnetic field (from both single point measurements and 24 hours logging) in the range 0-0.2μT. in the next graph in figure 3.9 the CDF graph from average value of the magnetic field in the bedroom over 24 hours logging is given.

Figure (3.9): Cumulative distribution function showing how much percent of houses are below a certain value for the magnetic field coming only from 24 hours logging in the bedroom

The third section shows the THD value in a bar graph showing number of houses with a certain THD value this graph is depicted in figure 3.10.

Figure (3.10) bar graph showing number of houses with a certain magnetic field value

This graph shows that most houses have high value for THD. The cumulative distribution function (CDF) for THD is also given in figure 3.11 However after doing single point measurements in a number of houses and receiving strange values for the THD frequencies up to 10 Hz were filtered to reject the effects of noise and improve the THD values in figure 3.11 CDF graph for THD in the houses that this 10 Hz filter was included is given it is evident that the THD value is improved.

Figure (3.11) CDF for THD

Finally in the last part in a graph in figure 3.12 it is shown how much percent of the houses have the highest magnetic field in each level as explained in chapter two. It comes from this graph that most houses have the highest value for the magnetic field on the ground level

Figure (3.13) : Bar graph showing percent of the houses with highest magnetic field in each level

In the appendix a summary table including results for all 97 houses is given.

,

Chapter 4

It is aimed in this chapter to have a discussion over the results of this study. This study shows that 90% of the houses have the magnetic value in the range between 0-0.2 µT which is reasonable according the studies over the health hazards associated with exposure to low frequancy magnetic fields. however this value is not the net magnetic field for the house but it comes from a weighted average showing the average magnetic field exposed to people in the houses based on the average hours people spend in each room. This study also tried to give some information regarding the harmonics forming the total RMS and it was seen that the largest component is in the 50 Hz that demonstrates the magnetic field in low frequencies is mainly coming from the power lines. However the total harmonic distortion THD has some abnormal values and at the beginning it was thought this can be a result of the noise or shaking of the instrument and a 10 Hz filter was applied to reject frequencies up to 10 Hz and results were improved. In the the figure 4.1 CDF for THD befor appling the 10 Hz filter is represented and comering it with the CDF of the THD after applying 10 Hz filter.

Spectrum of these single point measurements could be a useful tool to dig more into details and seek for the reasons of such strange values for THD unfortunately the MFM 3000 did not have this possibility to have the FFT of all single point measurements but it calculates the FFT of the last measurements but in this study the FFT values were all zero so this could be due to some problems with the instrument.

It was observed as well that in majority of the cases the largest signal in the harmonics is at 50 Hz and the second largest signal is at 0 H.