MEASURED MAGNETIC FIELD of EARTH by ROTATING COILS

Dwi Maryanti Putri* , Meili Yanti , Nurul Muthmainnah Herman

Laboratorium Fisika Modern Jurusan Fisika FMIPA

Universitas Negeri Makassar

Abstract. Have performed experiments on measuring magnetic field of earth by rotating coils The purpose

of this lab is to determine the components of Earth's magnetic field and determine the angle of inclination of the

earth's magnetic field . The magnetic field is the area immediately surrounding the magnet is still affected by the

magnet. Inclination angle is the angle formed by the Earth's magnetic field with the Earth's rotation axis. Data

collected by the scientific method which in this experiment determine how Large component of the magnetic field

obtained in the direction of the x-axis rotation of 0,002711 tesla. Direction of the y-axis rotation of 0,002436 tesla

and direction of z-axis 0,000838 tesla The angle of inclination of the Earth's magnetic field direction obtained at

12,95 o. Besed on the data obtained it can be concluded that the value of each axis of the magnetic field observed

in the different.

KEYWORDS: magnetic field, inclination angle, Earth Magnets.

INTROCUCTION

One of the defense mechanisms of the

earth of radiation attacks and the waste of space

is the presence of Earth's magnetic field. The

Earth's magnetic field to form two magnetic

poles. North pole of the earth magnetic field

contained in the geographic south pole of the

Earth while the Earth's magnetic field south pole

is at the north pole of the earth. However, no

precise compass facing north because there are

differences in the geography of the earth lies the

northern axis of the earth with the axis of the

magnetic south pole. The angle formed by the

irregularities of the earth's magnetic field with

the geographical direction of the earth is also

called the angle of inclination.

The existence of Earth's magnetic field

is used by humans in terms that facilitate human

navigation in determining direction. Magnetic

field whose origin is still not fully understood by

scientists, capable of capturing particles of high

energy nuclear, generally in the form of protons

and electrons.

Research shows irregularities of the

earth's magnetic field due to the mineral

constituent is no magnetic rocks such as

Magnetite (Fe3O4), Hematite (Fe2O3), ilmenite

(FeTiO3) and Pyrrhotit (Fe2-XS). The atoms in

a mineral are arranged geometrically in which

the individual and the range of the electron orbit

is directed through a certain small zone a few

microns in diameter and are known as magnetic

domains, causing the magnetic minerals. The

power of magnetism depends on the proportion

of the range of the electrons in the same direction

or reverse each other. Magnetite and pyrrhotit

have strong magnetism because the electrons in

the same direction, while hematite and ilmenite

strength is weak because of the surrounding

electrons tend to reverse direction. At

temperatures above the Curie temperature /

critical temperature (55oC-600oC) motions of

atoms are so large that there is no magnetic

domeinnya and the resulting properties of

magnetism is lost. When the temperature drops

below the critical temperature, the direction is

set again by the influence of the earth's magnetic

field.

THEORI

Scientists are of the opinion that the

magnetic field generated by an electric current

due to the iron-nickel core of the planet, and the

current generated due to the rotation of the

planet. This explanation is nothing more than a

theory that it can not explain why the planet

Jupiter which has a nickel-iron core at most, and

in the interior may consist of metallic hydrogen,

also has a magnetic field. Then the core of the

Sun is made up of super-hot plasma composed

mostly of hydrogen and helium, also has a

magnetic field. [1]

In 1830 to 1842, Karl Frederick Gauss

conduct detailed observations of the Earth's

magnetic field. He concluded that the source of

Earth's magnetic field comes from the earth. He

also stated that the Earth's magnetic field also

has a close relationship with the rotation of the

earth because the earth's magnetic poles close to

the Earth's spin axis. In addition to the Earth's

magnetic field axis move around a lot. In the

history of the earth has happened a few times

where the earth's north pole reversal becomes

south and south becomes north. Since 160

million years ago has happened hundreds of

times a magnetic pole reversal. Although it has

happened hundreds of times, this magnetic pole

reversal does not show a specific pattern of

repetition so it is difficult to predict when the

magnetic poles will reverse again. [1]

In 1927, Jacob Clay serorang Dutch

scientists have found evidence that the primary

cosmic radiation influenced by the Earth's

magnetic field. In air travel to Indonesia, he

found that the intensity of cosmic radiation is

reduced when approaching the equator of the

Earth's magnetic field. Earth's magnetic field

emanating from the earth extends to far into

space. The magnetic field forming an invisible

shield called the magnetosphere. This shield

protects us from cosmic radiation and the

enormity of the dangers that come from the sun.

These hazards include storm the sun (in the form

of a continuous stream of electrically charged

particles), the explosion of the Sun (which is

within a few minutes can release energy

equivalent to billions of hydrogen bombs), and

coronal mass hurling / Coronal Mass Ejections.

Regional Earth's magnetic field that traps

particles high-speed nuclear particles form a belt

that was first discovered by a team of American

scientists led by James S. van Allen. James Van

Allen continued his research even successful

shows a radiation belt around the Earth. The

radiation belts last named Van Allen radiation

belts.

The lines of magnetic force of the earth

that extends far into space, capturing charged

particles moving encircling lines of magnetic

force. Because these lines are most common in

polar regions, then in this region of electrically

charged particles to penetrate into Earth's

atmosphere and causing a nature show called

polar light or aurora.

Review a induction coil with winding

number N and the cross-sectional area 𝐴 = 𝜋𝑅2.

When the coil is rotated with angular velocity ω

in a uniform magnetic field B, the diameter d, as

the coil axis, then the resulting magnetic flux Φ

by:

Φ = 𝜋𝑅2𝑁𝐵 cos(𝜔𝑡) (1)

By using the time of revolution T = 2π/ω iinduksi

peak value of AC is given by

𝑉 =2𝜋𝑁𝑅2

𝑇𝐵 = 𝑎𝐵 (2)

with

𝑎 =2𝜋𝑁𝑅2

𝑇 (3)

When the coil is directed to the rotation axis z,

the amplitude of the voltage is given by

𝑉𝑧 = 𝑎√𝐵𝑥2 + 𝐵𝑦2 (4)

This value is induced into the earth's magnetic

field;

�⃑� = (

𝐵𝑥

𝐵𝑦

𝐵𝑧

) (5)

For reasons of symmetry, beraku on;

𝑉𝑥 = 𝑎√𝐵𝑧2 + 𝐵𝑦2 (6)

𝑉𝑧 = 𝑎√𝐵𝑧2 + 𝐵𝑦2 (7)

Furthermore, by using equation (5), (6) and (7)

obtained the components of the earth's magnetic

field;

𝐵𝑥 = √−𝑉𝑥2+𝑉𝑦2+𝑉𝑧2

2𝑎2 (8)

𝐵𝑦 = √𝑉𝑥2−𝑉𝑦2+𝑉𝑧2

2𝑎2 (9)

𝐵𝑧 = √𝑉𝑥2+𝑉𝑦2−𝑉𝑧2

2𝑎2 (10)

The angle of the direction of Earth's magnetic

field is obtained ∅

of the equation;

Tan𝜃 =𝐵𝑧

√𝐵𝑥2+𝐵𝑦2=√

𝑉𝑥2+𝑉𝑦2+𝑉𝑧2

2𝑉𝑧2 (11)

The above equation is mathematically correct,

the value of the root is likely to be negative when

the measurements were carried out around the

equator. [2]

EXPERIMENTAL METHODOLOGY

The experiments were done using a tool

components as follows: A pair of Helmholtz

coils, sensors Cassy, MV_box, Cassy Lab,

connecting cable ∅ 2.5 mm 2, 200 cm red and

blue, the experimental motors, control units for

motors and experimental PC with Windows

2000 to above.

The first thing that is done in this

experiment is to ensure that all components of

the equipment has been installed as shown

below:

FIGURE 1. Composition of the experimental

apparatus.

The next step is to connect all components

of a device to a voltage source PLN including

computers. Then Cassy clicking the icon on the

computer, after which it will appear cassy menu.

Then set the voltage range between -1 mV-

measurement 1mV and 20 second time limit.

Turning on the motor, then increase the speed

slowly approaching 0.3 rev / s. Set 2 connecting

cables red and blue to be wrapped around the

motor experiment and ensure the cable does not

come to the end. Furthermore, experimental data

recording the induced voltage as a function of

time by pressing F9 on the keyboard or select the

measurement on the menu Cassy.

For each data recording is completed, the

data storage process is done by selecting Save on

the File menu. The recording process is carried

out five times for each dimension, where data

recording is done in three-dimensional space, x,

y, and z.

EXPERIMENTAL RESULTS AND DATA

ANALYSIS

Magnetic field measurements performed using a

Helmholtz coil with the following sizes:

Number of turns (N) : 320

Diameter : 13,5 x 10-2 m

The radius (R) : 6,75 x 10-2 m

Plot the results of the data obtained in the

measurement of the voltage in the direction of

rotation of the x, y, and z.

GRAPH 1. Relationship between Period (T)

with voltage (V) in the X axis

GRAPH 2. Relationship between Period (T)

with voltage (V) in the Y axis

-0,4

-0,2

0

0,2

0,4

0 5 10 15 20

Vo

ltag

e (

mV

)

Period (s)

-0,4

-0,2

0

0,2

0,4

0 5 10 15 20

Vo

ltag

e (

mV

)

Period (s)

GRAPH 3. Relationship between Period (T)

with voltage (V) in the Z axis

Data Analysis

N = 320

R = 0,0675 m

On the X axis

V1 = 0,331 mV

V2 = 0,321 mV

V3 = 0,317 mV

V4 = 0,306 mV

Vx= 𝑉1+ 𝑉2+ 𝑉3+ 𝑉4

4

= (0,331+0,321+ 0,317+0,306) 𝑚𝑉

4

= 0,318 mV

T1 = 2,2 s

T2 = 4,4 s

Tx= T2 – T1

= ( 4,4 – 2,2 ) s

= 2,2 s

On the Y axis

V1 = 0,344 mV

V2 = 0,342 mV

V3 = 0,346 mV

V4 = 0,344 mV

Vy= 𝑉1+ 𝑉2+ 𝑉3+ 𝑉4

4

= (0,344+0,342+ 0,346+0,344) 𝑚𝑉

4

= 0,344 mV

T1 = 1,3 s

T2 = 3,6 s

Ty= T2 – T1

= ( 3,6 – 1,3 ) s

= 2,3 s

On the Z axis

V1 = 0,418 mV

V2 = 0,409 mV

V3 = 0,401 mV

V4 = 0,428 mV

Vz= 𝑉1+ 𝑉2+ 𝑉3+ 𝑉4

4

= (0,418+0,409+ 0,401+0,428) 𝑚𝑉

4

= 0,414 mV

T1 = 1,9 s

T2 = 4,3 s

Tz= T2 – T1

= ( 4,3 – 1,9 ) s

= 2,4 s

So the Earth's magnetic field strength on the X

axis

Bx = √− 𝑉𝑥

2 + 𝑉𝑦2 + 𝑉𝑧

2

2𝑎2

with

a = 2 𝜋 𝑁𝑅2

𝑇

= 2 (3,14)(320)(0,0675 𝑚)2

2,2 𝑠

= 2 (3,14)(320) (4,56 𝑥 10−3 𝑚2)

2,2 𝑠

= 4,165 𝑚2

𝑠

then

Bx = √− (0,318 𝑚𝑉)2 + (0,344 𝑚𝑉)2 + (0,414𝑚𝑉)2

2 (4,165 𝑚2

𝑠)2

= 0,002711 Tesla

-0,5

0

0,5

0 5 10 15 20

Vo

lta

ge

(mV

)

Period (s)

Earth's magnetic field strength on the Y

By = √𝑉𝑥

2− 𝑉𝑦2 + 𝑉𝑧

2

2𝑎2

with

a = 2 𝜋 𝑁𝑅2

𝑇

= 2 (3,14)(320)(0,0675 𝑚)2

2,3 𝑠

= 2 (3,14)(320) (4,56 𝑥 10−3 𝑚2)

2,3 𝑠

= 3,984 𝑚2

𝑠

then

By = √ (0,318 𝑚𝑉)2− (0,344 𝑚𝑉)2 + (0,414 𝑚𝑉)2

2(3,984 𝑚2

𝑠)2

= 0,002436 Tesla

Earth's magnetic field strength on the Z

Bz = √ 𝑉𝑥

2 + 𝑉𝑦2 − 𝑉𝑧

2

2𝑎2

with

a = 2 𝜋 𝑁𝑅2

𝑇

= 2 (3,14)(320)(0,0675 𝑚)2

2,4 𝑠

= 2 (3,14)(320) (4,56 𝑥 10−3 𝑚2)

2,4 𝑠

= 3,818 𝑚2

𝑠

then

Bz = √ (0,318 𝑚𝑉)2+ (0,344 𝑚𝑉)2 − (0,414 𝑚𝑉)2

2(3,818 𝑚2

𝑠)2

= 0,000838 Tesla

So, the total value of the Earth's magnetic field

is:

BT = √𝐵𝑥2 + 𝐵𝑦

2 + 𝐵𝑧2

= √(0,000007349 + 0,000005934 + 0,0000007022)𝑇𝑒𝑠𝑙𝑎

= √0,00001398 𝑇𝑒𝑠𝑙𝑎

= 0,003739 Tesla

The angle of the direction of Earth's magnetic

field is obtained ∅

Tan 𝜃 = 𝐵𝑧

√𝐵𝑥2+ 𝐵𝑦

2

= 0,000838

√(0,002711)2+(0,002436)2

= 0,000838

√0,000007349 + 0,000005934

= 0,000838

0,003644

= 0,229

𝜃 = arc tan 0,188

= 12,95 o

DISCUSSION

In this activity we perform measurements

of Earth's magnetic field with rotating coils.

Rotating coil in question is a Helmholtz coil is a

coil that can ignore the Earth's magnetic field

where his fingers as large as the distance

between the two coils. There are three axis

directions are analyzed, namely the direction of

the x, y, and z. The analysis is intended to

analyze in determining the value of the magnetic

field and the magnitude of the angle of

inclination earth’s generated. Large component

of the magnetic field obtained in the direction of

the x-axis rotation of 0,002711 tesla. Direction

of the y-axis rotation of 0,002436 tesla and

direction of z-axis 0,000838 tesla The angle of

inclination of the Earth's magnetic field direction

obtained at 12,95 o.

CONCLUSION

Based on the results of experimental data,

a large component of the magnetic field obtained

different in each direction of the axis of rotation

(x, y, and z). Large component of the magnetic

field obtained in the direction of the x-axis

rotation of 0,002711 tesla. Direction of the y-

axis rotation of 0,002436 tesla and direction of

z-axis 0,000838 tesla The angle of inclination of

the Earth's magnetic field direction obtained at

12,95 o.

REFERENCES

[1]Mukhlis Akhadi dan Hasnel Sofyan, 1999.

Medan Magnet Bumi. Buletin ALARA. Jakarta

[2]Subaer, dkk. 2014. Penuntun Praktikum

Eksperimen Fisika I Unit Laboratorium Fisika

Modern Jurusan Fisika FMIPA UNM