Submitted by: Muskaan. M. Nair XII-A
CBSE Roll No. :
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CERTIFICATE OF AUTHENTICITY This is to certify that, Muskaan.M.Nair, of grade XII, St. Joseph’s Residential School, Sriperumbudur has successfully completed the
research project on the topic ‘‘STUDY OF THE EARTH’S MAGNETIC FIELD USING A TANGENT GALVANOMETER’’ under the guidance of
Mr.Kaarthik (Physics Teacher). This project is absolutely genuine and does not n ot indulge in plagiarism of any kind. The references taken in making this project have been declared at the end of this Report.
Signature of the Candidate
Signature of the Principal
Signature of the Teacher In-Charge
Signature of the External Examiner Examiner
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Sl. No.
Contents
Page no.
1.
ACKNOWLEDMENT
04
2.
OBJECTIVES
05
3.
INTRODUCTION
06-08
4.
ABOUT THE TOPIC
09-11
5.
EXPERIMENT
12-13
6.
OBSERVATION TABLE
14-15
7.
BIBLIOGRAPHY
16
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ACKNOWLEDGMENT I would like to take this opportunity to express my deep sense of gratitude to all those people without whom this project could have never been completed. c ompleted. First and foremost, I’d like to thank my father for his inexhaustible
source of inspiration. I would like to thank my Principal Mr. James and school for providing me with the facilities required to complete this project. I am highly indebted to my Physics teacher Mr. Kaartik, for his invaluable guidance which has sustained my efforts in all the stages of this project work. My thanks and appreciation goes out to my fellow classmates and to the people who have willingly helped me out with this project to the best of their abilities.
Signature of the Candidate
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OBJECTIVES:
To determine the reduction factor of the given tangent galvanometer ( K ). ). To find out the horizontal component of earth’s magnetic field (Bh).
Tangent galvanometer diagram
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INTRODUCTION Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior to where it meets the solar wind, a stream of charged particles emanating from the Sun. Its magnitude at the Earth's surface ranges from 25 to 65 microtesla (0.25 to 0.65 gauss).Roughly speaking it is the field of a magnetic dipole currently tilted at an angle of about 10 degrees with respect to Earth's rotational axis, as if there were a bar magnet placed at that angle at the center of the Earth. Unlike a bar magnet, however, however, Earth's magnetic field changes over time because it is generated by a geodynamic (in Earth's case, the motion of molten iron alloys in its outer core).
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Most geomagneticians concern themselves with various dynamo various dynamo theories, whereby theories, whereby a source of energy in the core of the Earth causes a selfsustaining magnetic field. The Earth’s steady magnetic field is produced by many sources, both above and below the planet’s surface. From the core outward, these include the geomagnetic dynamo, geomagnetic dynamo, crustal crustal magnetization, magnetization, the ionospheric dynamo, the ring current, the magnetopause current, the tail current, field-aligned currents, and auroral, or convective, electrojets. The geomagnetic The geomagnetic dynamo is the most important source because, without the field it creates, the other sources would not exist. exist. Not far above the Earth’s surface the effect of other sources becomes as strong as or stronger than that of the geomagnetic geo magnetic dynamo. The Earth’s magnetic field is subject to variation on all timescales. Each of the major sources of the so-called steady field undergoes changes that produce transient produce transient variations, or disturbances. The main field has two major disturbances: quasiperiodic reversals and secular and secular variation. An entirely different type of magnetic variation is caused by magnetohydrodynamic (MHD) waves. These waves are sinusoidal variations in the electric and magnetic fields that are coupled to changes in particle density. They are the means by which information about changes in electric currents is transmitted, both within the Earth’s core and in its surrounding environment surrounding environment of charged particles.
Earth's magnetic field serves to deflect most of the solar wind, whose charged particles would otherwise strip away the ozone layer that protects the Earth from harmful ultraviolet radiation. One stripping
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mechanism is for gas to be caught in bubbles of magnetic field, which are ripped off by solar winds.
The intensity of the field is often measured in gauss (G), but is generally reported in nanoteslas (nT), with 1 G = 100,000 nT. A nanotesla is also referred to as a gamma (γ).The tesla is the SI u nit of the Magnetic field, B. The field ranges between approximately 25,000 and 65,000 nT (0.25 – (0.25 – 0.65 G).
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ABOUT THE TOPIC Tangent Galvanometer: Electric current is often measured using an instrument called a tangent galvanometer. tangent galvanometer. Able Able to measure the presence as well as the direction and power of currents, the instrument was first used in the early 1800s. It typically has a vertical copper wire coil, wrapped around a circular frame, and a compass in the middle. The compass needle generally responds to the magnetic field of the electrical current, which is compared to the Earth’s magnetic field in the experiment. This scientific This scientific instrument has been built in many forms and more modern ones often use beams of light to determine measurements, while some versions are used to measure the magnetic field of the Earth The instrument works based on the tangent law of magnetism. This principle defines the tangent of the angle, angle, traveled through by the compass needle, as being proportionate to a ratio of how strong two magnetic fields are. These fields are usually perpendicular to one another. Currents measured are typically proportional to the tangent of the same angle the needle goes through.
Circuit Diagram:
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When a bar magnet is suspended in two magnetic fields B and Bh, it comes to rest making an angle θ with the direction of Bh.
From Figure, B = Bh tanθ. This is known as tangent law of magnetism. If θ is the deflection of the needle, n eedle, then according to tangent law, B = Bh tanθ
(1)
Let I be the current passing through the coil of radius a with n turns, then the magnetic field generated by the current carrying coil is, B = µ0nI/2a
(2)
(a is the radius of the coil)
Equating (1) and (2), we get,
Bh tanθ = µ0nI/2a
(3)
2aBh/µ0n = I/tanθ
(4)
The left hand side of equation (4) is a constant and is called the reduction factor K of the given Tangent Galvanometer.
K = I/tanθ
(5)
Now from the equation (3) & (5), the horizontal intensity of Earth’s magnetic field B h is,
Bh = µ0nK /2a
(6)
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Applications Tangent Galvanometer can be used to measure the
magnitude of the horizontal component of the geomagnetic field. The principle can be used to compare the galvanometer constants.
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EXPERIMENT Aim: 1. To determine the reduction factor of the given tangent galvanometer ( K ). ). 2. To find out the horizontal component of earth’s magnetic field (Bh).
Apparatus:
Tangent galvanometer (TG), commutator (C), rheostat (R), battery (E), ammeter (A), key (k), connecting wires, meter scale etc.
Connections are made as shown in the figure given below, where K is the key, E the battery, A the ammeter, R the rheostat, C the commutator, and T.G the tangent galvanometer. The commutator co mmutator can reverse the current through the T.G coil without changing the current in the rest of the circuit. Taking the average of the resulting two readings for deflection for deflection averages out, any small error in positioning the TG coil relative to the earth’s earth’ s magnetic field B field Bh .
Principle & Formulae:
The reduction factor of T.G is K=I/tanθ, where I is the current flowing through the T.G which produces p roduces the deflection θ. The horizontal intensity of Earth’s magnetic field at a place. B h = µ0nK/2r, where n is the number of turns of the coil, µ0 = 4π×10-7 NA-2 is the permeability of free space, K is is the reduction factor of the T.G and r is the radius of the coil of the T.G.
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Procedure: 1. The circuit is made as shown in the diagram. The plane of the coil is made vertical by adjusting the leveling screws. The plane of the coil is made by adjusting the leveling screws. The plane of the coil is made parallel to (90-90) in the compass box. The whole T.G is rotated to read (0-0) at the ends of the aluminum pointer. Now the plane of the coil is in the magnetic magnetic meridian. 2. The Commutator keys are put. The rheostat should be adjusted for deflection in T.G between 10 and 60. For a current I, the deflections of the pointer θ1 & θ2 are noted. The Commutator is reversed. The deflections of the pointer θ 3 & θ4 are noted. The average of the four readings is the deflection θ. From the theory of the T.G, I=K tanθ. 3. By varying the current the experiment is repeated. Using a string the circumference of the coil is measured. Hence its radius r is found. Let n be the number of turns of the coil. The horizontal intensity at the place is given by, B h = µ0nK/2r
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OBSERVATION TABLES Table 1: For 1: For variation of θ with I. Deflection in T.G Ammeter Reading (A)
SL.No
Mean
K =I/tanθ
θ1
θ2
θ3
θ4
1
0.15
35
35
35
35
35
0.2142
2
0.20
49
47
60
64
53.6
0.1474
3
0.25
36
36
55
58
46.25
0.2389
4
0.30
50
50
65
68
58.2
0.1860
5
0.27
45
45
64
65
53.8
0.1976
Mean K = 0.19682
The reduction reduction factor of TH = 0.19682 Number of turns of the coil = 50 Cir cumference cumference of the coil (S) = 2π= 2π = 50.49 cm
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TABLE 2: For radius of tangent galvanometer. S.No.
Inner diameter d1 (cm)
Outer diameter d2 (cm)
Mean diameter d
1.
16.0 × 10−2
16.40 × 10−2
16.20 × 10−2
2.
16.16 × 10−2 16.06 × 10−2
3.
16.08 × 10−2
16.12 × 10−2
16.10 × 10−2
16.08 × 10−2
Mean radius
8.10 ×10−2 8.06 × 10−2 8.04 × 10−2
Mean radius of coil R = 8.04x10−2 Horizontal Intensity at the place Bh = µ0nK/2r =
-7
2πnK×10
/r = 7.6867×10-8 T
For different values of current I, deflections are noted and values are calculated. Knowing K, n and r the value of horizontal intensity Bh can be calculated.
Graph: From the graph,
B
tan θ A
C
Current I (A) 15 | P a g e
Slope of the straight line = BC G AC m = tan θ I
s
________(1)
Now, substitute (1) in formula μ0 2πN/4π RH =
Then, H = 7.6867×10-5 T
Result: 1. The reduction factor of T.G, K = 0.19682 A 2. Horizontal Intensity at the place, B h = 7.6867×10-5 T
Conclusion: Experiment in tangent galvanometer gives the reduction factor of galvanometer and horizontal intensity of Earth’s magnetic field.
BIBLIOGRAPHY Illustrative Oxford Book http://en.wikipedia.org Comprehensive Practical Physics www.wisegeek.com www.britannica.com www.amrita.edu
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