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Investigatory Project Physics Royal Gondwana Public School & Junior College Rushikesh Shendare Class

Physics Earth magnetic field using tangent galvanometer

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Investigatory Project

Physics

Royal Gondwana Public School & Junior College

Rushikesh Shendare Class XII

TABLE OF CONTENTSAcknowledgment………………………………………………………………………………………………………………..3Overview............................................................................................................................. 4 Aim of the Project......................................................................................................... 5 Apparatus and Materials required..................................................................... 6 Theory ................................................................................................................................. 7 Procedure.......................................................................................................................... 9 Observations and Graph…........................................................................................ 11 To determine the horizontal component of earth’s magnet Field (H) ..................................................................................................................11 From graph......................................................................................................... 12 Result ................................................................................................................................. 13 Precautions………………………………………………………………………………………………………………………....13

Sources of error……………………………………………………………………………………………………………….13 Facts.....................................................................................................................................14 Applications …..................................................................................................................14 Bibliography......................................................................................................................15

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ACKNOWLEDGEMENT “I would like to express my sincere gratitude to my Physics teacher, Mrs. Nitin Jassal for giving us the wonderful opportunity to do a case study and providing vital support, guidance and encouragement throughout the project. Without her

motivation and help, the successful completion of this project would not be possible. Secondly i would also like to thank my friends who helped me a lot in finalizing this project within the limited time frame.”

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OVERVIEW The tangent galvanometer was first

described in an 1837 by Claude-Servais- Mathias Pouillet, who later employed this sensitive form of galvanometer to verify Ohm’s law. To use the galvanometer, it is first set up on a level surface and the coil aligned with the magnetic north-south direction. This means that the compass needle at the middle of the coil is parallel with the plane of the coil when it carries no current. The current to be measured is now sent through the coil, and produces a magnetic field, perpendicular to the

plane of the coil and is directly proportional to the current.

The magnitude of the magnetic field produced by the coil is B; the magnitude of the horizontal component the Earth’s magnetic field is B’.The compass needle aligns itself along the vector sum of B and B’ after rotating through an angle Ø from its original orientation. The vector diagram shows that tan Ø = B/B’. Since the magnetic field of the Earth is constant, and B depends directly on the current, the current is thus proportional to the tangent of the angle through which the needle has turned.

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AIM OF THE PROJECTThe aim of the project is to study the Earth’s

magnetic field and find its value (BH) using a tangent galvanometer.

Tangent galvanometer made by Topview of a tangent galvanometer J.H. Bunnell Co. around 1890. made about 1950.

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APPARATUS AND MATERIALS REQUIRED

Tangent Galvanometer (TG), Commutator (C), Rheostat (R), Battery (E), Ammeter (A),

Key (K), etc

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THEORYTangent galvanometer is an early measuring

instrument for small electric currents. It consists of a coil of insulated copper wire wound on a circular non-magnetic frame. Its working is based on the principle of the tangent law of magnetism. When a current is passed through the circular coil, a magnetic field (B) is produced at the center of the coil in a direction perpendicular to the plane of the coil.

The working of tangent galvanometer is based on the tangent law. It is stated as when a magnet is suspended freely in magnetic field F and H, the magnet comes to rest making an angle θ with the direction H such that,

F = H tan θ (1)

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.

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Let a current I be passed through the coil of radius R, having turns N. Then magnetic field produced at the centre of coil is,

F=μ04 π2 π∈ ¿

R¿

(2)

Let H is the horizontal component of earth’s magnetic field and the magnetic needle comes to rest at angle θ with the direction of H, then according Eq. (1), Htanθ= μ0

4 π2π∈ ¿

R¿

Htanθ=10−72π∈ ¿R

¿

H=2π ×10−7∈ ¿Rtanθ

¿ (3)

by substituting the value of current I , from eq. (3),

tanθI =( μ04 π ) 2πNRH (4)

radius of coil of galvanometer R, deflection θ and N, the value of H can be calculated.

………….8

PROCEDUREConnections 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 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 averages out, any small error in positioning the TG coil relative to the earth’s magnetic field H .

PROCEDURE FOR PERFORMING THE EXPERIMENT

1.Make the circuit connections in accordance with the circuit diagram.

2.Using spirit level, level the base and the compass needle in compass box of tangent galvanometer by adjusting the leveling screw.

3.Now rotate the coil of the galvanometer about its vertical axis, till the magnetic needle, its image in the plane mirror fixed at the base of the compass box and the coil, i.e. all

4.these three lie in the same vertical plane. In this setting,

…………..95.the ends of the aluminium pointer should read zero-

zero. If this is not so, rotate the box without disturbing the position of the coil till at least one of the ends of the pointer stands at the zero marks.

6.By closing the key K, the current flow in the galvanometer. Read the both ends of the pointer. Now reverse the direction of current by using the

reversing key. When the mean values of both deflections shown by the pointer in the two cases (i.e. before and after reversing the current) differ by more than 1o, then turn slightly the vertical coil until the two values agree. This will set the plane of the coil exactly in the magnetic meridian.

7.By adjusting the rheostat, bring the deflection in galvanometer around 45o. The deflection should not be outside the range (30o-60o).

8.Record the reading of the ammeter and the deflection of the compass needle in the box shown by two ends of pointer on the scale.

9.Reverse the current in the coil of galvanometer and again record the current and deflection of needle.

10. By changing the value of current, take four or more set of readings and plot the graph between I and tanθ. The graph will be a straight line.

11. Measure the inner and the outer diameter of the coil with a half metre scale at least three times. ………….10

OBSERVATIONS1.Range of the Ammeter – 2. Least count of Ammeter – 3. Zero error in Ammeter – 4. Number of turns used (N) –

Table 1. For variation of θwith I

S.No. Value of deflection, θ(degree)

Mean tanθ Ammeter reading(A)

For direct current

For reverse current

θ1 θ2 θ3 θ4 Obs Corrected1.2.3.4.5.

3549365045

354736 5045

3560556564

3564586865

3553.6

46.2558.253.8

0.701.361.041.611.37

0.150.200.250.300.27

0.150.200.250.300.27

Table 2. For radius of tangent Galvanometer

S.No. Inner diameter d1

(cm)

Outer diameter d2

(cm)

Mean diameter

d

Mean radius(cm)

1.

2.

3.

16.0×10−2

16.16×10−2

16.06×10−2

16.40×10−2

16.08×10−2

16.10×10−2

16.20×10−2

16.12×10−2

16.08×10−2

8.10×10−2

8.06×10−2

8.04×10−2

Mean radius of coil R = 8.04×10−2……….…11

GRAPH

Slope of straight line = BCAC m = tanθI Now substitute the m in Eq. (4), m = μ04 π 2πNRH Then, H = 7.6867×10−8T

……….…12

RESULT The value of earth’s magnetic field by using a tangent galvanometer is

H = 7.6867×10−8T

PRECAUTIONS1.The battery should be freshly charged.2. The magnetic needle should swing freely in the

horizontal plane.3.The plane of coil must be set in magnetic meridian.4.There should be no parallax in noting down the

readings of ammeter and deflection.5.All the readings should be adjusted between 30o and

60o.

SOURCES OF ERROR1.There may a magnetic material around apparatus.2.The plane of coil will not be exactly in the magnetic

meridian.

……….…13

FACTSThe tangent galvanometer is an early measuring instrument for Current

The magnetic field produced by a circular coil carrying current I is Proportional to I .

The S.I unit of magnetic field is Tesla . The magnitude of horizontal intensity of earth’s

magnetic field is3.5x10⁻⁵ T . For better result while doing tangent galvanometer

experiment, the deflection should be in between 30o-60o.

The value of μ₀ is 4πx10⁻⁷ NA⁻²

APPLICATIONS T.G. 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.

For calibration of secondary instruments.

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BIBLIOGRAPHY

Tangent Galvanometer (Procedure) :Comprehensive Physics Activities Volume I : Laxmi Publications Pvt Ltd.

Tangent Galvanometer (Theory) : Comprehensive Physics Activities Volume I : Laxmi Publications Pvt Ltd.

Tangent Galvanometer (Precautions and Sources of error) : Comprehensive Physics Activities Volume I : Laxmi Publications Pvt Ltd.

Galvanometer: http://physics.kenyon.edu/EarlyApparatus/Electrical_Measurements/Tangent_Galvanometer/Tangent_Galvanometer.html

Galvanometer: Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Galvanometer

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