INDEX S.No Topic Page No 1 Aim 5 2 | Introduction 6-10 3 | Applications 10 4 | Apparatus and Materials required 11-12 5 | Theory 13-14 6 Procedure 14-16 7 | Observation and Calculation 16-17 8 | Graph and Result 17-18 9 Precautions 18 10 | Facts 19 11 | Bibliography 20AIM The aim of the project is to study the Earth’s magnetic field and find its value (BH) using a tangent galvanometer. Top view of a Tangent galvanometer6 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 microteslas (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, 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). The North and South magnetic poles wander widely, but sufficiently slowly for ordinary compasses to remain useful for navigation. However, at irregular intervals averaging several hundred thousand years, the Earth's field reverses and the North and South Magnetic Poles relatively abruptly switch places. These reversals of the geomagnetic poles leave a record in rocks that are of value to paleomagnetists in calculating geomagnetic fields in the past. Such information in turn is helpful in studying the motions of continents and ocean floors in the process of plate tectonics. The magnetosphere is the region above the ionosphere and extends several tens of thousands of kilometers into space, protecting the Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer that protects the Earth from harmful ultraviolet radiation. 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 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 | G = 100,000 nT. A nanotesla is also referred to as a gamma (7).The tesla is the SI unit of the Magnetic field, B.7 The field ranges between approximately 25,000 and 65,000 nT (0.25-0.65 G). Rotation axis Geographic north pole ~ Magnetic “north pole Magneric south pole Geographic south pole Near the surface of the Earth, its magnetic field can be closely approximated by the field of a magnetic dipole positioned at the center of the Earth and tilted at an angle of about 10° with respect to the rotational axis of the Earth. The dipole is roughly equivalent to a powerful bar magnet, with its South Pole pointing towards the geomagnetic North Pole. The north pole of a magnet is so defined because, if allowed to rotate freely, it points roughly northward (in the geographic sense). Since the north pole of a magnet attracts the south poles of other magnets and repels the north poles, it must be attracted to the South Pole.ee er ard a TANGENT GALVANOMETER Principle The tangent galvanometer works on the principle of tangent law. Tangent law of Magnetism + The tangent law of magnetism states that the tangent of the angle of a compass needle which is due to the movement under the influence of magnetic field is directly proportional to the ratio of strengths of two perpendicular magnetic fields9 + In simpler words, the tangent of the angle made by the moving needle under the magnetic field directly indicates the strength of the perpendicular magnetic fields. Definition + Tangent galvanometer is the device which was used to measure small amounts of electric current. Circular coll Compass box ‘erminals <— Leveling screns Construction + The working of tangent galvanometer is based on the principle of tangent law of magnetism. + It consists of a coil of insulated copper wire wound on a circular non-magnetic frame. + It is utmost necessary that the coil wound is done in helical arrangement otherwise, the field due to the wire will affect the compass needle, thus inducing an error in the reading. + This frame is mounted vertically on a horizontal base for support. + The coil of insulated copper wire is usually rotated on a vertical axis passing through its centre. + Assmall sized magnetic compass with a powerful magnetic needle is made to pivote at the centre of this coil, such that it is free to rotate ina horizontal plane.10 + The circular scale is used to read the movement of this magnetic needle which is divided into four quadrants, each ranging from 0° to 90°. + A pointer is attached to this needle at right angles, usually made up of thin alluminium as alluminium is lighter in m: + The usual way of discarding possibilities of parallax is also used ice placing of a plane mirror below the compass needle. Working + The instrument needle starts moving firstly under the influence of Earth's magnetic field + Movement continues untill the magnetic field of earth is parallel with the plane of coil. + Then, on application of an uknown current, a second magnetic field on the axis of the coil which is perpendicular to the Earth's magnetic field is created. + Hence the compass needle responds to the vector sum of the two fields. + This deflection angle is equal to the tangent of the ratio of those two fields. APPLICATIONS 1. T.G. can be used to measure the magnitude of the horizontal component of the geomagnetic field. 2. The principle can be used to compare the galvanometer constants. 3. For calibration of secondary instruments.APPARATUS AND MATERIALS REQUIRED > Tangent Galvanometer (TG), Commutator (C), Rheostat (R), Battery (E). Ammeter (A), Key (K), VVVVY Plug KeyRheostatTHEORY Tangent 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 0 with the direction H such that, Eq: F=H tan When a bar magnet is suspended in two Magnetic fields B and Bh, it comes to rest making an angle 0 with the direction of Bh. 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, Eq2: F=02nIN 4xn R Let H is the horizontal component of earth’smagnetic field and the magnetic needle comes to rest at angle @ with the direction of H, then according Eq. (1), HtanO =y0 2nIN 4nR HtanO = 107 27 R Eq3: H = 22x10 Rtan@ by substituting the value of current I, from eq. (3), Eq 4: tan@ I = 0 2nN 4m RH radius of coil of galvanometer R, deflection @ and N, the value of H can be calculated. PROCEDURE 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 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 T.G coil relative to the earth’s magnetic field H.CIRCUIT DIAGRAM 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. 5. In this setting, the ends of the aluminium pointer should read zero-zero. Tf 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 1°, 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 45°. The deflection should not be outside the range (30°-60°).lo 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 tan@. The graph will be a straight line. 11. Measure the inner and the outer diameter of the coil with a half metre ‘ale at least three times. OBSERVATIONS AND CALCULATIONS Table 1. For variation of @ with I IS.NO| Value of deflection 0 (degree) [Mean ffan @ - Ammeter Reading (A) For direct For reverse ~ [current current 1 oO. | 6 Oy Obs 1] 35 3s] 35 | 35 35 0.70 0.15 0.15 ae) 47| 00 | 04 53.6 0.20 3. | 36 3o| ss | 58 40.25 0.25 4.) 50 so| os | os 58.2 Lol] 0.30 0.30 5s. | 45 45 | 04 | 08 53.8 1.37 0.27 0.27Table 2. For radius of tangent Galvanometer S.No. Inner Outer Mean Mean diameter diameter d2 diameter radius dl (cm) (cm) d (cm) 1. 16.0* 107 | 16.40% 107 | 16.20* 107 | 8.10 ™ 107 2. | 16.16* 107} 16.08% 107 | 16.12* 10? | 8.06 x 107 3. | 16.06 x 10-2] 16.10 x 10-2 | 16.08 x 10-2 | 8.04 x 10-2 Mean radius of coil R = 8.04 « 107 GRAPH tanéSlope of straight line = BC AC m=tand I Now substitute the m in Eq. (4), m=n020N 4x RH Then, H == 7.6867 x 10°T RESULT The value of earth’s magnetic field by using a tangent galvanometer is H= 7.6867 x 10° T PRECAUTIONS 1. 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 30° and 60°. SOURCES OF ERROR 1. There may a magnetic material around apparatus. 2. The plane of coil will not be exactly in the magnetic meridian.19 FACTS The 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.1 unit of magnetic field is Tesla . > The magnitude of horizontal intensity of earth’s magnetic field is3.5x10° T. > For better result while doing tangent galvanometer experiment, the deflection should be in between 30°-60". > The value of po is 4ax107 NA,20 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/EarlyA pparatus/Electrical_Measurements/ Tangent_Galvanometer/Tangent_Galvanometer.html > Galvanometer: Wikipedia, the free encyclopediaen.wikipedia.org/wiki/Galvanometer