To study the earth’s magneticfield Contents Aim Requirements The Tangent galvanometer Theory and Working Procedure Observations and calculations Result Bibliography Aim To study the earth’s magnetic field using a tangent galvanometer Requirements Introduction A tangent galvanometer A commutator An ammeter A battery A plug key A rheostat A spirit level Connecting wires A piece of sand paper Introduction Although historically ancient travelers made abundant use of the earth’s magnetic field for the exploration of the earth, they were ignorant of its origin. In many respects the earth’s magnetic field exhibits characteristics similar to those of a bar magnet; nonetheless, the mechanisms responsible for generating each are vastly different.. Magnetic field lines appear to originate near the south geographic pole, i.e. magnetic north pole, and terminate near the north geographic pole, i.e. magnetic South Pole. Earth's magnetic field, also known as the geo magnetic field, is the mag netic field tha t extends from the Earth's interior to where it meets the solar wind, a stream of charg ed 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 geodynamo (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 topaleomagnetists 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. A Tangent galvanometer A tangent galvanometer is an early measuring instrument used for the measurement of electric current. It works by using a compass needle to compare a magnetic field generated by the unknown current to the magnetic field of the Earth. It gets its name from its operating principle, the tangent law of magnetism, which states that the tangent of the angle a compass needle makes is proportional to the ratio of the strengths of the two perpendicular magnetic fields. It was first described by Claude Pouillet in 1837. The tangent galvanometer A tangent galvanometer consists of a coil of insulated copper wire wound on a circular non-magnetic frame. The frame is mounted vertically on a horizontal base provided with leveling screws. The coil can be rotated on a vertical axis passing through its centre. A compass box is mounted horizontally at the centre of a circular scale. It consists of a tiny, powerful magnetic needle pivoted at the centre of the coil. The magnetic needle is free to rotate in the horizontal plane. The circular scale is divided into four quadrants. Each quadrant is graduated from 0° to 90°. A long thin aluminum pointer is attached to the needle at its centre and at right angle to it. To avoid errors due to parallax, a plane mirror is mounted below the compass needle. In operation, the instrument is first rotated until the magnetic field of the Earth, indicated by the compass needle, is parallel with the plane of the coil. Then the unknown current is applied to the coil. This creates a second magnetic field on the axis of the coil, perpendicular to the Earth's magnetic field. The compass needle responds to the vector sum of the two fields, and deflects to an angle equal to the tangent of the ratio of the two fields. From the angle read from the compass's scale, the current could be found from a table. [2] The current supply wires have to be wound in a small helix, like a pig's tail, otherwise the field due to the wire will affect the compass needle and an incorrect reading will be obtained. Theory and Working As depicted in Figure (A) the earth’s magnetic field Be can be decomposed into a component Bh which is parallel to the plane of the horizon and a component Bv which is perpendicular to the plane of the horizon. Thus, Be and Bh are related by Be = Bh /cos (θi) eq-1 Fig (A) Where θi is the angle of inclination. If a compass needle is subjected to a known external magnetic field Bx which acts perpendicularly to Bh, the compass needle will deflect through an angle θx away from magnetic south (See Figure (B)) Consequently, Bh is related to Bx by Bh = Bx/tan(θx) eq-2 Thus, Eq’s 2 and 1 relate the earth’s magnetic field, which is unknown, with the magnetic field Bx, which is known in principle. The tangent galvanometer is the primary piece of equipment used in performing the experiment. . The magnitude of the magnetic field Bx, in units of microtesla, at the center of the coil is Bx = N µ0I/ 2a × 106 = N (4π × 10−1 )I/ D , where µ0 = 4π × 10−7 , N is the number of turns which the coil comprises, 2a is the diameter of the coil measured in meters, and I is the current though the coil measured in amps. If θ is the deflection of the needle, then according to tangent law, Let I is the current passing through the coil of radius a with n turns, then the field generated by the current carrying circular coil is, Equating (1) and (2), we get, The left hand side of equation (4) is a constant and is called the reduction factor (K) of the given tangent galvanometer. Now from equation (3) & (5), the horizontal intensity of earth’s magnetic field Bh is, Procedure Calculating the horizontal component 1. Connect the galvanometer (N = 5), ammeter and power supply in series. 2. Align the galvanometer such that it creates a magnetic field perpendicular to that of Earth’s field (the compass needle should be parallel to the wire loop). Do not move the galvanometer while taking data. 3. Turn on the power supply to flow current through the galvanometer 4. Record the inclinations corresponding to each value of i (current) by varying the current in the table. 5. Record the inclinations for each value of current in both direct and reverse current by changing the commutator. 6. Record the values for about 7 different values of i. Observations calculations: and Number of turns in the coil = 5 Circumference of the coil, 2 Radius of the coil, a = 25/ π πa = 50 cm = 50x 10-2 m = 7.96 cm = 7.96 x 10-2 m 1. To determine the horizontal component of earth’s magnetic field (Bh): The Horizontal component of earth's magnetic field (B h) can be calculated using the formula, 2. To determine the reduction factor of T.G: Direct current Reverse current S.n Current θ 1 θ 2 θ 1 θ 2 Mean ( θ o ) i/tan θ (K) 1 0.6 35 35 30 30 32.5 0.941 2 0.8 40 40 37 37 38.5 1.006 3 0.9 45 45 40 40 42.5 0.982 4 1 50 50 44 44 47 0.932 5 1.1 50 50 42 42 46 1.062 6 1.2 55 55 46 46 50.5 0.989 7 1.4 60 60 50 50 55 0.980 Mean (k) = 0.986 Note: Take deflection between 30 and 60 degrees. Now Bh can be calculated by After Calculation we obtain Bh = 3.89147 x 10-5 T 3. From graph Reduction factor K of the tangent galvanometer be determined. From the graph drawn as, can Result The reduction factor of the given tangent galvanometer, K = 0.986 A Horizontal component of earth’s magnetic field, Bh = 3.891 x 10-5 T Bibliography http://iiith.vlab.co.in/?sub=1&brch=192&sim=1049&cnt=2 https://en.wikipedia.org/wiki/Earth%27s_magnetic_field http://virtuallabs.ket.org/physics/wpcontent/uploads/Lab_Pages/Lab_a-TanGalv_6_1_12.pdf