Helmholtz Galvanometer

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1 Helmholtz Galvanometer To plot a graph showing the variation of magnetic field with distance along the axis of a Helmholtz galvanometer and determine the reduction factor k. B.Tech-I, Physics Laboratory August 12, P age

2 OBJECTIVE To plot a graph showing the variation of magnetic field with distance along the axis of a Helmholtz galvanometer and determine the reduction factor k. APPARATUS REQUIRED Helmholtz galvanometer, variable power supply, an ammeter, commutator and connecting wires CIRCUIT DIAGRAM THEORY AND FORMULA USED Figure 1 For a coil consisting of n turns of wire and having a mean radius r, the magnetic field at a point on the axis at a distance x from the center of the coil is given by F = (1) Where, i is the current passing through the coil 2 P age

3 The rate of variation is given by- = -3x [ ] (2) = -6πni [ - 5 ] (3) From which x = ± r/2, if = 0 or = constant If there are two identical coils having the same axis and carrying the same current in the same direction with their centers r cm. apart, the rate of increase of field due to one coil at the midpoint between the coils is equal to the rate of decrease of field due to the other at the same point. Therefore, if one moves away along the axis from the midpoint, any reduction in the intensity of the field due to one coil is compensated by the increase in the field due to the other. So, as a combined effect, the field between the coils is practically uniform. The field at the midpoint is given by- F = 2 = (4) If the coils are in magnetic meridian, it will be perpendicular to H. If the needle shows the deflection θ, = H tan θ (5) Or, i = = k tan θ (6) 3 P age

4 Where, k (expressed in emu) is a constant for the galvanometer at a particular place called the reduction factor of the galvanometer. Also, k = i / tanθ (7) Where, k and i are in amperes. PROCEDURE 1. To set the coil in magnetic meridian and measurement of current (i) i. Place the magnetometer compass box on the sliding bench so that its magnetic needle is at the centre of the coil. By rotating the whole apparatus in the horizontal plane, set the coil in the magnetic meridian roughly. In this case all the three i.e.- (i)-coil, (ii)-needle, and (iii)-distance scale lie in the same vertical plane. Rotate the compass box till the pointer ends read 0-0 on the circular scale. ii. To set the coil exactly in the magnetic meridian set up the electrical connections as shown in circuit diagram and allow the flow of current in one direction with the help of commutator and note down the deflection of the needle. Now reverse the direction of the current and again note down the deflection. If the deflections are equal (for both forward and reverse direction of currents) then the coil is in magnetic meridian. Otherwise turn the apparatus a little more. iii. Using rheostat Rh adjust the current such that the deflection of nearly 45 0 is attained in both the ends of compass needle, for forward as well as reverse directions of currents. The current i is used in equ. (7) for the calculation of k. 4 P age

5 2. Measurement of angle tan θ (i) For East direction The magnetometer box when placed in the middle of coils the distance on the length scale is 17 cm at both ends (west and east). Now slowly move the scale over the bench (say in West direction) such that the distance on length scale is 32 cm in west end. In this way, the magnetometer box has been kept 15 cm away (32-17=15) from the middle position in the East direction. The deflection for both the sides of the pointer (i.e. east and west ends) is noted for direct current (this will give θ1 and θ2 values) as well as for reverse current (this will give θ3 and θ4 values). We see the readings on length scale in west end. The procedure is then repeated for varying the distance on length scale (at west end) at an interval of 2 cm (i.e. 32, 30, 28, 26, 24, 22 cm). Further, from the length 21 cm to 17 cm on scale, the reading is taken carefully at an interval of 1 cm (or 0.5 cm) only, because; in this range the magnetometer box enters the coil where there is a constant field. It is already mentioned that, at 17 cm on the length scale the magnetometer box is again in the middle of the coil. In this way, we have noted the variation of θ i.e. tan θ (Y-axis) versus distance x, (X axis, starting from 15 cm and finally for 0 cm) for east end, see observation table-1. This data will make the left half part of the curve as shown in Fig. 2. (i) For West direction Now, we again slowly move the scale over the bench and start monitoring our reading from 17 cm on the length scale. But this time we see the readings on length scale in east end. The deflection for both the sides of the pointer (i.e. east 5 P age

6 and west ends) is noted for direct current (this will give θ1 and θ2 values) as well as for reverse current (this will give θ3 and θ4 values). The procedure is repeated for varying the distance on length scale (at east end) at an interval of 1 cm until we reach to 21 cm on length scale (i.e. 17, 18, 19, 20, 21 cm). This is again because in these readings magnetometer box is inside the coil and going out of it. After that we again record the reading for 2.0 cm interval until 32 cm is achieved at the east end (ie. 22, 24, 26, 28, 30, and 32 cm). In this way, we have noted the variation of θ i.e. tan θ (Y-axis) versus distance x, (X axis, starting from 0 cm and finally for 15 cm) for west end, see observation table- 2. This data will make the right half part of the curve as shown in Fig Average of all the four θ values obtained in each reading will be used to calculate the tanθ. Since, we already have current (i), now, one can calculate reduction factor k also. 4. Plot graph taking distances along X-axis and tanθ along Y-axis. In a fixed distance the curve shows a constant variation. 6 P age

7 Figure 2 7 P age

8 OBSERVATIONS Number of turns in the coil =.(50) Current in ampere =.amp Table 1: For East end S. No. Distance along the axis from center (x, in cm) Deflection of the Needle Direct Reverse Mean θ tan θ θ1 θ2 θ3 θ (32 cm on the length scale on west end)* (30 cm on the length scale on west end) 3 11(28 cm on the length scale on west end) 4 9 (26 cm on the length scale on west end) 5 7 (24 cm on the length scale on west end) 6 5 (22 cm on the length scale on west end) 7 4 (21 cm on the length scale on west end) 8 3 (20 cm on the length scale on west end) 9 2 (19 cm on the length scale on west end) 10 1 (18 cm on the length scale on west end) 11 0 (17 cm on the length scale on west end) *Bracketed quantity [for example (32 cm on the length scale on west end)] is only to understand the length on scale and distance from mid position (x). It will not be used in real observations 8 P age

9 Table 2: For West end S. No. Distance along the axis from center (x, in cm) Deflection of the Needle Direct Reverse Mean θ tan θ θ1 θ2 θ3 θ (17 cm on the length scale on west end)* 2. 1 (18 cm on the length scale on west end) 3 2 (19 cm on the length scale on west end) 4 3 (20 cm on the length scale on west end) 5 4 (21 cm on the length scale on west end) 6 5 (22 cm on the length scale on west end) 7 7 (24 cm on the length scale on west end) 8 9 (26 cm on the length scale on west end) 9 11 (28 cm on the length scale on west end) (30 cm on the length scale on west end) (32 cm on the length scale on west end) *Bracketed quantity [for example (17 cm on the length scale on west end)] is only to understand the length on scale and distance from mid position (x). It will not be used in real observations 9 P age

10 CALCULATION K = H = amperes (k/10 is expressed in emu), [Coil circumference 2ᴨr=48cm and n=50] ERRORS (i) Standard Error (ii) % Error RESULTS The reduction factor of Helmholtz galvanometer for turns is( ±-----)ampere. Horizontal component of earth s magnetic field in the lab ( ±-----) (Standard value = 0.35 Gauss). 10 P age

11 PRECAUTIONS 1. The coil should be carefully adjusted in the magnetic meridian. 2. All the magnetic materials and current carrying conductors should be at a considerable distance from the apparatus. 3. The current passed in the coil should be of such a value as to produce a deflection of nearly Parallax should be removed while reading the position of the pointer. Both ends of the pointer should be read. 11 P age

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