DEFLECTION MAGNETOMETER
The deflection magnetometer consists of a compass box C kept C kept -at the centre of a wooden board W of W of length about one metre.
The compass box consists of a short magnetic needle pivoted horizontally at the centre of a graduated circular scale. A long and light aluminium pointer P is P is fixed at right angles to the magnetic needle. . The circular scale is divided into four quadrants. Each quadrant is -griduited in degrees, from 0 to 90 such that_ the 0-0 ^graduations and 90-90 graduations ar.&-diametriealiyopposite. A plane mirror is fixed below Jhe_circular scale, to avoid the parallax error while error while taking readings. The whole arrangement 'is enclosed in an ebonite or brass case with a glass cover on the top. The two halves of the wooden board are called the arms of the magnetometer, on which the given magnet may be kept.( See Fig. 13.17) ' Deflection magnetometer magnetometer makes use of the tangent law. It can be used to find the pole strength of a magnet, to compare magnetic moments, field strengths etc. XA^JO Adjustments The deflection magnetometer can be adjusted in two positions (/) tan A position or end-on position and (ii (ii ) tan B position position or broad side on position. (Q tan A position, tan A position is also called the first position of Gauss. In this position, the arm of the deflection magnetometer is arranged in the east-west direction and the magnet is placed parallel to the arm CD as CD as shown in Fig. 13.18.
The compass needle in the box and the magnet NS kept on the arm form the letter T, as the needle points along north-south and the magnet points along east-west. Now the magnetic field B due to the magnet and the horizontal component of the earth's field are perpendicular to each other. To adjust the deflection magnetometer in the tan A position, first only the compass box is rotated so that the line joining the zerozero reading is parallel to the arms of the magnetometer. After that, the deflection magnetometer as a whole is rotated till the aluminium pointer reads zero. Now the magnetometer is set in tan A position. (if) tan B position. This position is also called the second position of Gauss.In this position the" magnetometer is arranged with its arms in the north-south direction and the given magnet is kept perpendicular to its arm. The axis of the magnet is again in the east-west direction as shown in Fig. 13.19. Now also the needle in the box and the magnet NS kept on the arm form the letter T. The magnetic field B due to the magnet and the horizontal component B H of the earth's field are perpendicular to each other. To adjust the magnetometer in the tan B position only the compass box is first rotated such that the line joining 90-90 graduations is parallel to the arms of the magnetometer. After that the deflection magnetometer as a whole is rotated till the
aluminium pointer reads zero-zero. Now the magnetometer is set in tan B position. Experiment (i) To Compare the magnetic moments, (a) tan A Position - Equal Distance Method. The deflection magnetometer is adjusted in the tan A position. One of the magnets of magnetic moment M is placed on one of its arms so that its axial line passes through the centre of the compass box. TTie magnet is so adjusted that the deflection in the magnetometer is between 30° and 60°. The distance d between the centre of the compass box and the centre of the magnet is noted as d [See Fig. 13.20]. The readings of both the ends of the aluminium pointer are noted.
The magnet is reversed end to end in the same position and the readings of both the ends of the pointer are again noted. The magnet is now taken to the other arm and the readings are taken by keeping the magnet at the same distance d from the centre of the compass box. The average value of these eight readings is found out as 0,. The experiment is repeated with the second magnet of moment M2 , keeping the magnet at the same distance d from the centre of the compass box. The average of the eight readings is noted as 0 2. Let 2/j and 21 2 be the lengths of the two magnets. The magnetic fields produced by the magnets of moments Mx andM2 at the centre of the compass box are B and B 2 respectively. If B H is the horizontal component of the magnetic field at the place then, Mo
2M
\d
= IT , , = B h tan 0, ...(/) 1
4n (d2 - Z,2)
H1
Ho 2M2 d and B 2 = ---:-r- = Bff tan 02 ...(ii) 2
4n (d2 - I 2 ) " 2
From equations (i) and (ii) 2 Mi _ (d2 - I 2 )2 tan9, Ml ~ (d2 - l 22 ) * tan 92
Mi The experiment may be repeated for different values of d and the average value of is M, tan 0j calculated. If the magnets are of equal lengths or short then, 77- =0
-10 M2 tan 02
(ii) tan A position-null method. First the deflection magnetometer is adjusted in the tan A position. The first magnet of moment M, is kept on one arm at a distance dx from the centre of the compass box [See Fig. 13.21]. The second magnet of magnetic moment M2 is kept on
the other arm so that like poles of the two magnets face each other. The position of the second magnet is so adjusted that there is no deflection. The distance of the second magnet from the centre of the compass box is noted as d2 . The two magnets are reversed in their positions, and the experiment is repeated. When the compass box shows zero reading, the fields produced by the two magnets at the centre of the compass box are equal, B L = B 2 2 Midi _ 2 M2 d2 Mj _ d? - I, 2 )2 d2 2= 2 2 2 x (,d2 - i x2 (d2 - i 22 ) ) ' W 2 ~ d - i 2 f Ti
Mx The experiment is repeated for different values of dx and the average value of is M2 calculated.
Mi
= tan
...(i)
(d + I [ ) For the second magnet, M2 B
2 = d2 + ^2)3/2 = B H tan 02 -(")
From equations (i ) and («') Mi _ (d2 + Z,2)372 tan 6, w2 ~ (d2 + Z22)372 x tiiTe; Mi The experiment is repeated for different values of d and the average value of is M2 M] tan 0! calculated. If the magnets are short or of equal lengths, TT - = &M6
M2 tan 02
(ii) tan B position - null method. The deflection magnetometer is adjusted in the tan B position. The first magnet of moment Mx is placed on one arm at a distance dx from the compass box. The second magnet of moment M2 is kept on the other arm as shown in Fig. 13.23. The expt. is performed as mentioned in tan A position, null method.
The magnetic fields produced by the two magnets at the centre of the compass are equal and opposite. Mj _ M2 d\2 + h2 f /2 " (d2 2 + /2 2 )372 Mj _ (d2 + hY 2
deflection magnetometer is adjusted in the tan B position. The first magnet of moment Mx is placed on one arm at a distance dx from the compass box. The second magnet of moment M2 is kept on the other arm as shown in Fig. 13.23. The expt. is performed as mentioned in tan A position, null method. The magnetic fields produced by the two magnets at the centre of the compass are equal and opposite. Mj _ M2 d\2 + h2 f /2 " (d2 2 + /2 2 )372 Mj _ (d2 + hY 2 M2
(d2 2 + l 2 f /2
Mx
The experiment is repeated for different values of d x. The mean value of is found out. M\ d3 For short magnets, ~rr - r M2 d2 Comparison of Horizontal Intensities of Earth's Magnetic Field First the deflection magnetometer is arranged in the tan A position, at the place where the horizontal component of the earth's magnetic field is B H . The given bar magnet is placed at a suitable distance and the experiment is performed as described in the equal distance method. The average of the eight deflections fy is noted. The experiment is repeated at the place where the horizontal component of the earth's magnetic field is Let the average of the eight deflections be 0 2. Since the same bar magnet is used at the two places we have, B H. tan 82 F
=
Bh1 tan 0j = BH^ tan 02 , ^ = ^
13.18. I n an experiment to c ompare the magnetic moments of two magnets by the equal distance method the av erage of 8 d eflections produced by the two magnets are 30° and 50° respectiv ely. I f the magnets are of equal lengths find the ratio of the moments of the two magnets. Mi tan 0, tan 30° Ans. 0, = 30°, 02 = 50°, -- = - = = 0.48 1i
M2 tan 0! tan 50
13.19. I n an ex periment to compare the magnetic moments of two magnets by the null method, the first magnet was kept at a distance of 25 cm from the centre of the compass box. For getting null d eflection, the second magnet was kept at a distance of 20 cm from the centre of the compass box. Find the ratio of the magnetic moments, if they are of the same length. M> d,3 25 3
Ans, d, = 25 cm, d 2= 20 cm, - = Ar = ? = 1.9, Mx :M2 = 1.9:1 M2 d 2 20 13.20. The compass need le i n a d eflection magnetometer showed a d eflection of 40° at one place and 46° at another place, when it was adjusted i n the tan A position. Compare the horizontal component of the earth' s magnetic fiel ds at the two places. If the horizontal component of the earth' s magnetic fiel d at the fir st place i s 0.38 x KT* T what i s it s v al ue at the second place? Ans. 0! = 40° , 02 = 46° Let the horizontal component of earth's magnetic field at the first place be B x and that at the second place be B 2. El =
=
tan 46
=
^ B 2 tan 0, tan 40 '
Given B, = 0.38 x 10" 4 T, B 2 = ? g, 0.38x10^ Q31xl( w»T 82 ~ 1.234 " 1.234 -°-31xl ° T
