Earth's magnetic field by using tangentgalvanometer

Index  Introduction  Materials Required  Principle  Diagram  Theory  Procedure  Observations  Calculations  Result  Precautions  Sources of error  Bobliography

Materials Required  Tangent galvanometer (TG),  Rheostat (R),  Battery (E),  Ammeter (A),  Key (k)  Reversing key  Connecting wires  Metre scale

Principle 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.

Diagram

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 nonmagnetic 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 TG is arranged in such a way that the horizontal component of earth’s magnetic field (Bh) is in the direction of the

plane of the coil. The magnetic needle is then under the action of two mutually perpendicular fields. 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: For performing in real life Connections are made as shown in the figure, 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 Bh .

The magnetic field can be calculated as follows: 1. Make the circuit connections in accordance with the circuit diagram. 2. Using a spirit level, level the base and 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 of the mirror fixed at the base of the compass box and the coil ie all these three lie in the same vertical plane. In this setting, the ends of aluminum pointer should reads 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 mark. 4. By closing the key K, the current flows in the galvanometer. Read the both ends of the pointer. Now reverse the direction of current by using the reserve key. when the mean values of deflections shown by the pointer in 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.

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By adjusting the rheostat, bring the deflection in galvanometer around 45 degree. The deflection should not be outside the range(3060). Record the reading of the ammeter and the deflection of the compass needle in a box shown by two ends of pointer of the scale. Reverse the current in the coil of the galvanometer and again record the current and deflection of needle. By changing the value of current, take four more set of reading and plot the graph between I and tan. The graph will be a straight line. Measure the inner and outer diameter of the coil with a half metre scale at least 3 times.

Observations Range of ammeter r=_____________A Least count of ammeter = __________A Zero error in ammeter = __________A Number of turns used (N) = __________ Table for Variation of  with I. S. No.

Value of deflection,  For direct current 1 2

For reverse current 3 4

Mean 

Tan

Ammeter Reading (A) Observed Corrected

1. 2. 3. 4. 5.

Table for radius of tangent galvanometer S. no. Inner diameter d1 1. 2. 3.

Outer diameter d2

Mean Mean Diameter Radius d

Calculations Result The value of earth’s magnetic field by using tangent galvanometer is H = _________, G = _________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. All the readings must be adjusted between 30o and 600.

Sources of error 1. There may be a magnetic material around the apparatus. 2. The plane of the coil will not be exactly in the magnetic meridian.

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.

Bibliography  http://amrita.vlab.co.in/? sub=1&brch=192&sim=1049&cn t=2  Comprehensive Physics Practical Book  www.wikipedia.org/wiki/Galvano meter  o Tangent Galvanometer (Procedure) : Electricity & Magnetism Virtual Lab : Physical  Sciences : Amrita Vishwa Vidyapeetham Virtual Lab   amrita.vlab.co.in/? sub=1&brch=192&sim=10 49&cnt=2  o Tangent Galvanometer (Theory) : Electricity & Magnetism Virtual Lab : Physical

 Sciences : Amrita Vishwa Vidyapeetham Virtual Lab   amrita.vlab.co.in/? sub=1&brch=192&sim=10 49&cnt=1  o Tangent Galvanometer  http://physics.kenyon.edu/EarlyA pparatus/Electrical_Measurement s/Tangent_Galvan ometer/Tangent_Galvanometer.ht ml  o Galvanometer - Wikipedia, the free encyclopedia

Observations and Graph  Radius of the coil, a = 7.72cm  Number of turns in the coil = 2  Circumference of the coil,2πa = 48.5cm

Trail Numbe r

Ammete r Reading (A)

Pointer Deflection in Degrees Direct

ɵ1

Reverse

ɵ2 ɵ3

ɵ4

Mean

ɵ

(degre e)

tan

ɵ

(degre e)

K=1/tan

ɵ (A)

Bh

(I)

1. 2. 3. 4. 5. 6. 7. 8.

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.11

10 20 30 40 45 50 55 60

10 20 30 40 45 50 55 60

15 30 40 50 55 60 65 70

15 30 40 50 55 60 65 70

12 25 35 45 50 55 60 65

o.22 0.57 0.77 1.00 1.19 1.43 1.73 2.14

2.27 1.75 2.14 2.00 2.10 2.09 2.03 1.87

3.6 7 2.8 3 3.4 6 3.2 4 3.4 0 3.3 8 3.2 8 3.0 3

3.To determine the reduction factor of T.G. : Reduction factor K of the tangent galvanometer can be determined. From the graph drawn as, K=A B B C

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Result: The reduction factor of the given tangent galvanometer,  K = 2.03_A  Horizontal component of Earth’s magnetic field, Bh = 3.28x104 T

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