investigatory project

This is to certify that Miss.Damini Bhattacharya a student of class 12th A of Kendriya Vidyalaya AFS rajokri Roll no. 08 ,has completed his Physics Investigatory Project on the topic Horizontal component of earth’s magnetic field, under the guidance of Mr.Rakesh Sharma. Signature (Subject Teacher)

Date

Signature (Examiner)

It is through tremendous efforts of my teachers, parents and friends that I was able to complete my Investigatory Project in the best way possible. An investigatory project involves various difficult lab experiments, which have to obtain the observations and conclude the reports on a meaningful note. Thereby, I would like to thanks Mr.Rakesh Sharma sir for guiding me on a systematic basis and ensuring that in completed all my research with ease, helping me in the lab work by providing all the necessary materials and apparatus. I hope this project will help us all to look for the best alternative (renewable and pollution free) fuel – the biodiesel.

AIM To find out the horizontal component of earth’s magnetic field (H).

Materials Required Tangent Galvanometer

Battery Eliminator

Ammeter

Reversing Key

Rheostat

Spirit Level

One - way Key

Connecting Wires

A Tangent Galvanometer is a moving type galvanometer. It is used for measuring very small currents. Its working is based on the Tangent Law in magnetism.

Construction

It consists of a circular frame of a non-magnetic material, on which three coils having 2, 50 and 500 turns of fine insulated copper wire are wound. Ends of each coil are connected to screws at the horizontal turn table in which the frame is mounted vertically. A circular compass box of non-magnetic material is held at the center of the circular frame. This box has a small magnetic needle pivoted at its centre with a long thin aluminum pointer fixed at 90o to the needle. Both are free to move on a horizontal circular scale graduated in degrees and divided into four quadrants of 0o and 90o each. A small plane mirror is fixed at the base under the pointer. This would remove error due to parallax in reading the position of the pointer on the scale. The turn table is provided with leveling screws.

Setting

Adjust the leveling screws so that turn table is horizontal and the circular coil frame is vertical. Turn the frame so that the plane of the frame becomes parallel to the magnetic needle. This sets the frame in magnetic meridian. Turn the compass box so that ends of the aluminum pointer lie on 0-0 line.

When a current 1 ampere is passed through the coil, a magnetic field F (in tesla) is produced at the centre and along a direction perpendicular to the plane of the coil, given by where r is the radius of the coil (in m) and n is the number of turns in it.

F = µ° . 2πnI 4π r Since the plane of the coil is in magnetic meridian, the horizontal component of the earth’s magnetic field H, acts in the plane of coil. It means F and H are perpendicular to each other. Thus the magnetic needle of the compass box is under the combined effect of two perpendicular magnetic field F and H. The needle gets deflected and comes to rest making an angle (θ) with the direction of H. This angle is read from the end of the aluminum pointer. According to the tangent law –

F = H tan θ Or

µ° . 2πnI = H tan θ …..(1) 4π r

Or

I = 2πnI tan θ = K tan θ µ° n

Where K = 2πnI = Reduction Factor of the TG µ° n

Therefore, the Reduction Factor of the Tangent Galvanometer is defined as the current in amperes which when passed through the tangent galvanometer produces a deflection of 45°. From (1),

H = µ° . 2πnI X 1 4π r tan θ

TANGENT LAW

When a magnet is suspended under the combined actions of two uniform magnetic fields of intensities F and H, acting at 90° to each other, the magnet comes to rest making an angle θ with the direction of H such that – F = H tan θ

PROOF Consider a bar magnet of pole strength m, magnetic length 2l suspended under the combined action of two perpendicular magnetic fields F and H. the magnet rest making an angle θ with H. A torque acts on the magnet due to each field. As the magnet is in equilibrium, therefore clockwise torque due to field H., or mF x NA = mH x SA or

H

mH N θ θ

F

F = H .SA/NA = tanθ mF

i.e.

F = H tanθ

For the tangent galvanometer we have the relation I = K tanθ …..(i)

A

S

mH

mF

Putting the value of K we get,

H = µ°2πnI 4πr tan θ - Hence Proved From the above equation it is also clear that the graph of tanθ vs. I would be a straight line with a slope = µ° 2πn / 4πr H.

Make the circuit connections in accordance with the diagram connecting the positive terminal of the ammeter to the higher potential terminal of the battery and using 50 turns in the coil of the tangent galvanometer. Note the least count and the zero error of the ammeter. Measure the inner and the outer diameter of the coil of the tangent galvanometer three times with a meter scale. Make the initial setting in the tangent galvanometer. Switch on the current through the galvanometer by closing the key K. Read both ends of the pointer after gently trapping the compass box. Using the reversing key (R.K.), reverse the direction of the current through the coil and again read the values of the deflection shown by the pointer in the to cases (i.e., before and after reversing the current) differ by more then 1°, then turn slightly the vertical coil until the two value agree. This will set the plane of the coil exactly in the magnetic meridian. Now mark the positions of the leveling screws on the working table with a piece of chalk. Bring the deflection in the galvanometer reading around 45° by adjusting rheostat suitably & in on case the deflection should be outside range (30° - 60°).

Record the readings of the ammeter and the deflection of the compass needle shown by the two ends of the aluminum pointer on the scale. Now reverse the current through the coil of the tangent galvanometer by turning the reversing key & record the values of current & deflection of the compass needle as shown in above step. Change the current through the coil of the tangent galvanometer by shifting the position of rheostat in such a way that the deflection lies within (30° - 60°) range and record the readings as explained in above two steps. By changing the value of current through the coil, take fore more sets of observations keeping the deflection within 30° - 60° range. Measure the inner and outer diameters of the coil with a meter scale at least two times.

Range of the ammeter =

Least count of the ammeter =

Zero error of ammeter =

Number of turns used =

Radius (r) of the Tangent Galvanometer =

Value of Deflection (θ°)

S.No.

Mean Direct Current Reverse Current Deflection (θ°) θ1 θ2 θ3 θ4

tanθ

Ammeter Reading I (ampere)

Observed Corrected

Take two points A and B wide apart on the straight line graph. Draw perpendiculars from B on the x-axis and from A on y-axis intersecting each other at point C. Now, Slope of graph = BC / AC

= = tanθ / I =m = Now, substituting the value of m in the equation m = µ° 2πn / 4πr H Therefore,

H = µ° 2πn / 4πr m H= H=

The value of the horizontal component of Earth’s magnetic field is Make sure that the connections are neat and tight and the plugs are not loose. The battery or accumulator used should be freshly charged. The reversing key should be switched off when the readings are not being taken. The magnetic needle should swing freely in the horizontal plane. Leveling and other setting for this purpose should be done carefully. All the magnetic materials and current carrying wires should be carefully set in the magnetic meridian. This is the most essential requirement of this experiment. Both the ends of the pointer should be read for direct as well as reverse current and the mean of the four readings should be used. While noting down the deflection of the pointer ends, error due to parallax should be avoided and the compass box should be gently tapped before taking each reading. All values of deflection should be adjusted between 30° and 60° as the measurement of the instrument is maximum when the deflection is around 45°.