Engineering Physics Lab

PH-103 Experiment - 01

AIM: To study the magnetic field of a circular coil carrying current

APPARATUS REQUIRED: A Stewart and Gee type tangent galvanometer, a strong battery, a
rheostat, an ammeter, plug key, a commutator and connecting wires.

THEORY: The intensity of magnetic field at a point lying on the axis of a circular coil is given by
µ 0 2nr 2 i
B=
4π ( x 2 + r 2 ) 3 / 2

Where n = number of turns in the coil

r = radius of the coil
i = current in ampere flowing in the coil
x = distance of the point from the center of the coil
If the magnetic field B is made perpendicular to the horizontal component of earth’s magnetic field (H)
then
B=H tan θ
i.e. B × ∝ tan θ
Hence a graph between tan θ and x will be similar to the graph between B and x .

DESCRIPTION OF APPARATUS:
The apparatus used to study the variation in magnetic field with distance along the axis of a circular
coil is called Stewart and Gee’s tangent galvanometer shown in fig. It consists of a circular coil of
many thin insulated copper wires wound on a wooden or brass frame. It is fixed on a wooden bench
AB with its plane vertical to the bench. The free ends of the wire are connected to two terminals T1
and T2 fitted on the base. A deflection magnetometer compass box is placed inside the coil such that
it can slide on the pillars the bench in such a way that the center of the needle always lies on the axis of
tube coil. The distance of the needle from the center of the coil can be read on graduated scale on the
arms of the magnetometer.
PROCEDURE:

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(1) Place the magnetometer compass box on the sliding bench so that its magnetic needle is at
the center of the coil. By rotating the whole apparatus in the horizontal plane, set the coil in
magnetic meridian and the arms of the magnetometer lie roughly east and west roughly.
Keeping the eye a little above the coil set the coil, the needle and its image in the same
vertical plane by rotating the instrument in horizontal plane, rotate the compass box till the
pointer ends read 0-0 on the circular scale.
(2) In order to set the coil exactly in the magnetic meridian (setup the electrical) connect (ions)
the galvanometer to a battery through a rheostat, an ammeter, plug key and a commutator as
shown in fig.
(3) Send the current in one direction with the help of commutator and adjust its value such that
a deflection of nearly 70  - 75  is produced in compass needle. If the deflections are
equal then the coil is in magnetic meridian otherwise turn the apparatus a little, adjust the
pointer ends 0-0 till the deflections in both the directions become equal.
(4) Now pass the current in the coil and Slide the magnetometer along the axis of the coil. Find
out the position where the deflection of the pointer becomes maximum. Note the readings
of both the ends of the pointer. Take the mean of four readings this will give the mean
deflection at x = 0 .
(5) Now shift the compass needle in steps oft 2cm, along the axis of the coil. For each position
note down the mean deflection. Continue this process till the compass box reaches the end
of the bench.
(6) Repeat the measurements exactly the same manner on the other side of the coil ( x ) taking
along X − axis and tangent of mean deflection taking along Y −axis.

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 Engineering Physics Lab
PH-103 Experiment - 01

OBSERVATIONS:
Mean θ = tan θ Mean θ = tan θ
Distance moved (cm)(x)
S.No. Deflection on east Deflection on east
arm θ1 + θ 2 + θ 3 + θ 4 arm θ1 + θ 2 + θ 3 + θ 4
Current Current 4 Current Current 4
in one in rev. (in deg.) in one in rev. (in deg.)
direction direction direction direction
θ1 θ2 θ3 θ1 θ1 θ2 θ3 θ4

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

GRAPH: The variation of intensity of magnetic field with distance along the axis of a circular coil is
shown in the fig.

RESULT:
The graph shows the variation of magnetic field with distance along the axis of a circular coil.

PRECAUTIONS:
1. The coil should be carefully adjusted vertically and in magnetic meridian.
2. The magnetic materials and current carrying conductors should be kept at a considerable
distance from the
3. The value of current in soil should be adjusted so as to produce deflection of nearly 70  - 75 
4. The eye should be kept vertically above the pointer while taking to avoid any error due to
parallax.

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Reviewed By:- Approved By:-
Date:- Date:-

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 Engineering Physics Lab
PH-103 Experiment - 02

OBJECT:- To study the laser beam characteristics like; wave length, aperture & divergence etc.

APPARATUS: A laser, a kinfe-edge mounted on a micropositioner, a photodetector of a large linear

range, a lens of sufficiently large aperture and an optical bench.

1. Power distribution within the beam

THEORY
The method involves the power measurement by using a knife-edge, which is inserted slowly in the
beam. Let us assume that the laser is oscillating in TEM 00 (Transverse Electro Magnetic) mode so that
the spatial distribution of the beam is gaussian. Let P0 be the total power in the beam spot of size
2w0 . Then the irradiance distribution I ( x, y ) as a function of the Cartesian coordinates ( x, y )

measured from the beam centre perpendicular to the direction of propagation is given by

2 P0  2( x 2 + y 2 ) 
I ( x, y ) = exp −  … (1.1)
πw0
2 2
 w0 
The power P transmitted past a knife-edge blocking off all points for which x ≤ a is, therefore,
given by
∞∞
P0 a 2 
P= ∫∫ I ( x, y )dxdy
−∞a
=
2
erfc 
 w 
 0 
 … (1.2)

where a is the depth of knife-edge in the beam.

Thus the integrated power past a knife-edge inserted in a gaussian beam is given by the complementary
error function. For other spatial distribution, an integrated power curve can be obtained from which the
power distribution in the beam can be realized.

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BLOCK DIAGRAM:

PROCEDURE:
The schematic of the experimental setup for measuring power distribution within the beam is
shown in Fig. 1. The knife-edge is mounted normal to the beam at any desired plane. A lens of
sufficiently large aperture is placed close to the knife-edge to gather all the diffracted light and focus
the beam on the photo-detector. An interference filter can be mounted in front of the detector.
The knife-edge is manually inserted in the beam and corresponding output of the detector is
noted. As the spot size is very small, the movement of knife-edge has to be precise. This can be
possible if the knife-edge is mounted on a micro positioner. Alternatively a diverging lens can be used
to increase the beam size. Then output of the detector is recorded by changing the position of the knife-
edge. The measurements are done when the knife-edge is either inserted or being withdrawn.

TABLE:
Sr. No. Position of knife-edge Power meter reading (mw)
Brightness to Darkness Darkness to Brightness
1
2
3

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 Engineering Physics Lab
PH-103 Experiment - 02
GRAPH:
The output of the detector (powermeter reading) is plotted as a function of the position of the
knife-edge. This gives one-dimensional power distribution curve, which represents a complementary
error function.

2. Spot size of the beam

THEORY
Considering the irradiance distribution represented by Eqn. (1.1): w0 is the radius at which
irradiance falls to e −2 times its central value. Therefore the spot size is taken as 2w0 .
A gaussian beam remains gaussian as it propagates in vaccum or in a homogeneous medium.
The output of a laser oscillating in TEM00 mode is gaussian, and the spot size 2w0 refers to the planer
wavefront. At any other plane the wave front will be either converging or diverging and will have spot
size larger than 2w0 . Thus it is meaningful to measure to spot size for a gaussian beam only. Eqn.
(1.1) can be rewritten in the form of a well known gaussian distribution by setting w0 = 2 w1 , as

I ( x, y ) 1  (x2 + y2 ) 
= exp−  … (1.3
2πw1
2 2
P0  2w1 

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 where w1 is the standard deviation.
Similarly, Eqn. (1.2) can be rewritten as
P 1  a 
= erfc   … (1.4)
P0 2  2w 
 1 

The normalised gaussian distribution and the complementary error functions are illustrated in Fig. 3(a)
and (b) respectively.

It is easy to show that the points for

25% and 75% relative powers are located at
distances equal to the proable error
e p = 0.6745 w1 ) on either side of the
maximum of the gaussian distribution.
Therefore w1 can be determined from the
experimentally obtained relative power Vs
knife-edge position curve and the beam spot
size 2w0 ( = 4 w1 ) can be easily
calculated.

PROCEDURE:
The set up and the procedure for
measurement is same as the previous
section. In one such experiment draw the
graph between knife-edge position and the
power meter reading as shown in Fig. 4.

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