43545

1. 16. Small Fields
Construct a device based upon a
compass needle and use your device to
measure the Earth’s magnetic field.
17th International Young
Physicist’Tournament
POLAND
Stanisław Staszic
Secondary School in Warsaw

2. South magnetic pole
coordinates
81.0° N
110.0° W
North magnetic pole
coordinates
64.6° S
138.3° E
XIV LO coordinates
52.21° N
21° E
EARTH’S MAGNETIC FIELD
EARTH
Magnetic pole N
Geographic pole S
Geographic pole N
Magnetic pole S

3. EARTH’S MAGNETIC FIELD
Geographic North Pole
Magnetic South Pole
Geographic South Pole
Magnetic North Pole

4. EARTH’S MAGNETIC FIELD
q
Horizontal
component Hz
Vertical
component Hv
Earth’s magnetic
field’s lines
Inclination q

5. Tangent
galvanometer
Sine galvanometer
Lamont’s variation
method
Magnetic needle
oscillations
Gauss’s method
Rotary coil
MEASUREMENT METHODS
Tangent
galvanometer

6. TANGENT GALVANOMETER
Magnetic field with known
value (Hk)
Earth’s
magnetic field
(Hz)
a
tan
k
H A
z m
H a
  
 

7. A
POWER SUPPLY
EXPERIMENTAL SET-UP
A
AMMETER
HELMHOLTZ COILS

8. HELMHOLTZ COILS
2
3
2 2 2
2 ( )
n I r A
c m
r z
H  
 
  
 
n number of turns
I current
r radius of the coil
Hc magnetic field intensity
z distance from the coil
Magnetic field intensity
at distance z from one
coil on the coil’s axis:
r
z

9. HELMHOLTZ COILS
n number of turns
I current
r radius of the coil
Hc magnetic field intensity
generated by coils
Magnetic field from two coils
is nearly uniform in the
middle between those coils
r
r/2 r/2
8
5 5
nI A
c m
r
H   
 
The strength of such
magnetic field is
described by this formula:

10. 0.5
0.25
0
-0.25
-0.5
100
75
50
25
x
y
x
y
HELMHOLTZ COILS
Because of the superposition of the
I=50 mA n=240 r=0.1325 m
d – distance from the centre
of the device.
Hc – Magnetic field intensity.
Hc
d [m]
Nearly uniform
magnetic field.

11. MEASURING DEVICE

12. 1st experiment
a
a=20.0°
I=5.1 mA

13. a
a=43.0°
I=12.7 mA
2nd experiment

14. a
a=48.0°
I=15.4 mA
3rd experiment

15. 4th experiment
I=26 mA
a
a=62.0°

16. 5th experiment
I=54.6 mA
a
a=76.0°

17. MEASUREMENT RESULTS
I Hc a Hz
1. 5.1 mA 6.6 A/m 20.0° 18.2 A/m
2. 12.7 mA 16.5 A/m 43.0° 17.7 A/m
3. 15.4 mA 20.0 A/m 48.0° 18.0 A/m
4. 26.0 mA 33.7 A/m 62.0° 17.9 A/m
5. 54.6 mA 70.8 A/m 76.0° 17.7 A/m
tan
c
H A
z m
H a
  
 
a Magnetic needle deviation
angle
Hc Intensity of magnetic field
generated by the coils
Hz Horizontal component of
Earth’s magnetic field
I Current intensity

18. Intensity of magnetic field generated by Hemholtz
coils vs deviation angle
-10
10
30
50
70
90
-0,5 0.5 1.5 2.5 3.5 4.5
tana
Hc [A/m]
MEASUREMENT RESULTS

19. VERTICAL COMPONENT
magnetic
needle
Helmholtz’s
coils

20. VERTICAL COMPONENT
Earth’s magnetic
field’s lines
Coils’ magnetic
field
We add magnetic field with known value and opposite direction
to the vertical component of the Earth’s magnetic field

21. VERTICAL COMPONENT
Earth’s magnetic
field’s lines
Coils’ magnetic
field
If the vertical component and the coils’ magnetic field are
equal, the needle aligns with the horizon

22. VERTICAL COMPONENT-RESULTS
magnetic needle the needle
aligned with the horizon when
the current was 33 mA:
we calculated intensity of
magnetic field generated by
coils:
the magnetic field generated
by coils and vertical
component are equal, so:
mA
I 33

 
m
A
z
H 2
.
0
7
.
42 

 
m
A
c
H 2
.
0
7
.
42 


23. CONCLUSIONS
Our device based on Helmholtz coils gave us precise
experimental data.
Inaccuracy in our measurements approaches maximally ca.
3,4 %, hence the results are quite good.
Our final results:
Horizontal component:
Vertical component:
Inclination:
Total Earth’s magnetic field’s intensity:
 
m
A
z
H 3
.
0
0
.
18 

 
m
A
v
H 2
.
0
7
.
42 


 2
.
67
q
 
m
A
H 4
.
0
3
.
46 


24. LITERATURE
B. Jaworski, A. Dietław, L. Miłkowska Phisics course t. II
W. Gorzkowski, A. Kotlicki Physic olympiad
F. Kohlrausch Laboratory physics
A Zawadzki, H. Hofmokl Laboratorium fizyczne
Paul G. Hewitt Fizyka wokół nas
Jan Gaj Laboratorium fizyczne w domu
E. M. Purcell Elektryczność i magnetyzm
http://www.pilot.pl
We used programs:
Scientific WorkPlace
The Gimp 1.2

25. THE END
17th Young Physicists’
Tournament 2004
Stanisław Staszic
Secondary School
Warsaw, Poland

27. DISCUSSION

28. MAGNETIC NEEDLE’S OSCILLATIONS

29. I- Moment of inertia of the needle
m- Magnetic dipole moment
m0- Vacuum magnetic permeability
T- Needle’s oscillations period
Hz- Horizontal component of Earth’s
magnetic field
 
s
T z
mH
I
0
2 m


 
m
A
Tm
I
z
H 0
2
m


 
2
12
2
m
kg
I Md


18,5 A
z m
H   
 
MAGNETIC NEEDLE’S OSCILLATIONS
From these:
we get:
and finally:

30. Magnetic needle oscillations
18,5 A
z m
H   
 
0,6
m 
7
0 4 10 H
m
m  
 
7 2
9,3 10
I kg m

 
  
 

31. Intensity of Earth’s magnetic field
cos
z
H
H q

52,0 A
m
H   
 
Hz Horizontal component of
Earth’s magnetic field
q inclination

32. Induction
0
z z
B H
mm


33. Innacuracy of the results
Innacurancy of amperometer
Metal elements in a stand for the needle
Neglecting movement resistances of the
magnetic needle
Simplification of the magnetic needle shapes

34. 3 3
2 2
2 2 2 2 2
1 1 1
0
2 2 2
{[ ( ) ] [ ( ) ] }
B Ib b x b b x b
m  
     

35. ERROR ANALYSIS
2
1 2
1
x
x
y x
f
x
f




 



For our analysis it comes to the function:
H H
I
H I a a
 
 
    
Where:
( , ) ctg
z
H I tI
a a
  2
3/2
2
2
2
nr
t
r
r

 
 

 
 
 
 
 
The formula for the measurement error:
and

36. ERROR ANALYSIS
Hence:
2
tg sin
z
I I
H t a
a a
 

   
 
 
1296,08
t 
We calculate t as:
Digital amperometer  
0,1
MAX
I mA
 
Computer angle measurements 0,5
MAX
a
  

37. ERROR CALCULATIONS
Angle
a
Current
I
Hz Error |Hz|
1 20,0° 5,1 mA 18,2 A/m 0,1 A/m
2 43,0° 12,7 mA 17,7 A/m 0,2 A/m
3 48,0° 15,4 mA 18,0 A/m 0,2 A/m
4 62,0° 26,0 mA 17,9 A/m 0,3 A/m
5 76,0° 54,6 mA 17,7 A/m 0,6 A/m

39. INCLINATION - MEASUREMENTS
67,0°
67,5° 67,0°
We have expected the inclination to be from 60 to
70 degrees. Our experiment confirmed that.

40. INCLINATOR
magnetic needle freely moving
round horizontal axis.
Fishing string
Two stands
S N
.
This is how our
inclinator looks like.

41. INCLINATION - MEASUREMENT
67,0°
67,5° 67,0°
We have expected the inclination to be from 60 to
70 degrees. Our experiment confirmed that.