TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS
8. HORIZONTAL COMPONENT OF THE EARTH'S MAGNETIC FIELD
1. Objective
Determining the horizontal component of magnetic induction of the magnetic field of Earth.
2. Equipment needed
Tangent galvanometer, ammeter, electric switch, adjustable DC power supply.
3. Theory
Shape of Earth's magnetic field is approximately alike magnetized ball's field. Earth's
magnetic poles drift slowly. Presently they are close to geographic poles (see figure 8.1).
According to Canada's geologic survey has Earth's magnetic South Pole drifted with a mean
speed of about 11 km/year in past century. It should be noted that since 1970 the speed has
increased up to 40 km/year. 100 years ago magnetic South Pole was located about 1900 km
from geographical North Pole. In 2005 the distance was decreased to 800 km (angular
distance about 7,30). Value of induction of Earth's magnetic field changes slowly in time as
well. It has decreased about ≈10 % in past one hundred and fifty years.
North
South
Figure 8.1
On the magnetic equator magnetic induction of Earth's magnetic field is directed horizontally
and vertically on magnetic poles. In other places of our planet vector of magnetic induction is
tilted with respect to the vertical direction i.e. it has both horizontal and vertical components.
Direction of horizontal component of induction of Earth's magnetic field is also called the
direction of a magnetic meridian. Angle of inclination (angle β in figure 1) is the angle
between direction of horizontal component of Earth's magnetic induction and horizontal
plane. Angle between geographic and magnetic meridians in the same place is called angle of
declination.
Magnetic needle that is able to rotate around its vertical axis only, turns in horizontal plane
due to the horizontal component B H of Earth's magnetic field. This property of magnetic
needle (compass needle) is exploited in a tangent galvanometer for measuring horizontal
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TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS
component of Earth's magnetic field.
Note that in the whole work the horizontal component of induction of Earth's magnetic field is
referred to as the horizontal component of Earth's magnetic field.
Tangent galvanometer used in present work consists of an inductor with 4 turns of wire with a
compass placed on inductors horizontal axis. Figure 2 shows the device's horizontal crosssection.
If inductor is not energized, magnetic needle of the compass is oriented in direction of Earth's
magnetic meridian. If direct current (DC as opposite to alternating current i.e. AC) is
connected to inductor, its magnetic field also affects needle and latter is oriented in direction
of summary magnetic induction.
Mathematically it is much simpler to add vectors of magnetic induction with different
directions in case they are perpendicular to each other. Since direction of vector of inductors
magnetic induction (in inductors centre) is parallel to inductors axis, it is recommended to
orientate inductors axis perpendicular to Earth's magnetic meridian (see figure 8.2).
Inductor with 4 turns
Inductor axis
Figure 8.2
It could be demonstrated that (see figure 8.2):
BH =
BP
.
tan α
(1)
Formula of circularly flowing current can be used to calculate magnetic induction in inductors
centre if multiplied to number of turns N:
BP = µ 0⋅
I
⋅N ,
2r
(2)
where µ 0 = 4π ⋅ 10 −7 H/m, I is current in inductor and r – radius of inductors one turn. Using
formulas (1) and (2) one can write final formula for calculating the horizontal component of
induction of Earth's magnetic field:
BH =
µ 0⋅ I ⋅ N
.
2r ⋅ tan α
(3)
One only needs to measure magnetic needle’s angle α at given value of current through
inductor to calculate the seeked horizontal component. Values r (radius of inductors one
turn) and N (number of turns) are given.
Electrically present work consists of an adjustable DC supply with output voltage U (see
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TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS
figure 8.3), ammeter A for measuring current through inductor; resistor R and switch K.
Figure 8.3
4. Experimental procedure
1. Record the data of measuring devices and inductor.
2. Connect devices according to figure 3. Note that DC supply used in present work has an
3.
4.
5.
6.
7.
ammeter A built in – you do not need a separate instrument.
Orientate inductors axis perpendicular to magnetic needle.
Ask instructor to check connections and give an exact task.
Switch on the power supply and adjust current to starting value given by instructor.
Read and record the angle α 1 after compass needle has stabilized.
Reverse current through inductor with switch K, check that value of current through
inductor remains the same (if not, adjust supply's output voltage) and record the angle α 1
after compass needle has stabilized again. Record all data to table 1.
Table 1
Determining horizontal component of Earth's magnetic induction
r =...
Exp.
no.
I, A
α
1
α
N =...
α
2
tan α
B H ,i ,T
1.
...
10.
B H =...
8. Measure angles α 1 and α 2 at 7…10 different given currents and present your results to
instructor for final check.
9. Calculate mean of angles α
positive:
1
and α
2
for every current value assuming both angles being
α =
α 1+ α
2
2
.
10. Assuming α = α , and using formula (3), calculate horizontal component of Earth's
magnetic induction
BH ,i for each experiment (index i means number of experiment).
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TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS
Calculate arithmetic mean value B H and its A-type modifier uncertainty on level 0, 95.
(
11. Find the advanced combined uncertainty U c B H ,i
)
of
B H ,i for pre-determined by
instructor experiments (number i), taking in account ammeters biggest possible
uncertainty (limit of uncertainty), uncertainty induced by rounding readings of compasses
angle scale and uncertainty of inductors turns radius.
12. Calculate value of horizontal component of Earth's magnetic field at place of
measurement from found magnetic induction value. Compare results to approximate
measured values in Estonia given in literature („Füüsika ülesanded II”).
5. Questions and tasks
1. Define magnetic induction.
2. Define the unit of magnetic induction on an example of electrical current flowing through
3.
4.
5.
6.
7.
8.
9.
10.
11.
a frame.
What are relations of values H and B?
How is the direction of Earth's magnetic induction determined?
Define magnetic meridian and its direction.
Define angles of declination and inclination.
Why is the angle of magnetic needle in present work calculated as mean value of two
opposite angles?
How can one use tangent galvanometer for measuring value of electrical current?
Can we replace the DC supply in present work with an AC supply?
Find formula for calculating magnetic induction on the axis of circularly flowing current.
What is the direction of induction in that case?
What is the difference between magnetic and electrostatic fields?
6. Literature
1. Halliday, D., Resnick, R., Walker, J. Fundamentals of Physics.–6th ed. New York, John
Wiley & Sons, Inc., 2001, §§ 29-2, 30-1, 32-3.
2. Eichler, H. J., Kronfeldt, H.-D., Sahm, J. Das Neue Physikalische Grundpraktikum.–
2. Auflage. Berlin, Springer, 2006, § 27.
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