Determination of the horizontal component of mag. field of the Earth
The physical principle of measurement
The classic method of measuring the horizontal component B_{H} earth's magnetic field is tangent compass method. It is a device (Fig. 1), which consists of a circular coil with a larger average diameter and containing a small number of coils arranged in a narrow beam. In the center of the coil is a small magnet, which rotates around a vertical axis. 
Fig. 1  tangent compass zdroj: http://vnuf.cz/sbornik/prispevky/ soubory/04_21/image002.jpg

Fig. 2  composition the mag. vectors

Before measuring coil stand so that its plane agreed with the plane of the magnetic meridian, and thus the magnetic direction. Starts to flow through the coil current I arises at magnetic magnetic field whose magnetic flux B_{C} is given by the vector magnetic field B_{H} and magnetic field B generated by coil (see Figure 2). 
Due to the field coil, the vector B is perpendicular to the horizontal component B_{H} earth's magnetic field, the magnet is deflected from its original position by an angle φ and take a new equilibrium corresponding to the direction of the resultant magnetic field induction B_{C} (Fig. 2). After substituting the formula for B in the existing relationship: 
we obtain the final expression for the Earth's magnetism depending on the power coil current (ammeter can be measured) and the deflection of a compass (compass can be read on).
Measuring apparatus
In practice we usually have in the collections of tangent direction finding, we can measure the B_{H} improvise. To improvise you can use a simple solenoid of copper wire wound for packaging plastic bottles, cardboard fasten to the tourist compass (see right picture). For the relationship between electric current and magnetic induction coil then we substitute the classical expression for the solenoid.



In our laboratory we are not prepared for this experiment a bit more sophisticated design. We contacted several experiences with this experiment and we have proposed the following report. The principle is still the same attempt, but instead of simple circular coil, we used a special pair of coils which because of its configuration, the so called Helmholtz coils^{*)}. Using the Helmholtz coils, we not only have better access to the compass and thus its readability, but also more homogeneous magnetic field coils. Finally, we wanted to make high school students met with these coils, which are often used in practice and yet the hours when they speak of physics too. The expansion will follow the relationship for the magnetic field in the center of Helmholtz coils.

^{*) } 
Helmholtz coil pair consists of two identical circular magnetic coils that are placed symmetrically on each side of the experimental area along a common axis and are separated by a distance equal to their radius. The current two coils is the same and consistent direction. The resulting field between the coils is almost homogeneous. 
Measurement  applicable relations
Building on the aforementioned equation (1), where B is the magnetic induction coil, which deflects the compass needle by an angle φ from the direction of the local magnetic meridian ie the direction of the horizontal component of Earth's magnetic field B_{H}.
Substituting the expression for the magnetic induction Helmholtz coils:
we get the final relation:
^{ }B_{H} = 

μ_{0} 
N.I 
· 
1 



r 
tg φ 
that: 
N 

 number of turns of each coil; N = 240 
r 
[m] 
 radius of the coils (also distance between coils); r = 15 cm 
I 
[A] 
 electric current in the coils 
φ 
[°] 
 deviation of magnetic needle corresponding to the current I; 
μ_{0} 
[T.m/A] 
 permeability of vacuum (air); μ_{0} = 4π.10^{7} T.m/A 
Just a few measured values of the excitation coils of electric current I and the deviations φ. Searched value of the horizontal component of magnetic induction B_{H} Earth can then be determined as the arithmetic mean of partial results.
Processing using a spreadsheet:
When we realize that the obtained relationship can be modified into:
^{ }I = B_{H} · 
[ 
r^{ } 
· 

] 
^{ }· tg φ_{ } 

μ_{0}.N 

——— konst. ——— 
showing that the relationship between current I and the functions tg φ is linear (even direct proportion!). If we have enough measurements for different angles of deflection of the magnetic needle and the corresponding electric current coils, the value of current I and tg φ function to insert the chart. A look at the shape of the graph convince us, if our account of the interdependence true. If it was not a linear dependence means that measurements can be hampered by some bias  such as poorly in the rotating compass needle, etc.
Using a spreadsheet (MS Excel, OO Calc, etc.) can be obtained by linear regression of the value obtained by direct correlation. This value is the product of B_{H} and the constant term in parentheses. After dividing the numerical value of the constant expression of the brackets we get the required value the horizontal component of magnetic induction of the Earth.
