﻿ Determination of the horizontal component of Earth's mag. field
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Determination of the Earth's magnetic field

1. Measure the dependence of the compass declination angle in the Earth's magnetic field on the magnitude of the current flowing through the Helmholtz coils (or the dependence on the magnetic field generated by the Helmholtz coils). Plot the obtained dependence on the graph.

2. Determine the approximate (indicative) value of the Earth's magnetism from electric current (magnetism of Helmholtz coils) at which the compass needle has a deviation of 45°.

3. Recalculate the dependence obtained in point 1 on the dependence of the tangent of the compass deviation angle (tanφ) on the driving current of the Helmholtz coils. From this dependence, determine the horizontal component of the Earth's magnetic field, BH.

The measurement procedure

1. Start the NICoL remote experiment.

2. Use the controls to gradually set different values of the driving electric current to the Helmholtz coils.

3. For different values of the electric current, the deflection of the compass needle can be read and the measured values written in the table.1)

4. Adjust the amount of electric current so that the deviation compass needle was 45°. The current value and angle are recorded in the table.

5. After measuring the required number of data, the experimental value is saved to disk on your PC and the remote task is finished.

6. Open the resulting file in a spreadsheet program (MS Excel, Oo Calc, Kingsoft Spreadsheets…).

7. Construct (in a spreadsheet) a graph of the dependence of the compass deviation angle on the electric current of Helmholtz coils.

8. The shape of the dependence should be similar to the arctangent arctan().

9. Recalculate the values of the electric current to the value of the magnetic induction generated by the Helmholtz coils, according to the previously mentioned formula (2):

$B = ( 4 5 ) 3 2 · μ 0 · N · I r$
 where: N – number of turns in each coil; N = 240 r [m] – radius of the coils; r = 15 cm I [A] – electric current in the coils φ [°] – deviation of the magnetic needle corresponding to the current I μ0 [T·m/A] – permeability of vacuum (air); μ0 = 4π ·10–7 T.m/A
1. According to the above formula (1), we know that the value of the magnetic induction of the horizontal component of the earth's magnetism BH is determined by the ratio of the value of the magnetic induction B of Helmholtz coils and the tangent function of the compass needle angle (tanφ). From the partial values of magnetic induction BH obtained in this way, we determine the resulting mean value and its deviation.

2. Another way to obtain the required value of the magnetic induction of the horizontal component of the earth's magnetism BH is to use linear regression in a spreadsheet. The dependence of the values of the tangent of the angle of the compass needle (tanφ) on the excitation current of the Helmholtz coils shows a linear dependence (y = a·x + b). If we interpolate the graph of this dependence by linear regression with the regression coefficients shown, we not only verify this fact, but also obtain the desired regression coefficients a (or b).2)

3. The value of the linear coefficient a in the regression equation is closely related to the sought value of the magnetic induction of the horizontal component of the Earth's magnetism BH.

4. If we realize that (see chapter Apparatus → Measurement – applicable relations):

$a = ( 4 5 ) 3 2 · μ 0 · N r · 1 B H$

it is sufficient to quantify the value of the expression in brackets and then divide it by the value of the linear coefficient a just obtained.

1. We can We compare the determined value of BH with the value of the magnetic field at which the magnetic needle was deflected by 45°. Both values (within the tolerance) should coincide with the value of the magnetic induction corresponding to the Czech Republic.

 1) The control panel also displays the values of the magnetic induction field of the Helmholtz coils. This value is calculated from the magnitude of the electric current (according to the formula above). However, this value is not stored in the table. 2) The relationship between tan φ and electric current I is a direct one. So it seems that it would be useful to look for dependence of the linear regression of the form y = a·x. When measured, however, may exhibit small systematic error (caused by friction during rotation of the needle), which is measured in dependence apparent shift of the curve so that the line passes through the intersection of the axes. A more accurate determination of the slope is obtained from the general form of the regression line.