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

### Task and process of measurement

1. Measure the dependence of the compass deviation angle in the Earth's magnetic field on the size of passing an electric current through the Helmholtz coils (or dependence on the magnetic field generated by the Helmholtz coils). Plot the dependence obtained in the graph.

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

3. Recalculate the dependence obtained in point 1 to the dependence of the tangent of compass deviation angle (tanφ) on the drive current of the Helmholtz coils. Determine the horizontal component of the Earth's magnetic field BH from this dependence.

#### The measurement procedure

1. Run the remote experiment NICoL.

2. Use the controls gradually set various values of the drive electrical current to the Helmholtz coils.

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

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

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

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

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

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

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

B =
 ( 4 ) 3/2 5
· μ0·   N.I

r
 where: N - number of turns of 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 current I μ0 [T.m/A] - permeability of vacuum (air); μ0 = 4π·10–7 T.m/A
1. According to the previously mentioned 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 inductionBH thus obtained, we determine the resulting average 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 compass 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 displayed regression coefficients, we not only verify this fact, but above all we obtain the sought regression coefficients a (resp. 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 ) 3/2 5
·   μ0 · N  ]  ·
 1 BH

r

it is enough to quantify the value of the expression in parentheses 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 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 Helmholtz coils. This value is calculated from size of the electrical current (according to the formula above). However, this value is not saved in the table. 2) The relationship between tanφ and el. current I is a direct correlation. 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 needle), which is measured in dependence apparent shift of the curve so that the line passes through the axes intersection. A more accurate determination of the slope we obtain of the general form of the regression line.