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

## 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 in a magnetic field BH generated by the Helmholtz coils. Specify the horizontal component of Earth's magnetic field as a guideline values obtained by linear regression of dependence.

#### The measurement procedure

1. Run the remote experiment NICoL.

2. Use the controls (see below) gradually set various temperature 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 a graph (in a spreadsheet) of the compass deviation angle of the electrical current coil.

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. Plot the dependence of the tangent the angle of deviation compass needle (tanφ) to just obtained values of magnetic induction B Helmholtz coils to new graph. The resulting dependence should be in the form of linear function (direct correlation).

2. Interlace dependence in a spreadsheet by using linear regression (y = a.x + b) with displayed regression coefficients.2)

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

4. If we realize that (see Sec. Measurement - applicable relations):

a  BH ·  [ r  ·
 ( 5 ) 3/2 4
]

μ0·N

sufficient to quantify the value of the expression in parentheses, and then divide the value just obtained a linear coefficient a of this value.

1. Comparing the obtained value with the value of the magnetic field BH at which a deviation magnetic needle is 45°. Both values (within tolerance) should coincide with the corresponding to values of magnetic induction in 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), therefore it is not stored 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.