﻿ Description of apparatus - Determining the Earths magnetism description = Remote web role - Determination of the earths magnetism by tangent compass - Description of apparatus

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

### Apparatus

#### The physical principle of measurement Fig. 1 - tangent compass
zdroj: http://vnuf.cz/sbornik/prispevky/ soubory/04_21/image002.jpg

The classic method of measuring the horizontal component BH 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.

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 BC is given by the vector magnetic field BH and magnetic field B generated by coil (see Figure 2). Fig. 2 - composition the mag. vectors

Due to the field coil, the vector B is perpendicular to the horizontal component BH 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 BC (Fig. 2). After substituting the formula for B in the existing relationship:

 tg φ = B BH

(1)

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).

#### Control of the experiment

In practice we usually have in the collections of tangent direction finding, we can measure the BH 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 BH.

Substituting the expression for the magnetic induction Helmholtz coils:

B  =
 ( 4 ) 3/2 5
· μ0 ·   N·I

r

(2)

we get the final relation:

BH =
 ( 4 ) 3/2 5
· μ0 ·   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; μ0 [T.m/A] - permeability of vacuum (air); μ0 = 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 BH 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  = BH ·  [ r  ·
 ( 5 ) 3/2 4
]  · tg φ

μ0·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 BH 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.

#### Control of the experiment 1. Adjust the el. current - the electric current can be adjusted by moving the slider

2. Experimental values - the value of el. current is automatically loaded, angle compass needle is to be read from a webcam (Approximate value of the magnetic field is shown for primary school pupils, who does not specify Magn. Fields Helmholtz coils.)

3. Web camera - the camera shows the scale of the compass (magnetic latch is deflected by magn. field of Helmholtz coils)

4. Writing values to the table - measured values are entered into the table

5. Table of experimental values - the value of electric current and the angle of deflection of the compass needle (magnetic field, it is necessary to calculate the processing according to the current formula for Magn. fields Helmholtz coils)

6. Work with data in Table - see chart, save data, delete table