#### Terrestrial Magnetism, Physics tutorial

Terrestrial Magnetism

Introduction:

A magnetic needle, if hanged freely in such a way that it can turn in a horizontal and a vertical plane, turns till it comes to rest in one definite direction. This proposes that the Earth should have a few of the properties of a magnet. The Earth's magnet consists of a magnetic field that acts on the suspended magnets. As compared by the field of a bar magnet the Earth's field is extremely weak. The magnetic needle turns only when it is hanged on a thread; the Earth's field is not strong adequate to make the magnet rotate if it is lying on the table, for the magnetic force is not adequate to overcome the friction.

The direction and magnitude of the Earth's field differs with position over the surface of Earth and it as well seems to be changing steadily with time. The prototype of field lines is identical to that which would be given when there was a strong bar magnet at the centre of Earth.

At present there is no commonly accepted theory of the Earth's magnetism however is might be caused through electric currents circulating in its core due to convection currents occurring from the radioactive heating within the earth.

Magnetic Field of the Earth:

The pattern of the magnetic field of earth's lines is identical to that which would be given when there was a strong bar magnet at the centre of the earth.

The points of Earth at which the magnetic field intensity is directed vertically are termed as magnetic poles. The Earth consists of two such poles; the north magnetic pole (that is, in the southern hemisphere) and the south magnetic pole (that is, in the northern hemisphere).

The straight line passing via the magnetic poles is termed as the Earth's magnetic axis. The circumference of the great circle in the plane perpendicular to the magnetic axis is termed as the magnetic equator. The magnetic field intensity at point on the magnetic equator is directly horizontally.

Definitions of some Relevant Terms:

The geographic meridian is the vertical plane in the direction, geographic N and S, that is, which passes via the geographic poles of the Earth.

The magnetic meridian is the vertical plane in which the magnet sets itself at a specific place.

The angle of variation or declination of the compass is the angle between the magnetic and geographic meridians.

The angle of dip or inclination is the angle between the horizontal and magnetic axis of the magnet free to swing in the magnetic meridian around a horizontal axis. This is the angle between the directions of the magnetic field of the earth and the horizontal.

The earth's magnetic field often termed as the net intensity, is resolved for expediency into a horizontal component and a vertical component.

The quantities, declination, dip, total intensity, horizontal component and vertical component are termed as the magnetic elements. The magnetic field of earth at a specific place might be specified through the declination and any two of the magnetic elements.

This is suitable to resolve the strength of earth's field into horizontal and vertical components, correspondingly. We then have:

BH = BR cos α

Bv = BR sin α

As well, tan α = Bv/BH

Here, 'α' is the angle of dip and 'θ' is the variation or declination.

Note: Instruments like compass needles whose motion is imprisoned to a horizontal plane are influenced by BH only.

Determination of Declination:

The determination of the declination at a place comprises determining two direction, geographic N and magnetic North.

The former can be set up precisely only through an astronomical process - observation of the sun and star. This can be found by means of fair accuracy from the fact that the shadow of a vertical slide cast through the sun at mid-day is due to N.

Magnetic North is determined by hanging a bar magnet freely on the vertical axis. As the magnetic axis of the magnet might not coincide by its geometric axis, the magnet should be turned over and the mean of the two directions found.

The vertical and horizontals components of the earth's magnetic flux density can be measured through the earth inductor. The instrument comprises of a coil of wire that can be rotated around an axis capable of being set in any direction through turning a movable frame. The principle of the instrument is that the coil is turned via a right angle between positions if it is threaded through maximum magnetic flux and zero magnetic flux and the quantity of electricity, induced is evaluated through a ballistic galvanometer joined in series by the coil.

The quality of electricity induced is represented by:

Q = - N Φ/R

Here, 'N' is the number of turns in the coil; Φ is the change in the magnetic flux threading it and 'R' is the net resistance of the coil and ballistic galvanometer circuit.

Assume that the coil is perpendicular to the field of magnetic flux density 'B' and is then turned via a right angle in such a way that no magnetic flux threads it.

Then, Φ = BA

Here, A is the area of the coil.

∴ B = - QR/NA

To find out the horizontal component of the earth's magnetic flux density, the frame is made up of vertical and the whole instrument set magnetic E and W. In this place, the coil is perpendicular to the magnetic field of earth and the maximum horizontal magnetic flux threads it. The coil is turned via 90o (about its vertical axis in such a way that its plane then lies in the magnetic meridian and none of the earth's magneic flux threads it.

To find out the vertical component of the magnetic field frame of the earth is turned in such a way that the coil can move around a horizontal axis in the magnetic meridian. If the coil is rotate via 90o, say from the vertical to a horizontal position, the quantity of electricity induced is proportional to the vertical component.

Determination of Dip:

The angle of dip 'D' can be computed from the values of horizontal and vertical components employing

tan α = Bv/BH

Tan D = Vertical component/horizontal component = θvh

Here θv and θh are the throws of the ballistic galvanometer in the earth's inductor experiment.

The Deflection Magnetometer:

The two magnetic fields can be compared by means of the deflection magnetometer that comprises of a small magnet, pivoted on the vertical axis and carrying a light pointer that can move over a circular scale.

Generally one of the fields is the earth's horizontal component and the other field is arranged to be at right angles to this. The pivoted magnet sets itself all along the resultant of the two fields at an angle θ to its direction if it is merely in the earth's field. If BH is the magnetic flux density of the earths horizontal component and B is the magnetic flux density of the other field then,

B = BH tanθ

The horizontal component of the earth's magnetic flux density can be computed by using a deflection magnetometer.

The magnetic flux density at the centre of the circular coil of acknowledged radius and identified number of turns, if a measured current is passing via the coil can be computed. This can be compared through means of a deflection magnetometer, having the horizontal component of the earth's magnetic flux density, letting the latter to be determined.

A suitable instrument for the aim is a tangent galvometer that comprises of a circular coil, at the centre of which there is a deflection magnetometer. If 'N' is the number of turns in the coil, 'a' its radius, 'I' the current and 'B' the magnetic flux density at the centre of the coil, then

B = μo NI/2a

Using the similar nomenclature as above

B = BH tanθ

BH = μo NI/2a tan θ

Variation of Dip over the Earth's Surface:

The angle of dip is 0o just about at the geomagnetic equator. It rises steadily northward or southward, till it becomes 90° at the magnetic pole. In the northern hemisphere, the 'N' pole dips, and in the southern hemisphere, the S pole dips.

Changes in the values of the Magnetic Elements:

The magnetic field of earth at any place is not constant however is subject to changes which might be categorized as follows:

1) Secular Change:

The magnetic elements experience a gradual cycle of changes that extent over a long interval after which they return to their original values. Such changes are relatively large and occur steadily.

2) Annual Change:

These changes are periodic and the value of an element differs steadily between a maximum value when the declination at a place attains a maximum value in February and a minimum value in the course of a year. As an illustration and the minimum in August every year, then it is the annual change.

3) Daily Change:

The periodic change extending over 24-hours in the value of an element is as well noticed.  An element arrives at the maximum value at some hour of the day and the minimum value at some other hour, features of the element.

4) Magnetic Storm:

This has been found that throughout volcanic eruptions, display of Aurora Borealis, appearance of sunspots, and so on, sudden and violent changes take place in the indications of recording instruments computing the magnetic elements. Such changes are stated to be due to magnetic storms. They are not periodic.

Magnetic Maps:

The values of the magnetic elements at diverse places are not generally similar and magnetic maps have been drawn by joining such places on the geographical maps in which a magnetic element has equivalent values. In magnetic maps, we have the given lines.

1) Isogonic and Agonic Line:

Isogonic lines are lines connecting places on the map of the earth where the declination is similar. Agonic lines are such which pass via places having zero declination.

2) Isoclinic and Aclinic Lines:

Isoclinic lines are the lines connecting places on the map of the earth where the magnetic dip is similar. A line passing via places having no dip is termed as Aclinic line.

3) Isodynamic Lines:

Such lines join up places on the map of the earth where the value of horizontal intensity is similar.

The belt round the earth's surface passing via places of no dip is the magnetic equator. The part of the earth's surface comprised between the magnetic pole and the magnetic equator has been divided into 90 equivalent parts. Via each such point of division a circle has been drawn round the surface of earth parallel to the great circle of the magnetic equator. These circles are termed as the geomagnetic latitudes.

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