## Terresterial Magnetism

Subject: Physics

#### Overview

The quantities needed to specify the earth’s magnetic field at a place completely are called the elements of terrestrial magnetism. This note provides us an information on terrestrial magnetism.
##### Terresterial Magnetism

In 1600 A. D. Sir William Gilbert discovered that a freely suspended bar magnet aligns itself along geographical north-south direction. The earth behaves as if there were pole and magnetic a huge magnetic dipole embedded in it with magnetic N-pole near the geographical South Pole and magnetic S-pole and magnetic S-pole near the geographic North Pole. The magnetic poles of the earth are at the opposite side of the geographical pole. The difference between the geographical north and the geomagnetic north varies from point to point on the earth’s surface and the difference is known as magnetic declination.

The strength of the field at the surface varies from 3×10-5 T near the equator to 6×10-5 to at the poles. The study of magnetic rocks shows that the magnetic field can reverse its direction about every 100,000 – 1,000,000 years. The earth has large deposits of iron ore deep beneath the surface, but high temperature in the core prevents from retaining permanent magnetization as a bar magnet. It is considered that true source of magnetic field is the convection current in its core. The charged ions or electrons circulating in the liquid interior could produce a magnetic field just as a current loop.

### Elements of Terrestrial Magnetism

The quantities needed to specify the earth’s magnetic field at a place completely are called the elements of terrestrial magnetism. These are declination, inclination and horizontal component of the earth’s magnetic field.

#### Declination

The declination, $\theta$ at a place is the angle between the magnetic and the geographical meridian of the earth. It is mainly due to the earth’s magnetic axis not coinciding with its geographical axis. Angle of declination varies from place to place in the earth and even at a place, it shows the periodic variation.

#### Inclination or Angle of Dip

The angle of dip, $\delta$ at a place is defined as the angle between the earth’s magnetic field and horizontal direction in the magnetic meridian. When the magnetic needle free to rotate in the vertical plane is pivoted about its centre of gravity, it aligns itself along the earth’s magnetic field in the magnetic meridian at that place. The angle of dip varies at the earth’s surface from zero at the geomagnetic equator to the maximum of 90o at the geomagnetic poles.

#### Horizontal Component of the Earth’s Magnetic Field

The horizontal component of the earth’s magnetic field, H is the component of the earth’s magnetic field along horizontal direction in the magnetic meridian at a place.

Let I be the earth’s magnetic field at a place and H and be its horizontal and vertical components respectively. In the magnetic meridian, the horizontal component is

\begin{align*} H &= I\cos \delta \\ \text {and the vertical component is} \\ V &= I\sin \delta \\ \text { In the right angle triangle,} \\ H^2 + V^2 &= I^2\cos ^2\delta + I^2\sin ^2\delta = I^2 \\\text {or,}\:\: H^2 + V^2 &= I^2 \\ \text {And} \:\:\: \tan \delta = \frac VH \\ \end{align*}

These are the equating relating H, V, I and $\delta$ at a place. If the values of declination $\delta$, dip $\delta$ and horizontal component H are known at a place, we can specify the strength and direction of the earth’s magnetic field at that place.

##### Things to remember

The quantities needed to specify the earth’s magnetic field at a place completely are called the elements of terrestrial magnetism.

The declination, at a place is the angle between the magnetic and the geographical meridian of the earth.

The angle of dip, at a place is defined as the angle between the earth’s magnetic field and horizontal direction in the magnetic meridian.

The horizontal component of the earth’s magnetic field, H is the component of the earth’s magnetic field along horizontal direction in the magnetic meridian at a place.

The quantities needed to specify the earth’s magnetic field at a place completely are called the elements of terrestrial magnetism.

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