Question

(a) Define magnetic elements at a place.

(b) What are their mutual relations?

Answer 1

(a) Elements of the earth’s magnetism

The quantities, which describe the magnetic field of the earth at a particular place, completed, in magnitude as well as in direction, are known as the magnetic elements of earth of that place.

These are:

• Declination
• Dip or Inclination
• Horizontal component of the earth’s field.

(i) Declination (θ)

It is defined as the angle between the magnetic meridian and the geographical meridian at a place.

In Fig. let PQRO represent the magnetic meridian and PQ'R'O represent the geographical merdian at the place P. Then angle θ between these two planes, by definition, is the angle of declination at the place P.

(ii) Dip or inclination (δ)

Dip at a place is defined as the angle between the direction of the total intensity of the earth’s magnetic field and a horizontal line in the magnetic meridian. 

In Fig. \(\overrightarrow {PA}\)  represents the total or resultant intensity of the earth’s magnetic field in magnitude as well as in direction. As P makes an angle 8 with PQ ( a horizontal line in the magnetic meridian PQRO), the angle of dip at the place P is δ.

(iii) Horizontal Component (H)

It is the component of earth’s magnetic field along the horizontal direction and denoted by H.

The total intensity of the earth’s magnetic field at any point can be resolved into two rectangular components, one along the horizontal and the other along the vertical direction.

The component of the resultant intensity of the earth’s magnetic field in the horizontal direction in magnetic meridian is called its horizontal component. It is denoted by H. The component of the resultant intensity of the earth’s magnetic field in the vertical direction in magnetic meridian is called its vertical component. It is denoted by V.

(b) Relation between magnetic elements

The resultant intensity, i.e. R along \(\overrightarrow{PA}\)  has been resolved into two rectangular components. Clearly, the horizontal component along PQ.

i.e. H = R cos δ .............(1)

and the vertical component along PO

i.e., V = R sin δ ...........(2)

Dividing (2) by (1),. we get

\(\frac{V}{H} = \frac{R\ sin\ \delta}{R\ sin\ \delta}\) = tan δ .............(3)

Squaring (1) and (2) and adding, we get

H² + V² = R² cos² δ + R² sin² δ

= R² (cos² δ + sin² δ) = R²

∴ R = \(\sqrt {H^2 + V^2}\) .............(4)