# Magnetic elements of earth

In this topic we will discuss about the magnetic elements of earth. All three kinds of magnetic elements of earth , angle of dip,angle of declination and horizontal components of earth magnetic field.

**Magnetic elements of earth** –

*Magnetic elements of earth at a place are the quantities which describe completely the magnitude and direction of magnetic field at that place.*

There are three magnetic elements of earth-

(i) Magnetic declination (ϴ);

(ii) Magnetic inclination or angle of dip (ẟ);

(iii) Horizontal components of earth’s magnetic field(H).

(i) **Magnetic declination (****ϴ);-**

The small angle between magnetic and geographic axis at a place is known as magnetic declination at that place .

Or, In other words we can define , angle between geographic and magnetic meridian at a place on earth is known as the magnetic declination at that place.

(ii) **Magnetic inclination or angle of dip –**

Magnetic inclination at a place on the earth is the angle between total strength of magnetic field and horizontal lines in magnetic meridian.

The value of angle of dip at a place on the earth is measured using an instrument called ‘ **Dip circle’.**

(iii) **Horizontal component-**

It is the components of total field strength of earth’s magnetic field in the horizontal direction in magnetic meridian.

As shown in figure. , total field strength is represented by AK and angle <BAK = ẟ

Then the magnetic field along AB ( horizontal) is given as

H = R cos ẟ………..(i)

And magnetic field along AD is given as V= R sin ẟ ………….(ii)

Squiring and adding equation (i) and (ii) is given as

H^{2} + V^{2} = R^{2} ( Cos^{2}ẟ+ Sin^{2}ẟ) ;

So , R = √( H^{2} + V^{2}) …………(III)

Again if we divide (ii) by (i) we get

R sinẟ/Rcosẟ = V/H

Or, Tan ẟ = V/H …………………(iv)

[**** important information about angle of dip –

(1). At a place on the magnetic poles , total earth’s magnetic field is perpendicular to the surface of earth .( ẟ=90^{0} )

So, H = R cos 90^{0} = 0

It means R = V ( total magnetic field is only in vertical direction)

(2) At a place on equator , total magnetic field is parallel to the earth ( ẟ=0^{0})

So , V= Rsin0^{0} = 0

It means R = H ( total magnetic field is in horizontal direction).

(3) In a vertical plane at an angle ϴ with the magnetic meridian.

Then apparent H’ = H cos ϴ

Again, apparent V’ = V,

Therefore tanẟ’ = V’/H’ = V/Hcosϴ = tanẟ/cosϴ ; (ẟ’ is the apparent value of angle of dip).

(4) If ẟ_{1} and ẟ_{2} are observed angle of dip in two arbitrary vertical planes which are perpendicular to each other then the true angle of dip ẟ is given as –

Cot^{2}ẟ=cot^{2}ẟ_{1} + cot^{2}ẟ_{2}.

(5) If λ is the magnetic latitude at a place, then it can be shown that the angle of dip at that place is given as , tanẟ = 2 tan λ …]

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