Elements of Earth’s Magnetic Field

The magnetic field of the earth at any point on its surface is determined by using three physical quantities which are called elements of earth’s magnetic field. They are:

• Declination: Declination at a point of earth’s surface can be defined as the
  

  acute angle between the geographic meridian and magnetic meridian of the earth. Geographic meridian is the imaginary vertical plane passing through the geographical axis of the earth and magnetic meridian is the imaginary vertical plane passing through the magnetic axis of the earth. The value of declination varies from place to place on the

  earth’s surface. The maximum value of declination is 17^o towards east or west. In general, its value at a place is constant but it changes slightly with time and the same value is obtained after 960 years.

• Inclination or Angle of Dip: The angle made by the direction of earth’s magnetic field or a freely suspended magnet with the horizontal direction is called inclination or angle of dip at that place. When a magnetic compass is pivoted or rotated about its centre of gravity, it rests pointing downwards in the northern hemisphere and pointing upwards in the southern hemisphere. The angle made by this needle with the horizontal gives the angle of dip. Its value varies from 0^o to 90^o. At equator, the angle of dip is 0^o. The angle of dip is measured by using dip circle.
  

  A figure showing Angle of Dip with the help of Dip Circle

  Dip Circle

• Horizontal component of earth’s magnetic field: As the direction of earth’s magnetic field is inclined with the horizontal, it can be resolved into horizontal and vertical components.
  The component of earth’s magnetic field along the horizontal direction at a place is called horizontal component of earth’s magnetic field at that place. Let ‘δ’ be the angle of dip. Then the horizontal and vertical components of the earth’s magnetic field ‘B’ are:
  Horizontal component of earth’s magnetic field (B_H) = Bcosδ …. (i)
  Vertical component of earth’s magnetic field (B_v) = Bsinδ …. (ii)
  Dividing equation (ii) by (i),
  ^B_v/_BH= ^Bsinδ/_Bcosδ
  or, ^B_v/_BH= tanδ
  ∴ δ= tan^-1(^B_v/_BH)
  Squaring equations (i) and (ii) and adding both of them, we get,
  B_H² + B_v² = B²cos²δ + B²sin²δ
  or, B_H² + B_v² = B²(cos²δ + sin²δ) [∵ cos²δ + sin²δ = 1]
  or, B_H² + B_v² = B²
  ∴ B = √(B_H² + B_v²)