Gauss’s law in magnetism: It states that the surface integral of a magnetic field over a closed surface is always zero.

Magnetic field of the earth: Earth is a powerful magnet. Its magnetic field is present everywhere on the earth surface.

Elements or earth’s magnetic field: Earth is a powerful magnet. Its magnetic field is present everywhere on the earth surface.

Elements of earth’s magnetic field:

The earth magnetic field at a place can be completely described by three parameters which are called elements of earth’s magnetic field these are

1. Magnetic Declination
2. Angle of Dip or Magnetic Inclination
3. Horizontal components of earth’s magnetic field.

1. Magnetic declination: The angle between the geographical meridian and magnetic meridian at a place called the magnetic declination (α) at that place..
2. Angle of dip or Magnetic inclination: The angle made by the earth’s total magnetic field B with the horizontal direction in the magnetic meridian is called angle of dip (δ) at any place.
3. Horizontal component of earth’s magnetic field: It is the component of earth’s magnetic field in the horizontal direction in the magnetic meridian. If δ is the angle of dip at any place, then the horizontal component of

B_H = B cos δ

At the magnetic equator, δ = 0°, B_H = B cos 0 = B

At the magnetic equator, δ = 90°, B_H = B cos 90 = 0

Relation between elements of earth’s magnetic field:

In the fig. above, if δ is the angle of dip at any place, then the horizontal and vertical component of earth’s magnetic field B at that place is

B_H = B cos δ

B_V = B sin δ

∴ B_H/B_V = tanδ

Also

B_H² + B_H² = B² (cos²δ + sin²δ) = B²

Or B = (B_H² + B_H²)^1/2

Magnetizing field: When a magnetic material is placed in a magnetic field, a magnetism is induced in it known as magnetizing field.

B₀ = μ₀nl

Magnetizing field intensity: The ability of magnetizing field to magnetize a material medium is expressed by a vector H, called magnetizing field intensity. It is defined as “the no. of ampere turn (nI) flowing round the unit length of the solenoid required to produce the given magnetizing field. Thus

H = nI

 B₀ = μ₀nl = μ₀H

 H = B₀/μ₀

Its S.I. unit is ampere meter^-1.

Intensity of magnetization: The magnetic moment developed per unit volume of a material when placed in a magnetizing field is called intensity of magnetization.

M = M/V = nI_mA/A = nI_m