Question

The magnetic field of earth at the equator is approximately $4 \times {10^{ - 5}}\,T$. The radius of earth is $6.4 \times {10^6}\,m$. Then the dipole moment of the earth will be near the order of
A. ${10^{23}}\,A{m^2}$
B. ${10^{20}}\,A{m^2}$
C. ${10^{16}}\,A{m^2}$
D. ${10^{10}}\,A{m^2}$

Answer 1

Here we have to use the formula of earth’s magnetic field to get the answer. Earth's magnetism is created by the convection of molten iron and nickel in the centre of the earth. These streams contain flows of charged particles which produce magnetic fields.

Complete step by step answer:
Given,
Radius of earth, $d = 6.4 \times {10^6}\,m$. The magnetic field of earth at the equator, $m = 4 \times {10^{ - 5}}T$.
The dipole of the earth is given by:
$B = \dfrac{{{\mu _ \circ }m}}{{4\pi {d^3}}} \\\ B = \dfrac{{4 \times {{10}^{ - 7}}}}{{{{\left( {6.4 \times {{10}^6}} \right)}^3}}} \\\ \simeq {10^{23}}\,A{m^2} \\\$
Hence, option A is correct.

Additional information:
The planet has its own magnetic field lines due to the presence of metallic fluids found both at the outer core and at the inner core. The outer core consists of cast iron, while the inner core has solidified components.

At the surface of the Earth, the planet’s magnetic field can be applied in multiple ways. There are the elements that are responsible at a given position for the amplitude and orientation of the earth’s magnetic field:
- Magnetic declination
- Horizontal component of the earth’s magnetic field
- The angle of dip or magnetic inclination

Magnetic declination:
The angle created by the magnetic meridian with the geographic meridian is known as magnetic declination. The geographic meridian here is defined as the plane that passes through the earth’s north and south poles.

The angle of dip or magnetic inclination:
The angle with the horizontal axis produced by the north pole of the needle is known as the angle dip or magnetic inclination.

Horizontal component of the earth’s magnetic field:
The horizontal component is the horizontal orientation component of the magnetic field of the earth in the magnetic meridian.

Note: Here we have to also multiply the value of permeability of free space as ${\mu _ \circ } = 4\pi \times {10^{ - 7}}\,H{m^{ - 1}}$. Otherwise the answer would be wrong if we ignore it in confusion. Similar to the field found in near-Earth space, the field power increases radially inward towards the magnetic equator in the case of a dipole field. The result is that along a path that is tangent to the direction of rising field power, a charged particle can still drift.