Q.Discuss Earth's magnetic field in detail.

Neutral points are locations where the net magnetic field is zero, so the magnet's field B equals and opposes the earth's horizontal field B_H.

When a bar magnet is placed on a horizontal surface, neutral points are the positions where the magnetic field due to the magnet exactly balances the horizontal component of the earth's magnetic field.

At such a point the two fields are equal in magnitude and opposite in direction, so they cancel:

$B = B_H$

The resultant field there is zero (a compass needle placed there shows no preferred direction).

Declination = angle between the magnetic meridian and the geographic (true) meridian at a place.

The geographic meridian is the vertical plane through the geographic north–south line, while the magnetic meridian is the vertical plane containing the earth's magnetic field (the direction a freely suspended magnet points) at that place. The angle between these two planes is called the magnetic declination. (The angle of dip is a different quantity — the angle the field makes with the horizontal.)

Earth's magnetic dipole moment ≈ 8 × 10²² J T⁻¹.

The Earth behaves like a giant magnetic dipole. Its magnetic moment is approximately

$m \approx 8.0\times10^{22}\ \text{A m}^2 = 8.0\times10^{22}\ \text{J T}^{-1}$

(the unit A m² is identical to J T⁻¹). The small numbers 8.0, 11.5 or π J T⁻¹ are far too tiny for a planet-sized magnet.

The angle between the magnetic and geographic axes is the magnetic declination.

Declination is the horizontal angle between the geographic (true north) meridian and the magnetic meridian. The angle of dip is the angle the Earth's total field makes with the horizontal — a different quantity. These earth-magnetism terms are defined in the NCERT/CBSE Class 12 magnetism chapter.

Declination = angle between geographic north and magnetic north.

The resultant earth field magnitude satisfies B² = B_H² + B_V².

The earth's total magnetic field B resolves into a horizontal component B_H and a vertical component B_V, which are mutually perpendicular. Their vector sum gives

$B = \sqrt{B_H^2 + B_V^2}\quad\Rightarrow\quad B^2 = B_H^2 + B_V^2.$

(The angle of dip δ satisfies tan δ = B_V/B_H.)

Earth's surface magnetic field $B \sim 10^{-5}$ T.

The Earth behaves like a giant magnet. The magnitude of its magnetic field at the surface is only a few tenths of a gauss.

Since $1\ \text{gauss} = 10^{-4}\ \text{tesla}$, a typical value of $0.3$–$0.6$ gauss corresponds to

$B \approx (3\text{–}6)\times10^{-5}\ \text{T} \sim 10^{-5}\ \text{T}.$

Among the options, $10^{-5}$ T is the correct order of magnitude; the others ($10^{-1}$, $10^{-2}$, $10^{-3}$ T) are far too large.

The plane described is the geographic meridian.

At a place, the geographic meridian is the vertical plane that passes through the geographic (rotational) axis of the Earth — i.e. the vertical plane containing the longitude circle (line of longitude) through that place.

(For contrast, the magnetic meridian is the vertical plane through the magnetic axis / a freely suspended magnetic needle; the angle between the two is the magnetic declination.)

Together these three quantities fully specify the magnitude and direction of Earth's magnetic field at any location.

The three elements

1. Magnetic declination ($\theta$): the angle between the geographic (true) north and the magnetic north (as shown by a compass) at a given location.
2. Angle of dip / inclination ($\delta$ or $I$): the angle the Earth's total magnetic field makes with the horizontal plane at that location.
3. Horizontal component ($B_H$): the component of Earth's total magnetic field along the horizontal direction (pointing toward magnetic north).

Together, these three fully specify the magnitude and direction of Earth's magnetic field at any point.

Earth's magnetism is attributed to the dynamo effect: convective circulation of the molten, conducting outer core, driven by heat and the earth's rotation, sustains large-scale electric currents that produce the observed magnetic field.

The earth's core consists of a solid inner core and a fluid outer core made largely of molten iron and nickel, which are good electrical conductors. Radioactive heating and the earth's rotation (Coriolis effect) drive large-scale convective circulation of this electrically conducting fluid. Motion of a conductor through an existing (even very weak, seed) magnetic field induces electric currents in it (electromagnetic induction), and these currents in turn produce their own magnetic field. Under the right conditions this feedback becomes self-sustaining and amplifying — a natural magnetohydrodynamic 'dynamo' — maintaining a magnetic field over geological timescales, roughly (though not exactly) aligned along the earth's rotational axis, which is why it approximates a dipole field with poles near the geographic poles.

This dynamo mechanism is the currently accepted physical cause taught at this level, distinguishing it from a simple permanent-magnet explanation (the earth's interior is far too hot for permanent ferromagnetism, since it is well above the Curie temperature of iron).

Frequency of a magnetic needle: n = (1/2π)√(MB_H/I) ⇒ n² ∝ B_H.

A magnetic needle of magnetic moment M and moment of inertia I oscillating in a horizontal field B_H behaves like a torsional oscillator with time period

$T = 2\pi\sqrt{\frac{I}{M B_H}},\qquad n = \frac{1}{T} = \frac{1}{2\pi}\sqrt{\frac{M B_H}{I}}.$

Hence n ∝ √B_H, which means n² ∝ B_H.

Declination is the angle between true (geographic) north and magnetic north at a place.

At any point on the Earth's surface, the magnetic meridian (the vertical plane containing the Earth's magnetic axis, i.e. the direction a compass needle points) generally does not coincide exactly with the geographic meridian (the vertical plane containing the Earth's rotational/geographic axis, i.e. true north-south).

The angle of declination ($\theta$ or D) at a place is defined as the angle between the magnetic meridian and the geographic meridian at that place — equivalently, the angle by which a compass needle deviates from true geographic north.