12 min readConcept sheetSection A MCQ (1 mark) and objective (2 marks, two parts) on the elements of the Earth's field and on dia, para and ferro materials; Section B very short answer (2 marks)

Magnets, field lines, the Earth's magnetic field and magnetic materials

A magnet's two poles cannot be separated. The Earth acts like a giant magnet, described by dip, declination and B_H. Materials are dia, para or ferromagnetic.

Components of the Earth's fieldB_H = B cos δ (horizontal) and B_V = B sin δ (vertical), where δ is the angle of dip

Angle of diptan δ = B_V/B_H; δ = 0° at the magnetic equator and 90° at the magnetic poles

Angle of declination θThe angle between the magnetic meridian and the geographic meridian at a place

Curie temperatureAbove it a ferromagnet becomes paramagnetic: about 1043 K for iron and 631 K for nickel

Properties of magnets and of their field lines

Directive property: a magnet hung freely comes to rest roughly along the geographic north-south line. The end that points north is its north pole (N).
Attractive property: a magnet attracts iron, nickel and cobalt. The pull is strongest near its ends, called the poles.
Like poles repel, unlike poles attract. Repulsion is the sure test of a magnet, because a magnet attracts plain iron too.
Poles cannot be separated. Cut a magnet in two and each piece has its own N and S. The simplest magnet is a magnetic dipole, a pair of opposite poles.
Magnetic induction: bring a magnet near a piece of iron. The near end of the iron becomes an opposite pole, so the iron is pulled.
Field lines: the tangent to a line gives the direction of B. Where the lines are crowded, the field is strong.
Outside a magnet the lines run from N to S, and inside from S to N. So they form closed loops, and two lines never cross.

The Earth as a magnet: its three elements

The Earth behaves as if a huge bar magnet lies inside it. The south pole of this magnet is near the geographic north pole. That is why the N pole of a compass points north. The magnetic axis is tilted from the axis of rotation, so the magnetic poles are not at the geographic poles. The magnetic poles also wander slowly. Your NIOS lesson places them about 650 km from the geographic poles, the northern one in Canada. Today the northern one lies in the Arctic Ocean, drifting towards Siberia. The southern one lies off the coast of Antarctica, much farther from its geographic pole. The Earth's field also changes slowly with time. The vertical plane through the magnetic north and south at a place is the magnetic meridian; a compass needle lies in it. The vertical plane through the geographic north and south is the geographic meridian. Three quantities, the elements of the Earth's field, describe it fully. (a) Declination θ: the angle between the magnetic meridian and the geographic meridian. (b) Dip (inclination) δ: the angle that the Earth's total field B makes with the horizontal, in the magnetic meridian. A dip needle, free to turn in a vertical plane, shows it. (c) Horizontal component B_H of the field. Resolving B gives B_H = B cos δ and B_V = B sin δ. Squaring and adding gives B² = B_H² + B_V². Dividing gives tan δ = B_V/B_H.

Worked example: the Earth's total field and its vertical component

Problem

At a place, the horizontal component of the Earth's field is 3.0 × 10⁻⁵ T and the angle of dip is 30°. Find (a) the total field and (b) the vertical component. (cos 30° = 0.866, tan 30° = 0.577)

Working

Given: B_H = 3.0 × 10⁻⁵ T, δ = 30°.
(a) Formula: B_H = B cos δ, so B = B_H/cos δ.
B = 3.0 × 10⁻⁵ T ÷ 0.866 = 3.46 × 10⁻⁵ T.
(b) Formula: tan δ = B_V/B_H, so B_V = B_H tan δ.
B_V = 3.0 × 10⁻⁵ T × 0.577 = 1.73 × 10⁻⁵ T.
Check: B_H² + B_V² = (9.0 + 3.0) × 10⁻¹⁰ T² = 12 × 10⁻¹⁰ T², and √12 × 10⁻⁵ T = 3.46 × 10⁻⁵ T. It matches.

Answer

(a) B ≈ 3.5 × 10⁻⁵ T; (b) B_V ≈ 1.7 × 10⁻⁵ T (rounded to 2 significant figures)

Dia, para and ferromagnetic materials compared

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Near a strong magnet	Feebly repelled	Feebly attracted	Strongly attracted
A rod hung between the poles sets	Across the field	Along the field	Along the field, strongly
Its atoms	No magnetic moment of their own	Each atom is a tiny magnet, but they point every way	Tiny magnets lined up in regions called domains
Effect of heating	Almost none	Its magnetism becomes weaker	Becomes paramagnetic above the Curie temperature
Examples	Bismuth, copper, water	Aluminium, sodium, oxygen	Iron, nickel, cobalt, gadolinium

Domains: why iron becomes a strong magnet

In a ferromagnet, each atom acts as a permanent tiny magnet, and neighbouring atoms line up with each other. They do this in small regions called domains. Inside one domain, all the atomic magnets point the same way. In an ordinary iron nail the domains point in random directions. Their effects cancel, so the nail is not a magnet. In an outside field, the domains that point along the field grow at the cost of the others, as the domain walls (boundaries) move. The domains also turn a little towards the field. In a very strong field, nearly the whole sample acts as one domain, and its magnetism is saturated. When the field is removed, some magnetism stays. If a ferromagnet is heated above a certain temperature, the Curie temperature T_c, its domains break up and it becomes paramagnetic. Typical values: iron 1043 K, nickel 631 K, cobalt 1394 K and gadolinium about 293 K, just below room temperature. (Your NIOS lesson's table gives 317 K for gadolinium; the measured value is about 293 K.)

Activity: how to draw the field lines of a bar magnet and find its neutral points

You need a bar magnet, a small compass, white paper, a drawing board, pins, a pencil and chalk.

1
Hang the magnet from a thread tied at its middle. Mark the end that points north as N.
2
Place the compass on the table and draw a chalk line along its needle. This line is the magnetic meridian.
3
Pin white paper on the drawing board and draw a pencil line along it. Turn the board until the pencil line lies along the chalk line.
4
Place the magnet on the pencil line with its N pole pointing north. Draw its outline.
5
Put the compass near the N pole and mark a dot at each end of its needle. Move the compass until its tail is on the second dot, and mark again. Go on until you reach the S pole.
6
Join the dots with a smooth curve and draw an arrow from N towards S. Draw more lines from other starting points.
7★
Observe: at two points on the equatorial line, one on each side of the magnet, no line passes and the compass rests in any direction. These are the neutral points. Mark them with small circles.
8★
Repeat with the N pole pointing south. Observe: now the two neutral points lie on the axial line, one beyond each pole. Result: at a neutral point, the magnet's field is equal and opposite to the Earth's horizontal field B_H.

★ key step

In real life

The compass app in a mobile phone uses a tiny sensor that measures the Earth's magnetic field, so the map turns the way you face. Soft iron, a ferromagnet, forms the cores of transformers and motors.

Exam angle

2 marks: “Define the angle of dip and the angle of declination at a place.” Dip: the angle that the Earth's total magnetic field makes with the horizontal, in the magnetic meridian. Declination: the angle between the magnetic meridian and the geographic meridian at that place.

2 marks: “At a place, the vertical component of the Earth's field is √3 times its horizontal component. Find the angle of dip.” tan δ = B_V/B_H = √3, so δ = 60°.

3 marks: “What are domains? Use the domain idea to explain how an iron bar is magnetised in a field, and what happens when it is heated above its Curie temperature.” Domains: small regions in which all atomic magnets point the same way; normally random, so no net magnetism. In a field, domains along it grow and turn, so the bar is magnetised (saturated in a strong field). Above T_c the domains break up and the bar becomes paramagnetic.

Remember it

DDH describes the Earth's field: Declination, Dip and the Horizontal component. B_H = B cos δ and tan δ = B_V/B_H.