Earth's Magnetic Field: Declination, Dip and Magnetic Materials
Our Planet Is a Giant Magnet
A compass needle swings to point north almost anywhere on Earth. It does so because Earth itself behaves like an enormous bar magnet, surrounded by a magnetic field that guides navigators, shields life from charged particles streaming from the Sun, and creates the auroras near the poles. This tutorial covers Earth's magnetic field and magnetic materials as tested in WAEC, NECO and JAMB physics: the geographic and magnetic poles, declination, dip and the components of the field, the domain theory of magnetism, ferromagnetic, paramagnetic and diamagnetic materials, soft iron and steel, and methods of making and destroying magnets.
Earth's Magnetic Field
Earth's field is similar to the field of a huge bar magnet tilted slightly from the axis of rotation. It is produced by electric currents in the molten iron of Earth's outer core.
- The north pole of a compass points towards the geographic north. Because unlike poles attract, there must be a magnetic south pole near the geographic north pole.
- The magnetic poles are not exactly at the geographic poles, and they slowly drift over time.
- Field lines leave Earth in the southern hemisphere and enter it in the northern hemisphere.
The Magnetic Elements
Three quantities, called the magnetic elements, describe Earth's field at a place.
1. Declination (magnetic variation)
The angle of declination is the angle between the geographic meridian (the direction of true north) and the magnetic meridian (the direction a compass points). It is described as east or west, depending on which side of true north the compass points.
Worked example 1
At a place where the declination is 4° W, a compass gives the bearing of a hill as 050°. Find the true bearing.
Magnetic north is 4° west of true north, so every magnetic bearing is 4° larger than the true bearing. True bearing = 050° − 4° = 046°.
Navigators must correct compass readings for declination, which is why maps show its value.
2. Dip (inclination)
Earth's field is not horizontal at most places. The angle of dip δ is the angle between the direction of Earth's magnetic field and the horizontal. It is measured with a dip circle, a magnetised needle free to rotate in a vertical plane.
- At the magnetic equator, the field is horizontal, so the dip is 0°.
- At the magnetic poles, the field is vertical, so the dip is 90°.
- Nigeria lies close to the magnetic equator, so the angle of dip there is small.
3. Horizontal component
Earth's total field B can be split into a horizontal component H and a vertical component V:
H = B cos δ, V = B sin δ, and tan δ = V ÷ H
Also, B = √(H² + V²). A compass needle, which can only turn horizontally, responds only to H.
Worked example 2
At a place, Earth's total magnetic flux density is 5.0 × 10⁻⁵ T and the angle of dip is 30°. Find the horizontal and vertical components.
H = 5.0 × 10⁻⁵ × cos 30° ≈ 4.3 × 10⁻⁵ T.
V = 5.0 × 10⁻⁵ × sin 30° = 2.5 × 10⁻⁵ T.
Worked example 3
At another place, H = 3.0 × 10⁻⁵ T and V = 4.0 × 10⁻⁵ T. Find the angle of dip and the total field.
tan δ = 4.0 ÷ 3.0, so δ ≈ 53.1°. B = √(3.0² + 4.0²) × 10⁻⁵ = 5.0 × 10⁻⁵ T.
Neutral Points
When a bar magnet lies on a table, its field combines with Earth's horizontal field. At neutral points, the two fields are equal in size and opposite in direction, so the resultant field is zero and a compass placed there does not settle in any direction.
- With the magnet's north pole pointing north, the neutral points lie on the line through its equator (east and west of the magnet).
- With the magnet's north pole pointing south, the neutral points lie on its axis (north and south of the magnet).
The Domain Theory of Magnetism
Why are some materials magnetic? In iron, each atom acts as a tiny magnet. The atoms are grouped into small regions called domains, and within each domain all the atomic magnets point the same way.
- In an unmagnetised piece of iron, the domains point in random directions, so their effects cancel.
- When the iron is magnetised, the domains line up in the same direction, and their effects add.
- When all the domains are aligned, the material is magnetically saturated: it cannot be magnetised any further.
The theory explains several observations. Breaking a magnet gives two smaller magnets, each with a north and a south pole, because every piece still contains aligned domains. Heating or hammering a magnet weakens it, because the vibrations knock the domains out of line.
Types of Magnetic Materials
- Ferromagnetic materials are strongly attracted by magnets and can be magnetised: iron, nickel, cobalt and their alloys, such as steel. Above a certain temperature, the Curie temperature (about 770 °C for iron), they lose their ferromagnetism.
- Paramagnetic materials are attracted only very weakly: aluminium, platinum and oxygen, for example.
- Diamagnetic materials are very weakly repelled by a magnet: copper, bismuth, water and glass, for example.
Soft Iron and Steel
- Soft iron is magnetised easily but also loses its magnetism easily when the magnetising field is removed. It is used for temporary magnets: the cores of electromagnets, transformers, relays and electric bells.
- Steel is harder to magnetise, but it keeps its magnetism. It is used for permanent magnets: compass needles, loudspeakers and magnetic door catches.
Making and Destroying Magnets
Methods of magnetisation
- Single touch: stroke a steel bar repeatedly from one end to the other with one pole of a magnet, lifting it clear between strokes.
- Double touch: stroke from the middle outwards with opposite poles of two magnets at the same time.
- Electrical method: place the bar inside a solenoid carrying a direct current. This is the most effective method. The polarity of each end follows the right-hand grip rule.
- Induction: a piece of iron near a magnet becomes a temporary magnet itself, which is why magnets pick up chains of paper clips.
Methods of demagnetisation
- Place the magnet inside a solenoid carrying alternating current, east–west, and slowly withdraw it. This is the most effective method.
- Heat the magnet strongly, above its Curie temperature.
- Hammer it repeatedly while it lies east–west.
Storing magnets
Bar magnets slowly lose their strength, because the free poles at their ends tend to disturb the alignment of the domains. They are stored in pairs with unlike poles side by side, with soft-iron keepers across their ends, which close the magnetic circuit.
Magnetic shielding
A soft-iron ring placed in a magnetic field draws the field lines through itself, so the space inside the ring is almost field-free. This shields sensitive instruments, such as watches and meters, from external magnetic fields.
Common Mistakes with Earth's Magnetic Field
- Saying there is a magnetic north pole at the geographic north. It is actually a magnetic south pole, which is why it attracts the north pole of a compass.
- Confusing declination and dip. Declination is measured in the horizontal plane, from true north. Dip is measured in the vertical plane, from the horizontal.
- Swapping sin and cos in H = B cos δ and V = B sin δ.
- Thinking any metal is magnetic. Copper, aluminium and brass are not ferromagnetic.
- Using a.c. to make a magnet. A permanent magnet needs d.c. Alternating current is used for demagnetising.
Earth's Magnetic Field: Practice Questions
- What is the angle of dip at the magnetic equator, and at the magnetic poles?
- At a place, Earth's field is 4.0 × 10⁻⁵ T and the angle of dip is 60°. Find the horizontal component.
- A place has H = 2.4 × 10⁻⁵ T and V = 1.8 × 10⁻⁵ T. Find the total field and the angle of dip.
- The declination at a place is 3° E. A compass gives a bearing of 120°. What is the true bearing?
- Why is soft iron used for the core of an electromagnet but steel for a permanent magnet?
- Using the domain theory, explain why a magnet cannot be magnetised beyond a certain strength.
Answers: 1. 0° and 90°. 2. H = 4.0 × 10⁻⁵ × cos 60° = 2.0 × 10⁻⁵ T. 3. B = √(2.4² + 1.8²) × 10⁻⁵ = 3.0 × 10⁻⁵ T, and tan δ = 0.75, so δ ≈ 36.9°. 4. Magnetic north is 3° east of true north, so true bearing = 120° + 3° = 123°. 5. Soft iron is magnetised and demagnetised easily, so the electromagnet can be switched off. Steel keeps its magnetism. 6. Once every domain is aligned, the material is saturated, so there is nothing left to line up.
Conclusion
Earth behaves like a giant bar magnet, with a magnetic south pole near the geographic north pole. Its field at any place is described by the declination (the angle between true and magnetic north), the dip (the angle the field makes with the horizontal) and the horizontal component H = B cos δ, with V = B sin δ. The domain theory explains magnetisation, saturation and the weakening of magnets. Ferromagnetic materials such as iron, nickel and cobalt can be magnetised, soft iron makes temporary magnets and steel makes permanent ones, d.c. in a solenoid creates magnets, and a.c. destroys them.