In this article, we are going to talk about the Earth’s magnetism class 12, its causes, definitions of important terminologies, elements, and its variation. So let’s get started…
Earth’s magnetic field
[latexpage] As we know from the starting that the Earth is a powerful natural magnet. Magnetic field due to the earth being present everywhere near the earth’s surface, and we can also see it by the deflection of the compass needle. This magnetic field can be approximated to the field of the magnetic dipole of the dipole moment of $8\times 10^{22} Am^2$ assumed to be located at the center of the earth.
The axis of the dipole makes an angle of about 11° with the rotational axis of the earth. The magnetic north pole Nm of the earth lies somewhere near the geographic south pole Sg, while the magnetic south pole Sm of the earth lies somewhere near the geographic north Ng of the earth.
The magnitude of the magnetic field on the surface of the earth is typically about $10^{-4}T$ which is equal to one gauss (G). A gauss is also often called orested. Thus, the magnetic field of the earth is of the order of one orested.
| The branch of physics that deals with the study of earth magnetism are called terrestrial magnetism or geomagnetism. |
Experimental evidences in support of the earth’s magnetism.
Various experiments have been performed to answer the cause of the earth’s magnetism. Some experimental pieces of evidence that support earth magnetism are given below:
- A freely suspended magnetic needle always come rest to the north south direction. This suggests that the earth behaves like a huge magnet whose magnetic south pole lies somewhere near the geographic north pole and magnetic north pole lies somewhere near the geographic south pole.
- If a iron piece buried inside the earth then it becomes weakly magnetised after some time. This magnetism is induced in the iron piece by the earth’s magnetic field.
- Existence of neutral point near the bar magnet indicates the presence of earth’s magnetic field. At the point, magnetic field of the bar magnet is cancelled by the earth’s magnetic field.
Causes of earth’s magnetic field
It is thought that the magnetic field of the earth is approximately like that of a giant bar magnet embedded deep inside the earth. Many theories have been proposed in regards to the cause of the earth’s magnetic field from time to time. Some of the famous theory that proposed earth magnetism is mentioned below.
- In 1600, William Gilbert in his book ‘De magnete‘ first suggested that the earth behaves like a bar magnet and it’s magnetism is due to the magnetic material at its centre, which could be a permanent magnet. But the core of the earth is so hot that no permanent magnet could exist there.
- Proff. Blackett suggested that the earth’s magnetism is due to the rotation of the earth about it own axis. Every substance is made up of charged particles such as electrons and protons. When earth rotates, these particles also rotates with the earth and cause a circulating current, which is in turn, magnetise the earth.
- Cosmic rays causes the ionisation of the atmospheric gases. As the earth rotates, a strong electric current set up due to the movement of the charged ions. These current may be the source of earth’s magnetism.
- According to Geophysicist Edward Bullard, earth’s core is the deposits of larger magnetic materials such as iron, cobalt, and nickel etc. The core of the earth is very hot, and exist in molten state. The circulating ions in the highly conducting liquid in the outer layer of the earth’s core forms current loops that produces a magnetic field. Earth’s magnetic field due to this effect is sometimes is referred as Dynamo effect.
Suggested reading:
- Magnetic moment of a revolving electron, and Bohr magneton, class 12
- Magnetic moment of atoms, electrons, nucleus, molecules, and elementary particles
Watch this video for more reference.
Definitions of important terms related to earth’s magnetism
Definitions of important terms related to earth’s magnetism. See the magnetic field lines around the earth.
Some important terminologies
- Geographic axis – The straight line passing through the geographical north and south pole of the earth is called geographic axis. It is the rotation axis of the earth.
- Magnetic axis – The straight line passing through the magnetic north and south pole of the earth is called magnetic axis.
The magnetic axis of the earth makes an angle of nearly 20° with the geographic axis. At present, magnetic south pole Sm is located at a point in northern Canada at a latitude of 70.5°N and longitude of 96°W.
The magnetic north pole Nm is located diametrically to Sm i.e at a latitude of 70.5°S and a longitude of 84°E. The magnetic poles are nearly 20,00KM away from the Geographic poles. The magnetic equator intersects the geographic equator at the longitude of 6°W and 174°E.
- Magnetic equator – It is a great circle on the earth perpendicular to the magnetic axis.
- Magnetic meridian – The vertical plane passing through the magnetic axis of a freely suspended small magnet is called magnetic meridian. The earth’s magnetic field acts in the direction of the magnetic meridian.
- Geographic meridian – The vertical plane passing through the geographical north and south pole is called geographic meridian.
Elements of the earth’s magnetic field
Earth’s magnetic field at any place can be completely described by the three parameters called elements of the earth’s magnetic field. These elements are:
- Magnetic declination
- Angle of dip or magnetic inclination
- Horizontal component of the earth’s magnetic field
Magnetic declination
Magnetic declination – The angle between magnetic meridian and geographic meridian at a place is called magnetic declination at that place. It is not constant value and keeps changing depending upon the position on the earth’s surface and time.
The Greek letter δ is used as the symbol for magnetic declination and is also known as magnetic variation. But sometimes α (alpha) is used to denote the magnetic declination.
Reason of arise of magnetic declination
Magnetic declination arises because the magnetic axis of the earth does not coincide with the geographic axis.
Determination of magnetic declination at a place
To determine the magnetic declination at a place, set a compass needle in such a way that it is free to rotate in a horizontal plane about the vertical axis. See figure below.
The angle α that the magnetic needle makes with geographic North-South direction (Ng-Sg) is the magnetic declination. By knowing declination, we can determine the vertical plane in which the earth’s magnetic field lies.
In India, the values of α are very small. It is 0°41′ E for Delhi and 0°58′ W for Mumbai. This means that the North pole of the compass needle always points in the direction of the geographic north.
Angle of dip or magnetic inclination
The angle made by the earth’s total magnetic field $\vec{B}$ with the horizontal direction in the magnetic meridian is called angle of dip at any place.
The angle of dip is different at different places on the surface of the earth. Consider a dip needle, which is just another compass needle but pivoted horizontally so that it is free to rotate in a vertical plane coinciding with the magnetic meridian.
It orients itself so that its North pole exactly points in the direction of the total earth’s magnetic field. The angle between the horizontal and final direction of the dip, needle gives the angle of dip at a given location.
At the magnetic equator, the dip needle rests horizontally so that the angle of dip is zero at the magnetic equator. The dip needle rests vertically at the magnetic poles so that the angle of dip is 90° at the magnetic poles. At all the other places, the dip angle lies between 0° and 90°.
Horizontal components of the earth’s magnetic field
It is the components of the earth’s total magnetic field $\vec{B}$ in the direction of the magnetic meridian.
If δ is the angle of dip of any place, then the horizontal component of the earth’s magnetic field at that place is given as $$B_H=B\cos\delta$$
| At magnetic equator, δ = 0°, so: $B_H=B\cos0^{\circ}=B$ |
| At magnetic poles, δ = 90°, so: $B_H=B\cos{90}^{\circ}=0$ |
Thus, the value of $B_H$ is different at different places on the surface the earth.
Relation between elements of earth’s magnetic field
You can see in the figure above, the three elements of the earth’s magnetic field. If δ is the angle of dip at any place then the horizontal and vertical components of the earth’s magnetic field $\vec{B}$ at that place is given as: $$B_H=B\cos\delta$$ and $$B_V=B\sin\delta$$ $$\therefore\qquad \frac{B_V}{B_H}={\tan\delta}$$ and also
| ${B_H}^2 + {B_V}^2 = B^2(\sin^2{\delta}+\cos^2{\delta})=B^2$ |
or $$B=\sqrt{{B_H}^2 + {B_V}^2}$$
Watch this video for more reference.
Global variations in the earth’s magnetic field
Earth’s magnetic field changes both in magnitude and direction from place to place. Some of the noticeable global variations are given below:
- The magnitude of magnetic field on the earth’s surface is small, nearly $4\times 10^{-5} T$.
- Our own galaxy “milky way” has the smaller background field about $2\times 10^{-12}T$.
- If we assume that the earth’s magnetic field is due to the magnetic dipole of $8.0\times 10^{22}Am^2$ that is located at the centre of the earth, then the earth’s magnetic field will be less than $1\mu T (10^{-6})$ at a distance of 5 times of the radius of the earth i.e 32,000 KM. Upto this distance, magnetic field is completely governned by the earth.
- At a distance greater than 32,000 KM, magnetic field due to earth is severely distorted by the solar wind.
- Solar wind ionise the earth’s atmosphere near the earth’s magnetic poles. This ionisation of atmosphere causes the beautiful display of colours high into the sky, called auroras.
Temporal variations in the earth’s magnetic field
Temporal variations in the earth’s magnetic field: Earth’s magnetic field keeps changing in magnitude and direction as the passes time. These changes are the two types:
Short-term changes
The position of the earth’s magnetic poles keeps shifting slowly with the passes of time. In a period of 240 years, i.e from 1580 to 1820, the magnetic declination in London has been changed by 35°. The magnetic south pole in the northern arctic region of Canada has been found to be shifted in a northwest direction at the rate of 10km/year in recent times.
Long-term changes
The changes in the earth’s magnetic field over a long term or a geological time scale are interesting. The studies of basalt revealed that the magnetic field of earth reverses it’s the direction every million years or so. This means that once in a million years or so, currents in the earth’s core cool down and take a halt and pick up speed in opposite directions of the previous one.
Basalt which contains iron is emitted during a volcanic eruption. As it cools and solidifies, it provides the pictures of earth’s magnetic field.
Neutral point
Neutral point: It is the point where the magnetic field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.
The resultant magnetic field at the neutral point is zero. If a compass needle is placed at such a point, it can stay in any position.
Magnet placed in the magnetic meridian with its north pole pointing north
The figure shows the magnetic lines of force of a bar magnet placed in the magnetic meridian with its north-pole pointing towards the geographic north of the earth. The fields due to the magnet and the earth are in the same directions at points on the axial line and are in the opposite directions at points on the equatorial line. So the resultant field is stronger at axial points and weaker at equatorial points. The two neutral points P and Q lie on the equatorial line.
Let $r$ be the distance of each neutral point from the center of the magnet. $2l$ is the length of the magnet, and $m$ is the magnetic moment of the magnet.
Then the magnetic field strength at each neutral point is $$B_{equa}=\frac{\mu_0}{4\pi}\cdot\frac{m}{(r^2+l^2)^{\frac{3}{2}}}$$ For a short magnet, $l<<<r$, therefore magnetic field is $$B_{equa}=\frac{\mu_0}{4\pi}\cdot\frac{m}{r^3}$$
At the neutral point, the field of the bar magnet is balanced by the horizontal components $B_H$ of the earth’s magnetic field, so that $$B_{H}=\frac{\mu_0}{4\pi}\cdot\frac{m}{r^3}$$
Knowing $r$ and $B_H$, we can find the magnetic moment of the magnet.
Suggested reading:
- Derive an expression of the magnetic field at the axial point of a bar magnet class 12
- Derive an expression of magnetic field at a point on the equatorial line of a bar magnet class 12
Magnet placed in the magnetic meridian with its south-pole pointing north
The figure below shows the magnetic lines of force of a bar magnet placed in the magnetic meridian with its south-pole pointing towards the geographic north of the earth.
Here the fields due to the magnet and the earth are in the same direction at points on the equatorial line and are in opposite directions at points on the axial line of the magnet. So the resultant field is weaker at axial points and is stronger at equatorial points. In this case, the two neutral points P and Q lie on the axial line near the ends of the magnet.
Let $r$ is the distance of each neutral point from the centre of the magnet. $2l$ is the length of the magnet, and $m$ is the magnetic dipole moment of the magnet. Then the magnetic field strength at each neutral point is $$B_{axial}=\frac{\mu_0}{4\pi}\cdot\frac{2mr}{(r^2-l^2)^{2}}$$ For a short magnet, $l<<<r$, therefore magnetic field is $$B_{axial}=\frac{\mu_0}{4\pi}\cdot\frac{2m}{r^2}$$
Again, at the neutral point, the field of the bar magnet is balanced by the horizontal components $B_H$ of the earth’s magnetic field, so that $$B_{H}=\frac{\mu_0}{4\pi}\cdot\frac{2m}{r^2}$$ Knowing $r$ and $B_H$, we can find the magnetic moment of the magnet.
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