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What is The Earth's Magnetism?
What is The Earth's Magnetism?
Earlier we have referred to the magnetic field of the earth. The strength of the earth’s magnetic field varies from place to place on the earth’s surface; its value being of the order of 10–5 T.What causes the earth to have a magnetic field is not clear. Originally the magnetic field was thought of as arising from a giant bar magnet placed approximately along the axis of rotation of the earth and deep in the interior. However, this simplistic picture is certainly not correct. The magnetic field is now thought to arise due to electrical currents produced by convective motion of metallic fluids (consisting mostly of molten iron and nickel) in the outer core of the earth. This is known as the dynamo effect.
The magnetic field lines of the earth resemble that of a (hypothetical) magnetic dipole located at the centre of the earth. The axis of the dipole does not coincide with the axis of rotation of the earth but is presently titled by approximately 11.3° with respect to the later. In this way of looking at it, the magnetic poles are located where the magnetic field lines due to the dipole enter or leave the earth. The location of the north magnetic pole is at a latitude of 79.74° N and a longitude of 71.8° W, a place somewhere in north Canada. The magnetic south pole is at 79.74° S, 108.22° E in the Antarctica.
The pole near the geographic north pole of the earth is called the north magnetic pole. Likewise, the pole near the geographic south pole is called the south magnetic pole. There is some confusion in the nomenclature of the poles. If one looks at the magnetic field lines of the earth (Fig. 5.8), one sees that unlike in the case of a bar magnet, the field lines go into the earth at thenorth magnetic pole (Nm ) and come out from the south magnetic pole (Sm ).
FIGURE 5.8 The earth as a giant magnetic dipole
The convention arose because the magnetic north was the direction to which the north pole of a magnetic needle pointed; the north pole of a magnet was so named as it was the north seeking pole. Thus, in reality, the north magnetic pole behaves like the south pole of a bar magnet inside the earth and vice versa.
EXAMPLE 8
The earth’s magnetic field at the equator is approximately 0.4 G. Estimate the earth’s dipole moment.
SOLUTION
From Eq. (5.7), the equatorial magnetic field is,
\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa % aaleaacaWGfbaabeaakiabg2da9maalaaabaGaeqiVd02aaSbaaSqa % aiaaicdaaeqaaOGaamyBaaqaaiaaisdacqaHapaCcaWGYbWaaWbaaS % qabeaacaaIZaaaaaaaaaa!40C7! {B_E} = \frac{{{\mu _0}m}}{{4\pi {r^3}}}\)
We are given that BE ~ 0.4 G = 4 × 10–5 T. For r, we take the radius of the earth 6.4 × 106 m. Hence,
\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGTb % Gaeyypa0ZaaSaaaeaacaaI0aGaey41aqRaaGymaiaaicdadaahaaWc % beqaaiabgkHiTiaaiwdaaaGccqGHxdaTdaqadaqaaiaaiAdacaGGUa % GaaGinaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacaaI2aaaaaGc % caGLOaGaayzkaaWaaWbaaSqabeaacaaIZaaaaaGcbaGaeqiVd02aaS % baaSqaaiaaicdaaeqaaOGaai4laiaaisdacqaHapaCaaGaeyypa0Ja % aGinaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacaaIYaaaaOGaey % 41aq7aaeWaaeaacaaI2aGaaiOlaiaaisdacqGHxdaTcaaIXaGaaGim % amaaCaaaleqabaGaaGOnaaaaaOGaayjkaiaawMcaamaaCaaaleqaba % GaaG4maaaakiaaykW7caaMc8UaaGPaVpaabmaabaGaeqiVd02aaSba % aSqaaiaaicdaaeqaaOGaai4laiaaisdacqaHapaCcqGH9aqpcaaIXa % GaaGimamaaCaaaleqabaGaeyOeI0IaaG4naaaaaOGaayjkaiaawMca % aaqaaiabg2da9iaaigdacaGGUaGaaGimaiaaiwdacqGHxdaTcaaIXa % GaaGimamaaCaaaleqabaGaaGOmaiaaiodaaaGccaWGbbGaamyBamaa % CaaaleqabaGaaGOmaaaaaaaa!7CFE! \begin{array}{l} m = \frac{{4 \times {{10}^{ - 5}} \times {{\left( {6.4 \times {{10}^6}} \right)}^3}}}{{{\mu _0}/4\pi }} = 4 \times {10^2} \times {\left( {6.4 \times {{10}^6}} \right)^3}\,\,\,\left( {{\mu _0}/4\pi = {{10}^{ - 7}}} \right)\\ = 1.05 \times {10^{23}}A{m^2} \end{array}\)
This is close to the value 8 × 1022 A m2 quoted in geomagnetic texts.
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Magnetic declination and dip
Magnetic declination and dip
Consider a point on the earth’s surface. At such a point, the direction of the longitude circle determines the geographic north-south direction, the line of longitude towards the north pole being the direction of true north. The vertical plane containing the longitude circle and the axis of rotation of the earth is called the geographic meridian. In a similar way, one can define magnetic meridian of a place as the vertical plane which passes through the imaginary line joining the magnetic north and the south poles. This plane would intersect the surface of the earth in a longitude like circle. A magnetic needle, which is free to swing horizontally, would then lie in the magnetic meridian and the north pole of the needle would point towards the magnetic north pole. Since the line joining the magnetic poles is titled with respect to the geographic axis of the earth, the magnetic meridian at a point makes angle with the geographic meridian. This, then, is the angle between the true geographic north and the north shown by a compass needle. This angle is called the magnetic declination or simply declination (Fig. 5.9).
FIGURE 5.9 A magnetic needle free to move in horizontal plane, points toward the magnetic north-south direction.
The declination is greater at higher latitudes and smaller near the equator. The declination in India is small, it being 0°4\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabGioayaafa % aaaa!36C4! 1'\) E at Delhi and 0°5\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabGioayaafa % aaaa!36C4! 8'\) W at Mumbai. Thus, at both these places a magnetic needle shows the true north quite accurately.
There is one more quantity of interest. If a magnetic needle is perfectly balanced about a horizontal axis so that it can swing in a plane of the magnetic meridian, the needle would make an angle with the horizontal (Fig. 5.10). This is known as the angle of dip (also known as inclination).
FIGURE 5.10 The circle is a section through the earth containing the magnetic meridian. The angle between BE and the horizontal component HE is the angle of dip.
Thus, dip is the angle that the total magnetic field BE of the earth makes with the surface of the earth. Figure 5.11 shows the magnetic meridian plane at a point P on the surface of the earth. The plane is a section through the earth. The total magnetic field can be resolved into a horizontal component HE and a vertical component ZE. The angle that BE makes with HE is the angle of dip, I.
FIGURE 5.11 The earth’s magnetic field, BE, its horizontal and vertical components, HE and ZE. Also shown are the declination, D and the inclination or angle of dip, I.
In most of the northern hemisphere, the north pole of the dip needle tilts downwards. Likewise in most of the southern hemisphere, the south pole of the dip needle tilts downwards.
To describe the magnetic field of the earth at a point on its surface, we need to specify three quantities, viz., the declination D, the angle of dip or the inclination I and the horizontal component of the earth’s field HE. These are known as the element of the earth’s magnetic field.
Representing the verticle component by ZE, we have
ZE = BE sinI [5.10(a)]
HE = BE cosI [5.10(b)]
which gives,
\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg % gacaGGUbGaaGPaVlaaykW7caaMc8Uaamysaiabg2da9maalaaabaGa % amOwamaaBaaaleaacaWGfbaabeaaaOqaaiaadIeadaWgaaWcbaGaam % yraaqabaaaaaaa!42EE! \tan \,\,\,I = \frac{{{Z_E}}}{{{H_E}}}\) [5.10(c)]
EXAMPLE 9
In the magnetic meridian of a certain place, the horizontal component of the earth’s magnetic field is 0.26G and the dip angle is 60°. What is the magnetic field of the earth at this location?
Solution
It is given that HE = 0.26 G. From Fig. 5.11, we have
\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaciGGJb % Gaai4BaiaacohacaaMc8UaaGOnaiaaicdadaahaaWcbeqaaiablIHi % Vbaakiabg2da9maalaaabaGaamisamaaBaaaleaacaWGfbaabeaaaO % qaaiaadkeadaWgaaWcbaGaamyraaqabaaaaaGcbaGaamOqamaaBaaa % leaacaWGfbaabeaakiabg2da9maalaaabaGaamisamaaBaaaleaaca % WGfbaabeaaaOqaaiGacogacaGGVbGaai4CaiaaiAdacaaIWaWaaWba % aSqabeaacqWIyiYBaaaaaaGcbaGaeyypa0ZaaSaaaeaacaaIWaGaai % OlaiaaikdacaaI2aaabaWaaeWaaeaacaaIXaGaai4laiaaikdaaiaa % wIcacaGLPaaaaaGaeyypa0JaaGimaiaac6cacaaI1aGaaGOmaiaadE % eaaaaa!58C3! \begin{array}{l} \cos \,{60^ \circ } = \frac{{{H_E}}}{{{B_E}}}\\ {B_E} = \frac{{{H_E}}}{{\cos {{60}^ \circ }}}\\ = \frac{{0.26}}{{\left( {1/2} \right)}} = 0.52G \end{array}\)
WHAT HAPPENS TO MY COMPASS NEEDLES AT THE POLES?
A compass needle consists of a magnetic needle which floats on a pivotal point. When the compass is held level, it points along the direction of the horizontal component of the earth’s magnetic field at the location. Thus, the compass needle would stay along the magnetic meridian of the place. In some places on the earth there are deposits of magnetic minerals which cause the compass needle to deviate from the magnetic meridian. Knowing the magnetic declination at a place allows us to correct the compass to determine the direction of true north.
So what happens if we take our compass to the magnetic pole? At the poles, the magnetic field lines are converging or diverging vertically so that the horizontal component is negligible. If the needle is only capable of moving in a horizontal plane, it can point along any direction, rendering it useless as a direction finder. What one needs in such a case is a dip needle which is a compass pivoted to move in a vertical plane containing the magnetic field of the earth. The needle of the compass then shows the angle which the magnetic field makes with the vertical. At the magnetic poles such a needle will point straight down.
EARTH MAGNETIC FIELD
It must not be assumed that there is a giant bar magnet deep inside the earth which is causing the earth’s magnetic field. Although there are large deposits of iron inside the earth, it is highly unlikely that a large solid block of iron stretches from the magnetic north pole to the magnetic south pole. The earth’s core is very hot and molten, and the ions of iron and nickel are responsible for earth’s magnetism. This hypothesis seems very probable. Moon, which has no molten core, has no magnetic field, Venus has a slower rate of rotation, and a weaker magnetic field, while Jupiter, which has the fastest rotation rate among planets, has a fairly strong magnetic field. However, the precise mode of these circulating currents and the energy needed to sustain them are not very well understood. These are several open questions which form an important area of continuing research.
The variation of the earth’s magnetic field with position is also an interesting area of study. Charged particles emitted by the sun flow towards the earth and beyond, in a stream called the solar wind. Their motion is affected by the earth’s magnetic field, and in turn, they affect the pattern of the earth’s magnetic field. The pattern of magnetic field near the poles is quite different from that in other regions of the earth.
The variation of earth’s magnetic field with time is no less fascinating. There are short term variations taking place over centuries and long term variations taking place over a period of a million years. In a span of 240 years from 1580 to 1820 AD, over which records are available, the magnetic declination at London has been found to change by 3.5°, suggesting that the magnetic poles inside the earth change position with time. On the scale of a million years, the earth’s magnetic fields has been found to reverse its direction. Basalt contains iron, and basalt is emitted during volcanic activity. The little iron magnets inside it align themselves parallel to the magnetic field at that place as the basalt cools and solidifies. Geological studies of basalt containing such pieces of magnetised region have provided evidence for the change of direction of earth’s magnetic field, several times in the past.