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78-446: The magnitude of Earth's magnetic field at its surface ranges from 25 to 65 μT (0.25 to 0.65 G). As an approximation, it is represented by a field of a magnetic dipole currently tilted at an angle of about 11° with respect to Earth's rotational axis, as if there were an enormous bar magnet placed at that angle through the center of Earth. The North geomagnetic pole ( Ellesmere Island , Nunavut , Canada) actually represents

156-472: A 1/ r rate of decrease, dipole moments have a 1/ r rate, quadrupole moments have a 1/ r rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipole term, it dominates at large distances. Therefore, at large distances any magnetic source looks like a dipole of the same magnetic moment . Magnetic dip Magnetic dip , dip angle, or magnetic inclination

234-450: A ring current . This current reduces the magnetic field at the Earth's surface. Particles that penetrate the ionosphere and collide with the atoms there give rise to the lights of the aurorae while also emitting X-rays . The varying conditions in the magnetosphere, known as space weather , are largely driven by solar activity. If the solar wind is weak, the magnetosphere expands; while if it

312-467: A current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is where δ ( r ) is the Dirac delta function in three dimensions. Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole. If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping

390-413: A permanent magnetic moment. This remanent magnetization , or remanence , can be acquired in more than one way. In lava flows , the direction of the field is "frozen" in small minerals as they cool, giving rise to a thermoremanent magnetization . In sediments, the orientation of magnetic particles acquires a slight bias towards the magnetic field as they are deposited on an ocean floor or lake bottom. This

468-412: A presently accelerating rate—10 kilometres (6.2 mi) per year at the beginning of the 1900s, up to 40 kilometres (25 mi) per year in 2003, and since then has only accelerated. The Earth's magnetic field is believed to be generated by electric currents in the conductive iron alloys of its core, created by convection currents due to heat escaping from the core. The Earth and most of the planets in

546-489: A region can be represented by a chart with isogonic lines (contour lines with each line representing a fixed declination). Components of the Earth's magnetic field at the surface from the World Magnetic Model for 2020. Near the surface of the Earth, its magnetic field can be closely approximated by the field of a magnetic dipole positioned at the center of the Earth and tilted at an angle of about 11° with respect to

624-455: A simple compass can remain useful for navigation. Using magnetoreception , various other organisms, ranging from some types of bacteria to pigeons, use the Earth's magnetic field for orientation and navigation. At any location, the Earth's magnetic field can be represented by a three-dimensional vector. A typical procedure for measuring its direction is to use a compass to determine the direction of magnetic North. Its angle relative to true North

702-586: A third of NASA's satellites. The largest documented storm, the Carrington Event , occurred in 1859. It induced currents strong enough to disrupt telegraph lines, and aurorae were reported as far south as Hawaii. The geomagnetic field changes on time scales from milliseconds to millions of years. Shorter time scales mostly arise from currents in the ionosphere ( ionospheric dynamo region ) and magnetosphere, and some changes can be traced to geomagnetic storms or daily variations in currents. Changes over time scales of

780-504: A year or more mostly reflect changes in the Earth's interior , particularly the iron-rich core . Frequently, the Earth's magnetosphere is hit by solar flares causing geomagnetic storms, provoking displays of aurorae. The short-term instability of the magnetic field is measured with the K-index . Data from THEMIS show that the magnetic field, which interacts with the solar wind, is reduced when

858-456: Is 1–2 Earth radii out while the outer belt is at 4–7 Earth radii. The plasmasphere and Van Allen belts have partial overlap, with the extent of overlap varying greatly with solar activity. As well as deflecting the solar wind, the Earth's magnetic field deflects cosmic rays , high-energy charged particles that are mostly from outside the Solar System . Many cosmic rays are kept out of

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936-554: Is amplified with the proximity to either magnetic pole. To compensate for turning errors, pilots in the Northern Hemisphere will have to "undershoot" the turn when turning north, stopping the turn prior to the compass rotating to the correct heading; and "overshoot" the turn when turning south by stopping later than the compass. The effect is the opposite in the Southern Hemisphere. The acceleration errors occur because

1014-543: Is approximately dipolar, with an axis that is nearly aligned with the rotational axis, occasionally the North and South geomagnetic poles trade places. Evidence for these geomagnetic reversals can be found in basalts , sediment cores taken from the ocean floors, and seafloor magnetic anomalies. Reversals occur nearly randomly in time, with intervals between reversals ranging from less than 0.1 million years to as much as 50 million years. The most recent geomagnetic reversal, called

1092-447: Is called compositional convection . A Coriolis effect , caused by the overall planetary rotation, tends to organize the flow into rolls aligned along the north–south polar axis. A dynamo can amplify a magnetic field, but it needs a "seed" field to get it started. For the Earth, this could have been an external magnetic field. Early in its history the Sun went through a T-Tauri phase in which

1170-430: Is called detrital remanent magnetization . Thermoremanent magnetization is the main source of the magnetic anomalies around mid-ocean ridges. As the seafloor spreads, magma wells up from the mantle , cools to form new basaltic crust on both sides of the ridge, and is carried away from it by seafloor spreading. As it cools, it records the direction of the Earth's field. When the Earth's field reverses, new basalt records

1248-446: Is distorted further out by the solar wind. This is a stream of charged particles leaving the Sun's corona and accelerating to a speed of 200 to 1000 kilometres per second. They carry with them a magnetic field, the interplanetary magnetic field (IMF). The solar wind exerts a pressure, and if it could reach Earth's atmosphere it would erode it. However, it is kept away by the pressure of

1326-406: Is generally reported in microteslas (μT), with 1 G = 100 μT. A nanotesla is also referred to as a gamma (γ). The Earth's field ranges between approximately 22 and 67 μT (0.22 and 0.67 G). By comparison, a strong refrigerator magnet has a field of about 10,000 μT (100 G). A map of intensity contours is called an isodynamic chart . As the World Magnetic Model shows,

1404-406: Is in the opposite direction. The torque can be obtained from the formula The magnetic scalar potential ψ produced by a finite source, but external to it, can be represented by a multipole expansion . Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance r from the source. Monopole moments have

1482-407: Is shown below . Declination is positive for an eastward deviation of the field relative to true north. It can be estimated by comparing the magnetic north–south heading on a compass with the direction of a celestial pole . Maps typically include information on the declination as an angle or a small diagram showing the relationship between magnetic north and true north. Information on declination for

1560-585: Is shown in the image. This forms the basis of magnetostratigraphy , a geophysical correlation technique that can be used to date both sedimentary and volcanic sequences as well as the seafloor magnetic anomalies. Paleomagnetic studies of Paleoarchean lava in Australia and conglomerate in South Africa have concluded that the magnetic field has been present since at least about 3,450  million years ago . In 2024 researchers published evidence from Greenland for

1638-458: Is strong, it compresses the magnetosphere and more of it gets in. Periods of particularly intense activity, called geomagnetic storms , can occur when a coronal mass ejection erupts above the Sun and sends a shock wave through the Solar System. Such a wave can take just two days to reach the Earth. Geomagnetic storms can cause a lot of disruption; the "Halloween" storm of 2003 damaged more than

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1716-419: Is the declination ( D ) or variation . Facing magnetic North, the angle the field makes with the horizontal is the inclination ( I ) or magnetic dip . The intensity ( F ) of the field is proportional to the force it exerts on a magnet. Another common representation is in X (North), Y (East) and Z (Down) coordinates. The intensity of the field is often measured in gauss (G) , but

1794-519: Is the angle made with the horizontal by Earth's magnetic field lines . This angle varies at different points on Earth's surface. Positive values of inclination indicate that the magnetic field of Earth is pointing downward, into Earth, at the point of measurement, and negative values indicate that it is pointing upward. The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in

1872-436: Is the latitude of the point on Earth's surface. The phenomenon is especially important in aviation. Magnetic compasses on airplanes are made so that the center of gravity is significantly lower than the pivot point. As a result, the vertical component of the magnetic force is too weak to tilt the compass card significantly out of the horizontal plane, thus minimizing the dip angle shown in the compass. However, this also causes

1950-481: The Boothia Peninsula in 1831 to 600 kilometres (370 mi) from Resolute Bay in 2001. The magnetic equator is the line where the inclination is zero (the magnetic field is horizontal). The global definition of the Earth's field is based on a mathematical model. If a line is drawn through the center of the Earth, parallel to the moment of the best-fitting magnetic dipole, the two positions where it intersects

2028-501: The Brunhes–Matuyama reversal , occurred about 780,000 years ago. A related phenomenon, a geomagnetic excursion , takes the dipole axis across the equator and then back to the original polarity. The Laschamp event is an example of an excursion, occurring during the last ice age (41,000 years ago). The past magnetic field is recorded mostly by strongly magnetic minerals , particularly iron oxides such as magnetite , that can carry

2106-466: The North and South Magnetic Poles abruptly switch places. These reversals of the geomagnetic poles leave a record in rocks that are of value to paleomagnetists in calculating geomagnetic fields in the past. Such information in turn is helpful in studying the motions of continents and ocean floors. The magnetosphere is defined by the extent of Earth's magnetic field in space or geospace . It extends above

2184-479: The electric dipole , but the analogy is not perfect. In particular, a true magnetic monopole , the magnetic analogue of an electric charge , has never been observed in nature. However, magnetic monopole quasiparticles have been observed as emergent properties of certain condensed matter systems. Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles . Because magnetic monopoles do not exist,

2262-476: The electrical conductivity σ and the permeability μ . The term ∂ B /∂ t is the partial derivative of the field with respect to time; ∇ is the Laplace operator , ∇× is the curl operator , and × is the vector product . The first term on the right hand side of the induction equation is a diffusion term. In a stationary fluid, the magnetic field declines and any concentrations of field spread out. If

2340-402: The ionosphere , several tens of thousands of kilometres into space , protecting Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer that protects Earth from harmful ultraviolet radiation . Earth's magnetic field deflects most of the solar wind, whose charged particles would otherwise strip away

2418-401: The Earth's dynamo shut off, the dipole part would disappear in a few tens of thousands of years. In a perfect conductor ( σ = ∞ {\displaystyle \sigma =\infty \;} ), there would be no diffusion. By Lenz's law , any change in the magnetic field would be immediately opposed by currents, so the flux through a given volume of fluid could not change. As

Earth's magnetic field - Misplaced Pages Continue

2496-419: The Earth's magnetic field cycles with intensity every 200 million years. The lead author stated that "Our findings, when considered alongside the existing datasets, support the existence of an approximately 200-million-year-long cycle in the strength of the Earth's magnetic field related to deep Earth processes." The inclination is given by an angle that can assume values between −90° (up) to 90° (down). In

2574-432: The Earth's magnetic field. The magnetopause , the area where the pressures balance, is the boundary of the magnetosphere. Despite its name, the magnetosphere is asymmetric, with the sunward side being about 10  Earth radii out but the other side stretching out in a magnetotail that extends beyond 200 Earth radii. Sunward of the magnetopause is the bow shock , the area where the solar wind slows abruptly. Inside

2652-437: The Earth's surface are called the North and South geomagnetic poles. If the Earth's magnetic field were perfectly dipolar, the geomagnetic poles and magnetic dip poles would coincide and compasses would point towards them. However, the Earth's field has a significant non-dipolar contribution, so the poles do not coincide and compasses do not generally point at either. Earth's magnetic field, predominantly dipolar at its surface,

2730-565: The Solar System by the Sun's magnetosphere, or heliosphere . By contrast, astronauts on the Moon risk exposure to radiation. Anyone who had been on the Moon's surface during a particularly violent solar eruption in 2005 would have received a lethal dose. Some of the charged particles do get into the magnetosphere. These spiral around field lines, bouncing back and forth between the poles several times per second. In addition, positive ions slowly drift westward and negative ions drift eastward, giving rise to

2808-400: The Solar System, as well as the Sun and other stars, all generate magnetic fields through the motion of electrically conducting fluids. The Earth's field originates in its core. This is a region of iron alloys extending to about 3400 km (the radius of the Earth is 6370 km). It is divided into a solid inner core , with a radius of 1220 km, and a liquid outer core . The motion of

2886-715: The South pole of Earth's magnetic field, and conversely the South geomagnetic pole corresponds to the north pole of Earth's magnetic field (because opposite magnetic poles attract and the north end of a magnet, like a compass needle, points toward Earth's South magnetic field. While the North and South magnetic poles are usually located near the geographic poles, they slowly and continuously move over geological time scales, but sufficiently slowly for ordinary compasses to remain useful for navigation. However, at irregular intervals averaging several hundred thousand years, Earth's field reverses and

2964-429: The airplane's compass to give erroneous readings during banked turns (turning error) and airspeed changes (acceleration error). Magnetic dip shifts the center of gravity of the compass card, causing temporary inaccurate readings when turning north or south. As the aircraft turns, the force that results from the magnetic dip causes the float assembly to swing in the same direction that the float turns. This compass error

3042-404: The basis for magnetostratigraphy , a way of dating rocks and sediments. The field also magnetizes the crust, and magnetic anomalies can be used to search for deposits of metal ores . Humans have used compasses for direction finding since the 11th century A.D. and for navigation since the 12th century. Although the magnetic declination does shift with time, this wandering is slow enough that

3120-508: The compass card tilts on its mount when under acceleration. In the Northern Hemisphere, when accelerating on either an easterly or westerly heading, the error appears as a turn indication toward the north. When decelerating on either of these headings, the compass indicates a turn toward the south. The effect is the opposite in the Southern Hemisphere. Compass needles are often weighted during manufacture to compensate for magnetic dip, so that they will balance roughly horizontally. This balancing

3198-543: The correct plane. The value can be measured more reliably with a special instrument typically known as a dip circle . Dip angle was discovered by the German engineer Georg Hartmann in 1544. A method of measuring it with a dip circle was described by Robert Norman in England in 1581. Magnetic dip results from the tendency of a magnet to align itself with lines of magnetic field. As Earth's magnetic field lines are not parallel to

Earth's magnetic field - Misplaced Pages Continue

3276-435: The current strength are within the normal range of variation, as shown by the record of past magnetic fields recorded in rocks. The nature of Earth's magnetic field is one of heteroscedastic (seemingly random) fluctuation. An instantaneous measurement of it, or several measurements of it across the span of decades or centuries, are not sufficient to extrapolate an overall trend in the field strength. It has gone up and down in

3354-459: The electric and magnetic fields exert a force on the charges that are flowing in currents (the Lorentz force ). These effects can be combined in a partial differential equation for the magnetic field called the magnetic induction equation , where u is the velocity of the fluid; B is the magnetic B-field; and η = 1/σμ is the magnetic diffusivity , which is the reciprocal of the product of

3432-428: The existence of the magnetic field as early as 3,700 million years ago. Starting in the late 1800s and throughout the 1900s and later, the overall geomagnetic field has become weaker; the present strong deterioration corresponds to a 10–15% decline and has accelerated since 2000; geomagnetic intensity has declined almost continuously from a maximum 35% above the modern value, from circa year 1 AD. The rate of decrease and

3510-815: The field B c = − μ o ∇ ϕ c = μ o 4 π [ 3 r ^ ( r ^ ⋅ m ) − m r 3 ] {\displaystyle {\textbf {B}}_{c}=-\mu _{o}\nabla \phi _{c}={\frac {\mu _{o}}{4\pi }}{\big [}{\frac {3{\hat {\textbf {r}}}({\hat {\textbf {r}}}\cdot {\textbf {m}})-{\textbf {m}}}{r^{3}}}{\big ]}} for magnetic moment m {\displaystyle {\textbf {m}}} and position vector r {\displaystyle {\textbf {r}}} on Earth's surface. From here it can be shown that

3588-420: The fluid is sustained by convection , motion driven by buoyancy . The temperature increases towards the center of the Earth, and the higher temperature of the fluid lower down makes it buoyant. This buoyancy is enhanced by chemical separation: As the core cools, some of the molten iron solidifies and is plated to the inner core. In the process, lighter elements are left behind in the fluid, making it lighter. This

3666-428: The fluid moved, the magnetic field would go with it. The theorem describing this effect is called the frozen-in-field theorem . Even in a fluid with a finite conductivity, new field is generated by stretching field lines as the fluid moves in ways that deform it. This process could go on generating new field indefinitely, were it not that as the magnetic field increases in strength, it resists fluid motion. The motion of

3744-421: The geodynamo. The average magnetic field in the Earth's outer core was calculated to be 25 gauss, 50 times stronger than the field at the surface. Magnetic dipole In electromagnetism , a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of

3822-434: The inclination I {\displaystyle I} as defined above satisfies (from tan ⁡ I = B r / B θ {\displaystyle \tan I=B_{r}/B_{\theta }} ) tan ⁡ I = 2 tan ⁡ λ {\displaystyle \tan I=2\tan \lambda } where λ {\displaystyle \lambda }

3900-583: The inclination. The inclination of the Earth's field is 90° (downwards) at the North Magnetic Pole and –90° (upwards) at the South Magnetic Pole. The two poles wander independently of each other and are not directly opposite each other on the globe. Movements of up to 40 kilometres (25 mi) per year have been observed for the North Magnetic Pole. Over the last 180 years, the North Magnetic Pole has been migrating northwestward, from Cape Adelaide in

3978-537: The intensity tends to decrease from the poles to the equator. A minimum intensity occurs in the South Atlantic Anomaly over South America while there are maxima over northern Canada, Siberia, and the coast of Antarctica south of Australia. The intensity of the magnetic field is subject to change over time. A 2021 paleomagnetic study from the University of Liverpool contributed to a growing body of evidence that

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4056-403: The interior. The pattern of flow is organized by the rotation of the Earth and the presence of the solid inner core. The mechanism by which the Earth generates a magnetic field is known as a geodynamo . The magnetic field is generated by a feedback loop: current loops generate magnetic fields ( Ampère's circuital law ); a changing magnetic field generates an electric field ( Faraday's law ); and

4134-410: The last few centuries. The direction and intensity of the dipole change over time. Over the last two centuries the dipole strength has been decreasing at a rate of about 6.3% per century. At this rate of decrease, the field would be negligible in about 1600 years. However, this strength is about average for the last 7 thousand years, and the current rate of change is not unusual. A prominent feature in

4212-421: The liquid in the outer core is driven by heat flow from the inner core, which is about 6,000 K (5,730 °C; 10,340 °F), to the core-mantle boundary , which is about 3,800 K (3,530 °C; 6,380 °F). The heat is generated by potential energy released by heavier materials sinking toward the core ( planetary differentiation , the iron catastrophe ) as well as decay of radioactive elements in

4290-477: The magnet is suspended so it can turn freely. Since opposite poles attract, the North Magnetic Pole of the Earth is really the south pole of its magnetic field (the place where the field is directed downward into the Earth). The positions of the magnetic poles can be defined in at least two ways: locally or globally. The local definition is the point where the magnetic field is vertical. This can be determined by measuring

4368-413: The magnetic field at a large distance from any static magnetic source looks like the field of a dipole with the same dipole moment. For higher-order sources (e.g. quadrupoles ) with no dipole moment, their field decays towards zero with distance faster than a dipole field does. In classical physics , the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as

4446-639: The magnetic field once shifted at a rate of up to 6° per day at some time in Earth's history, a surprising result. However, in 2014 one of the original authors published a new study which found the results were actually due to the continuous thermal demagnitization of the lava, not to a shift in the magnetic field. In July 2020 scientists report that analysis of simulations and a recent observational field model show that maximum rates of directional change of Earth's magnetic field reached ~10° per year – almost 100 times faster than current changes and 10 times faster than previously thought. Although generally Earth's field

4524-406: The magnetic moment aligned with the z-axis, then the field strength can more simply be expressed as The two models for a dipole (current loop and magnetic poles), give the same predictions for the magnetic field far from the source. However, inside the source region they give different predictions. The magnetic field between poles is in the opposite direction to the magnetic moment (which points from

4602-465: The magnetic orientation is aligned between Sun and Earth – opposite to the previous hypothesis. During forthcoming solar storms, this could result in blackouts and disruptions in artificial satellites . Changes in Earth's magnetic field on a time scale of a year or more are referred to as secular variation . Over hundreds of years, magnetic declination is observed to vary over tens of degrees. The animation shows how global declinations have changed over

4680-601: The magnetic pole limit, and hence the magnetic field strength (or strength of the H-field) is The magnetic field strength is symmetric under rotations about the axis of the magnetic moment. In spherical coordinates, with z ^ = r ^ cos ⁡ θ − θ ^ sin ⁡ θ {\displaystyle \mathbf {\hat {z}} =\mathbf {\hat {r}} \cos \theta -{\boldsymbol {\hat {\theta }}}\sin \theta } , and with

4758-478: The magnetosphere is the plasmasphere , a donut-shaped region containing low-energy charged particles, or plasma . This region begins at a height of 60 km, extends up to 3 or 4 Earth radii, and includes the ionosphere. This region rotates with the Earth. There are also two concentric tire-shaped regions, called the Van Allen radiation belts , with high-energy ions (energies from 0.1 to 10  MeV ). The inner belt

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4836-400: The negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right (above for mobile users)). Clearly, the limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material. If a magnetic dipole is formed by making

4914-701: The non-dipolar part of the secular variation is a westward drift at a rate of about 0.2° per year. This drift is not the same everywhere and has varied over time. The globally averaged drift has been westward since about 1400 AD but eastward between about 1000 AD and 1400 AD. Changes that predate magnetic observatories are recorded in archaeological and geological materials. Such changes are referred to as paleomagnetic secular variation or paleosecular variation (PSV) . The records typically include long periods of small change with occasional large changes reflecting geomagnetic excursions and reversals. A 1995 study of lava flows on Steens Mountain , Oregon appeared to suggest

4992-434: The north poles, it must be attracted to the south pole of Earth's magnet. The dipolar field accounts for 80–90% of the field in most locations. Historically, the north and south poles of a magnet were first defined by the Earth's magnetic field, not vice versa, since one of the first uses for a magnet was as a compass needle. A magnet's North pole is defined as the pole that is attracted by the Earth's North Magnetic Pole when

5070-477: The northern hemisphere, the field points downwards. It is straight down at the North Magnetic Pole and rotates upwards as the latitude decreases until it is horizontal (0°) at the magnetic equator. It continues to rotate upwards until it is straight up at the South Magnetic Pole. Inclination can be measured with a dip circle . An isoclinic chart (map of inclination contours) for the Earth's magnetic field

5148-442: The ozone layer that protects the Earth from harmful ultraviolet radiation. One stripping mechanism is for gas to be caught in bubbles of the magnetic field, which are ripped off by solar winds. Calculations of the loss of carbon dioxide from the atmosphere of Mars , resulting from scavenging of ions by the solar wind, indicate that the dissipation of the magnetic field of Mars caused a near total loss of its atmosphere . The study of

5226-418: The past for unknown reasons. Also, noting the local intensity of the dipole field (or its fluctuation) is insufficient to characterize Earth's magnetic field as a whole, as it is not strictly a dipole field. The dipole component of Earth's field can diminish even while the total magnetic field remains the same or increases. The Earth's magnetic north pole is drifting from northern Canada towards Siberia with

5304-421: The past magnetic field of the Earth is known as paleomagnetism. The polarity of the Earth's magnetic field is recorded in igneous rocks , and reversals of the field are thus detectable as "stripes" centered on mid-ocean ridges where the sea floor is spreading, while the stability of the geomagnetic poles between reversals has allowed paleomagnetism to track the past motion of continents. Reversals also provide

5382-411: The points having zero dip is called the magnetic equator or aclinic line . The inclination I {\displaystyle I} is defined locally for the magnetic field due to Earth's core, and has a positive value if the field points below the horizontal (i.e. into Earth). Here we show how to determine the value of I {\displaystyle I} at a given latitude, following

5460-400: The product of magnetic pole-charge and distance constant, the limiting field is These fields are related by B = μ 0 ( H + M ) , where is the magnetization . The force F exerted by one dipole moment m 1 on another m 2 separated in space by a vector r can be calculated using: or where r is the distance between dipoles. The force acting on m 1

5538-414: The reversed direction. The result is a series of stripes that are symmetric about the ridge. A ship towing a magnetometer on the surface of the ocean can detect these stripes and infer the age of the ocean floor below. This provides information on the rate at which seafloor has spread in the past. Radiometric dating of lava flows has been used to establish a geomagnetic polarity time scale , part of which

5616-409: The rotational axis of the Earth. The dipole is roughly equivalent to a powerful bar magnet , with its south pole pointing towards the geomagnetic North Pole. This may seem surprising, but the north pole of a magnet is so defined because, if allowed to rotate freely, it points roughly northward (in the geographic sense). Since the north pole of a magnet attracts the south poles of other magnets and repels

5694-491: The second means the potential satisfies the Laplace equation ∇ 2 ϕ c = 0 {\displaystyle \nabla ^{2}\phi _{c}=0} . Solving to leading order gives the magnetic dipole potential ϕ c = m ⋅ r 4 π r 3 {\displaystyle \phi _{c}={\frac {{\textbf {m}}\cdot {\textbf {r}}}{4\pi r^{3}}}} and hence

5772-410: The solar wind would have had a magnetic field orders of magnitude larger than the present solar wind. However, much of the field may have been screened out by the Earth's mantle. An alternative source is currents in the core-mantle boundary driven by chemical reactions or variations in thermal or electric conductivity. Such effects may still provide a small bias that are part of the boundary conditions for

5850-461: The source shrinks to a point while keeping the magnetic moment m constant. For the current loop, this limit is most easily derived from the vector potential : where μ 0 is the vacuum permeability constant and 4 π r is the surface of a sphere of radius r . The magnetic flux density (strength of the B-field) is then Alternatively one can obtain the scalar potential first from

5928-411: The subscript c {\displaystyle c} denotes the core as the origin of these fields. The first means we can introduce the scalar potential ϕ c {\displaystyle \phi _{c}} such that H c = − ∇ ϕ c {\displaystyle {\textbf {H}}_{c}=-\nabla \phi _{c}} , while

6006-586: The surface, the north end of a compass needle will point upward in the Southern Hemisphere (negative dip) or downward in the Northern Hemisphere (positive dip). The range of dip is from -90 degrees (at the South Magnetic Pole ) to +90 degrees (at the North Magnetic Pole ). Contour lines along which the dip measured at Earth's surface is equal are referred to as isoclinic lines . The locus of

6084-568: The treatment given by Fowler. Outside Earth's core we consider Maxwell's equations in a vacuum, ∇ × H c = 0 {\displaystyle \nabla \times {\textbf {H}}_{c}={\textbf {0}}} and ∇ ⋅ B c = 0 {\displaystyle \nabla \cdot {\textbf {B}}_{c}=0} where B c = μ 0 H c {\displaystyle {\textbf {B}}_{c}=\mu _{0}{\textbf {H}}_{c}} and

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