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57-803: The earth inductor compass was first patented by Donald M. Bliss in 1912 and further refined in the 1920s by Paul R. Heyl and Lyman James Briggs of the United States National Bureau of Standards , and in 1924 by Morris Titterington at the Pioneer Instrument Company in Brooklyn, New York . Heyl and Briggs were awarded the Magellan Medal of the American Philosophical Society for this work in 1922. Designed to compensate for

114-473: A magnetic monopole is a hypothetical particle (or class of particles) that physically has only one magnetic pole (either a north pole or a south pole). In other words, it would possess a "magnetic charge" analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Some theories (such as Grand Unified Theories ) have predicted

171-459: A magnetometer . Important classes of magnetometers include using induction magnetometers (or search-coil magnetometers) which measure only varying magnetic fields, rotating coil magnetometers , Hall effect magnetometers, NMR magnetometers , SQUID magnetometers , and fluxgate magnetometers . The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around

228-461: A distance of about 2,000 miles (3,200 km) – he was able to navigate with a cumulative error of about 10 miles (16 km) in landfall, or about one half of one percent of the distance travelled, by computing his heading at hourly intervals for a dead reckoning estimate of position. Bliss' original design consisted of two armatures spinning on a single vertical axle. One armature was connected to commutators that were 90 degrees offset from

285-419: A field line produce synchrotron radiation that is detectable in radio waves . The finest precision for a magnetic field measurement was attained by Gravity Probe B at 5 aT ( 5 × 10  T ). The field can be visualized by a set of magnetic field lines , that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at

342-409: A large number of points (or at every point in space). Then, mark each location with an arrow (called a vector ) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and

399-420: A magnetic H -field is produced by fictitious magnetic charges that are spread over the surface of each pole. These magnetic charges are in fact related to the magnetization field M . The H -field, therefore, is analogous to the electric field E , which starts at a positive electric charge and ends at a negative electric charge. Near the north pole, therefore, all H -field lines point away from

456-503: A magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics , the term magnetic field is used for two distinct but closely related vector fields denoted by the symbols B and H . In the International System of Units , the unit of B , magnetic flux density,

513-424: A magnetized material, the quantities on each side of this equation differ by the magnetization field of the material. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin . Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force , one of

570-429: A magnetized object is divided in half, a new pole appears on the surface of each piece, so each has a pair of complementary poles. The magnetic pole model does not account for magnetism that is produced by electric currents, nor the inherent connection between angular momentum and magnetism. The pole model usually treats magnetic charge as a mathematical abstraction, rather than a physical property of particles. However,

627-402: A north and a south pole. The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m ). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet. For simple magnets, m points in

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684-603: A redetermination of Newton's constant of gravitation using a torsion balance. In 1928, Heyl served as president of the Philosophical Society of Washington . He retired form the NBS in 1942. He won the Potts medal in 1943. He married Lucy Knight Daugherty; they had two daughters, one of whom died in infancy. Magnetic field A magnetic field (sometimes called B-field ) is a physical field that describes

741-500: A small distance vector d , such that m = q m   d . The magnetic pole model predicts correctly the field H both inside and outside magnetic materials, in particular the fact that H is opposite to the magnetization field M inside a permanent magnet. Since it is based on the fictitious idea of a magnetic charge density , the pole model has limitations. Magnetic poles cannot exist apart from each other as electric charges can, but always come in north–south pairs. If

798-452: A small magnet is proportional both to the applied magnetic field and to the magnetic moment m of the magnet: τ = m × B = μ 0 m × H , {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} =\mu _{0}\mathbf {m} \times \mathbf {H} ,\,} where × represents the vector cross product . This equation includes all of

855-408: A torque proportional to the distance (perpendicular to the force) between them. With the definition of m as the pole strength times the distance between the poles, this leads to τ = μ 0 m H sin  θ , where μ 0 is a constant called the vacuum permeability , measuring 4π × 10 V · s /( A · m ) and θ is the angle between H and m . Mathematically, the torque τ on

912-501: Is tesla (symbol: T). The Gaussian-cgs unit of B is the gauss (symbol: G). (The conversion is 1 T ≘ 10000 G. ) One nanotesla corresponds to 1 gamma (symbol: γ). The magnetic H field is defined: H ≡ 1 μ 0 B − M {\displaystyle \mathbf {H} \equiv {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} } where μ 0 {\displaystyle \mu _{0}}

969-557: Is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) into regions of higher magnetic field. Any non-uniform magnetic field, whether caused by permanent magnets or electric currents, exerts a force on a small magnet in this way. The details of the Amperian loop model are different and more complicated but yield the same result: that magnetic dipoles are attracted/repelled into regions of higher magnetic field. Mathematically,

1026-491: Is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below. The first term in

1083-417: Is no net force on that magnet since the force is opposite for opposite poles. If, however, the magnetic field of the first magnet is nonuniform (such as the H near one of its poles), each pole of the second magnet sees a different field and is subject to a different force. This difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque. This

1140-422: Is particularly true for magnetic fields, such as those due to electric currents, that are not generated by magnetic materials. A realistic model of magnetism is more complicated than either of these models; neither model fully explains why materials are magnetic. The monopole model has no experimental support. The Amperian loop model explains some, but not all of a material's magnetic moment. The model predicts that

1197-449: Is strictly only valid for magnets of zero size, but is often a good approximation for not too large magnets. The magnetic force on larger magnets is determined by dividing them into smaller regions each having their own m then summing up the forces on each of these very small regions . If two like poles of two separate magnets are brought near each other, and one of the magnets is allowed to turn, it promptly rotates to align itself with

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1254-418: Is that of maximum increase of m · B . The dot product m · B = mB cos( θ ) , where m and B represent the magnitude of the m and B vectors and θ is the angle between them. If m is in the same direction as B then the dot product is positive and the gradient points "uphill" pulling the magnet into regions of higher B -field (more strictly larger m · B ). This equation

1311-550: Is the tesla (in SI base units: kilogram per second squared per ampere), which is equivalent to newton per meter per ampere. The unit of H , magnetic field strength, is ampere per meter (A/m). B and H differ in how they take the medium and/or magnetization into account. In vacuum , the two fields are related through the vacuum permeability , B / μ 0 = H {\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} } ; in

1368-449: Is the vacuum permeability , and M is the magnetization vector . In a vacuum, B and H are proportional to each other. Inside a material they are different (see H and B inside and outside magnetic materials ). The SI unit of the H -field is the ampere per metre (A/m), and the CGS unit is the oersted (Oe). An instrument used to measure the local magnetic field is known as

1425-476: The Barnett effect or magnetization by rotation . Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example. Specifying the force between two small magnets is quite complicated because it depends on the strength and orientation of both magnets and their distance and direction relative to each other. The force is particularly sensitive to rotations of

1482-642: The National Bureau of Standards in Washington D.C. With Lyman J. Briggs , Heyl invented the Heyl–Briggs earth inductor compass . The compass used a spinning electric coil mounted in an airplane to determine the airplane's bearing in relation to the Earth's magnetic field . This invention won for Heyl and Briggs the 1922 Magellan Medal of the American Philosophical Society . At the NBS, Heyl worked on

1539-583: The "magnetic field" written B and H . While both the best names for these fields and exact interpretation of what these fields represent has been the subject of long running debate, there is wide agreement about how the underlying physics work. Historically, the term "magnetic field" was reserved for H while using other terms for B , but many recent textbooks use the term "magnetic field" to describe B as well as or in place of H . There are many alternative names for both (see sidebars). The magnetic field vector B at any point can be defined as

1596-600: The "number" of field lines through a surface. These concepts can be quickly "translated" to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field. Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines". Magnetic field "lines" are also visually displayed in polar auroras , in which plasma particle dipole interactions create visible streaks of light that line up with

1653-591: The Lorentz equation is from the theory of electrostatics , and says that a particle of charge q in an electric field E experiences an electric force: F electric = q E . {\displaystyle \mathbf {F} _{\text{electric}}=q\mathbf {E} .} The second term is the magnetic force: F magnetic = q ( v × B ) . {\displaystyle \mathbf {F} _{\text{magnetic}}=q(\mathbf {v} \times \mathbf {B} ).} Using

1710-522: The area of the loop and depends on the direction of the current using the right-hand rule. An ideal magnetic dipole is modeled as a real magnetic dipole whose area a has been reduced to zero and its current I increased to infinity such that the product m = Ia is finite. This model clarifies the connection between angular momentum and magnetic moment, which is the basis of the Einstein–de Haas effect rotation by magnetization and its inverse,

1767-499: The armature through a universal joint . The armature was mounted on gimbals to prevent it from tilting with the airplane's pitch and roll. Tilting the armature could have changed the angle of the Earth's flux to the armature, resulting in erroneous readings. The gyroscopic effect of the spinning armature also helped to keep it properly aligned. Paul R. Heyl Paul Renno Heyl (1872 in Philadelphia – 22 October 1961)

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1824-452: The charge carriers in a material through the Hall effect . The Earth produces its own magnetic field , which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass . The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force. The first is the electric field , which describes

1881-407: The commutators connected to the other armature. When one set of commutators is aligned with the earth's magnetic field no current is produced, but an offset angle creates a positive or negative current in proportion to the sine of the offset angle. Since the sine of the angle peaks at 90 degrees, a reading could indicate either a certain direction or the exact opposite direction. The solution to this

1938-403: The definition of the cross product, the magnetic force can also be written as a scalar equation: F magnetic = q v B sin ⁡ ( θ ) {\displaystyle F_{\text{magnetic}}=qvB\sin(\theta )} where F magnetic , v , and B are the scalar magnitude of their respective vectors, and θ is the angle between the velocity of

1995-428: The direction of a line drawn from the south to the north pole of the magnet. Flipping a bar magnet is equivalent to rotating its m by 180 degrees. The magnetic field of larger magnets can be obtained by modeling them as a collection of a large number of small magnets called dipoles each having their own m . The magnetic field produced by the magnet then is the net magnetic field of these dipoles; any net force on

2052-408: The existence of magnetic monopoles, but so far, none have been observed. In the model developed by Ampere , the elementary magnetic dipole that makes up all magnets is a sufficiently small Amperian loop with current I and loop area A . The dipole moment of this loop is m = IA . These magnetic dipoles produce a magnetic B -field. The magnetic field of a magnetic dipole is depicted in

2109-411: The figure. From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength. Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current I and an area a . Such a current loop has a magnetic moment of m = I a , {\displaystyle m=Ia,} where the direction of m is perpendicular to

2166-522: The first. In this example, the magnetic field of the stationary magnet creates a magnetic torque on the magnet that is free to rotate. This magnetic torque τ tends to align a magnet's poles with the magnetic field lines. A compass, therefore, turns to align itself with Earth's magnetic field. In terms of the pole model, two equal and opposite magnetic charges experiencing the same H also experience equal and opposite forces. Since these equal and opposite forces are in different locations, this produces

2223-551: The force acting on a stationary charge and gives the component of the force that is independent of motion. The magnetic field, in contrast, describes the component of the force that is proportional to both the speed and direction of charged particles. The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences. There are two different, but closely related vector fields which are both sometimes called

2280-520: The force and torques between two magnets as due to magnetic poles repelling or attracting each other in the same manner as the Coulomb force between electric charges. At the microscopic level, this model contradicts the experimental evidence, and the pole model of magnetism is no longer the typical way to introduce the concept. However, it is still sometimes used as a macroscopic model for ferromagnetism due to its mathematical simplicity. In this model,

2337-408: The force on a small magnet having a magnetic moment m due to a magnetic field B is: F = ∇ ( m ⋅ B ) , {\displaystyle \mathbf {F} ={\boldsymbol {\nabla }}\left(\mathbf {m} \cdot \mathbf {B} \right),} where the gradient ∇ is the change of the quantity m · B per unit distance and the direction

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2394-474: The force on the particle when its velocity is v ; repeat with v in some other direction. Now find a B that makes the Lorentz force law fit all these results—that is the magnetic field at the place in question. The B field can also be defined by the torque on a magnetic dipole, m . τ = m × B {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} } The SI unit of B

2451-414: The four fundamental forces of nature. Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics . Rotating magnetic fields are used in both electric motors and generators . The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits . Magnetic forces give information about

2508-432: The local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow , in that they represent a continuous distribution, and a different resolution would show more or fewer lines. An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as

2565-763: The local direction of Earth's magnetic field. Field lines can be used as a qualitative tool to visualize magnetic forces. In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension , (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. "Unlike" poles of magnets attract because they are linked by many field lines; "like" poles repel because their field lines do not meet, but run parallel, pushing on each other. Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel , that have been magnetized, and they have both

2622-465: The magnet is a result of adding up the forces on the individual dipoles. There are two simplified models for the nature of these dipoles: the magnetic pole model and the Amperian loop model . These two models produce two different magnetic fields, H and B . Outside a material, though, the two are identical (to a multiplicative constant) so that in many cases the distinction can be ignored. This

2679-768: The magnetic influence on moving electric charges , electric currents , and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet 's magnetic field pulls on ferromagnetic materials such as iron , and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism , diamagnetism , and antiferromagnetism , although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of

2736-413: The magnets due to magnetic torque. The force on each magnet depends on its magnetic moment and the magnetic field of the other. To understand the force between magnets, it is useful to examine the magnetic pole model given above. In this model, the H -field of one magnet pushes and pulls on both poles of a second magnet. If this H -field is the same at both poles of the second magnet then there

2793-449: The motion of electrons within an atom are connected to those electrons' orbital magnetic dipole moment , and these orbital moments do contribute to the magnetism seen at the macroscopic level. However, the motion of electrons is not classical, and the spin magnetic moment of electrons (which is not explained by either model) is also a significant contribution to the total moment of magnets. Historically, early physics textbooks would model

2850-444: The north pole (whether inside the magnet or out) while near the south pole all H -field lines point toward the south pole (whether inside the magnet or out). Too, a north pole feels a force in the direction of the H -field while the force on the south pole is opposite to the H -field. In the magnetic pole model, the elementary magnetic dipole m is formed by two opposite magnetic poles of pole strength q m separated by

2907-415: The offset from the intended heading, rather than the full range of compass directions. The revised design allowed the user to rotate the commutators in such a way that zero current would be produced when the craft was traveling in the intended direction. A single galvanometer was then used to show if the pilot was steering too far to the left or to the right. Lindbergh's compass used an anemometer to spin

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2964-442: The particle and the magnetic field. The vector B is defined as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. In other words, [T]he command, "Measure the direction and magnitude of the vector B at such and such a place," calls for the following operations: Take a particle of known charge q . Measure the force on q at rest, to determine E . Then measure

3021-420: The particle's velocity , and × denotes the cross product . The direction of force on the charge can be determined by a mnemonic known as the right-hand rule (see the figure). Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle

3078-401: The vector that, when used in the Lorentz force law , correctly predicts the force on a charged particle at that point: F = q E + q ( v × B ) {\displaystyle \mathbf {F} =q\mathbf {E} +q(\mathbf {v} \times \mathbf {B} )} Here F is the force on the particle, q is the particle's electric charge , v , is

3135-601: The weaknesses of the magnetic compass , the Earth inductor compass provided pilots with a more stable and reliable reference instrument. They were used in the Douglas World Cruisers in 1924 during the Around-the-World flight by the U.S. Army Air Corps . Charles Lindbergh used the compass on his transatlantic flight in the Spirit of St. Louis in 1927. Over the transatlantic leg of his voyage –

3192-498: Was a second armature with commutators offset by 90 degrees to help distinguish the two opposite directions. The direction of travel was read by comparing the indications on two independent galvanometers , one for each armature. The galvanometers had to be calibrated with the correct headings, since the voltage was proportional to the sine of the angle. Readings could be impacted by the armature's speed of rotation and by stray magnetic fields. Later versions simplified readings to show

3249-794: Was an American inventor, physicist, and author. Born in Philadelphia, Heyl earned his PhD in physics in 1899 from the University of Pennsylvania . For several years he taught in high schools in Pennsylvania. In 1907, he won the Franklin Institute 's Boyden Premium. In 1910, he joined the physics staff of the Commercial Research Corporation in New York. In 1920, he was employed as a physicist at

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