What is the unit of measurement for magnetic force?
Magnetometer
Magnetic fields are vector quantities characterized by both strength and direction. The strength of a magnetic field is measured in units of tesla in the SI units, and in gauss in the cgs system of units. 10,000 gauss are equal to one tesla. Measurements of the Earth's magnetic field are often quoted in units of nanotesla (nT), also called a gamma. The Earth's magnetic field can vary from 20,000 to 80,000 nT depending on location, fluctuations in the Earth's magnetic field are on the order of 100 nT, and magnetic field variations due to magnetic anomalies can be in the picotesla (pT) range. "Gaussmeters" and "teslameters" are magnetometers that measure in units of gauss or tesla, respectively. In some contexts, magnetometer is the term used for an instrument that measures fields of less than 1 millitesla (mT) and gaussmeter is used for those measuring greater than 1 mT.
Physics of magnetic resonance imaging
The magnet is the largest and most expensive component of the scanner, and the remainder of the scanner is built around it. The strength of the magnet is measured in teslas (T). Clinical magnets generally have a field strength in the range 0.1–3.0 T, with research systems available up to 9.4 T for human use and 21 T for animal systems.
In the United States, field strengths up to 4 T have been approved by the FDA for clinical use.
Magnetic moment
where N is the newton (the SI unit of force), T is the tesla (the SI unit of magnetic flux density), and J is the joule (the SI unit of energy).
Nuclear magnetic moment
The measured values of "g" for the neutron and the proton are twice their magnetic moment (either the neutron magnetic moment or the proton magnetic moment). In nuclear magneton units, for the neutron and for the proton.
Spin magnetic moment
Just like the "total spin angular momentum" cannot be measured, neither can the "total spin magnetic moment" be measured. Equations (), (), () give the physical observable, that component of the magnetic moment measured along an axis, relative to or along the applied field direction. Assuming a Cartesian coordinate system, conventionally, the "z"-axis is chosen but the observable values of the component of spin angular momentum along all three axes are each ±"ħ"/2. However, in order to obtain the magnitude of the total spin angular momentum, be replaced by its eigenvalue, , where "s" is the spin quantum number. In turn, calculation of the magnitude of the total spin magnetic moment requires that () be replaced by:
Ponderomotive force
The ponderomotive force F is expressed by
which has units of newtons (in SI units) and where "e" is the electrical charge of the particle, "m" is its mass, "ω" is the angular frequency of oscillation of the field, and "E" is the amplitude of the electric field. At low enough amplitudes the magnetic field exerts very little force.
Tesla (unit)
A particle, carrying a charge of one coulomb, and moving perpendicularly through a magnetic field of one tesla, at a speed of one metre per second, experiences a force with magnitude one newton, according to the Lorentz force law. As an SI derived unit, the tesla can also be expressed as
Magnetometer
The gauss, the CGS unit of magnetic flux density was named in his honour, defined as one maxwell per square centimeter; it equals 1×10 tesla (the SI unit).
Magnetic field
where the gradient is the change of the quantity per unit distance and the direction is that of maximum increase of . To understand this equation, note that the dot product , where and represent the magnitude of the and vectors and is the angle between them. If is in the same direction as then the dot product is positive and the gradient points 'uphill' pulling the magnet into regions of higher -field (more strictly larger ). This equation 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 then summing up the forces on each of these very small regions.
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. Mathematically, it is the ratio of magnetization (magnetic moment per unit volume) to the applied magnetizing field intensity . This allows a simple classification of most materials' response to an applied magnetic field into two categories: an alignment with the magnetic field, χ>0, called paramagnetism, or an alignment against the field, χ<0, called diamagnetism.
Magnetoelectric effect
Historically, the first and most studied example of this effect is the linear magnetoelectric effect. Mathematically, while the electric susceptibility formula_1 and magnetic susceptibility formula_2 describe the electric and magnetic polarization responses to an electric, resp. a magnetic field, there is also the possibility of a magnetoelectric susceptibility formula_3 which describes a linear response of the electric polarization to a magnetic field, and vice versa:
The tensor formula_6 must be the same in both equations. Here, P is the electric polarization, M the magnetization, E and H the electric and magnetic fields. The SI Unit of α is [s/m] which can be converted to the practical unit [V/(cm Oe)] by [s/m]=1.1 x10 ε [V/(cm Oe)]. For the CGS unit, [unitless] = 3 x 10 [s/m]/(4 x π)
Magnet
For most engineering applications, MKS (rationalized) or SI (Système International) units are commonly used. Two other sets of units, Gaussian and CGS-EMU, are the same for magnetic properties and are commonly used in physics.
G-force
The unit of measure of acceleration in the International System of Units (SI) is m/s. However, to distinguish acceleration relative to free fall from simple acceleration (rate of change of velocity), the unit g (or g) is often used. One "g" is the acceleration due to gravity at the Earth's surface and is the standard gravity (symbol: "g"), defined as  metres per second squared, or equivalently  newtons of force per kilogram of mass. Note that the "unit definition" does not vary with location—the g-force when standing on the moon is about 0.181 g.
Magnetic field
Often the magnetic field is defined by the force it exerts on a moving charged particle. It is known from experiments in electrostatics that a particle of charge in an electric field experiences a force . However, in other situations, such as when a charged particle moves in the vicinity of a current-carrying wire, the force also depends on the velocity of that particle. The velocity dependent portion can be separated such that the force on the particle satisfies the "Lorentz force law",
Here is the particle's velocity and × denotes the cross product. The vector is termed the magnetic field, and it is "defined" as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. This definition allows the determination of in the following way
Lorentz force velocimetry
The principle of Lorentz force velocimetry is based on measurements of the Lorentz force that occurs due to the flow of a conductive fluid under the influence of a variable magnetic field. According to Faraday's law, when a metal or conductive fluid moves through a magnetic field, eddy currents generate there by electromotive force in zones of maximal magnetic field gradient (in the present case in the inlet and outlet zones). Eddy current in its turn creates induced magnetic field according to Ampère's law. The interaction between eddy currents and total magnetic field gives rise to Lorentz force that breaks the flow. By virtue of Newton's third law "actio=reactio" a force with the same magnitude but opposite direction acts upon its source - permanent magnet. Direct measurement of the magnet's reaction force allows to determine fluid's velocity, since this force is proportional to flow rate. The Lorentz force used in LFV has nothing to do with magnetic attraction or repulsion. It is only due to the eddy currents whose strength depends on the electrical conductivity, the relative velocity between the liquid and the permanent magnet as well as the magnitude of the magnetic field.
Pound (force)
The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.
Astrionics
This device measures the strength of the Earth's magnetic field in one direction. For measurements on all three axes, the device would consist of three orthogonal magnetometers. Given the spacecraft's position, the magnetic field measurements can be compared to a known magnetic field which is given by the International Geomagnetic Reference Field model. Measurements made by magnetometers are affected by noise consisting of alignment error, scale factor errors, and spacecraft electrical activity. For near Earth orbits, the error in the modeled field direction may vary from 0.5 degrees near the Equator to 3 degrees near the magnetic poles, where erratic auroral currents play a large role. The limitation of such a device is that in orbits far from Earth, the magnetic field is too weak and is actually dominated by the interplanetary field which is complicated and unpredictable.
Force between magnets
For purpose of expressing the strength of a permanent magnet in same terms as that of an electromagnet, a permanent magnet is thought of as if it contains small current-loops throughout its volume,
and then the magnetic strength of that magnet is found to be proportional to the current of each loop (in Ampere), and proportional to the surface of each loop (in square meter), and proportional to the density of current-loops in the material (in units per cubic meter), so the dimension of strength of magnetism of a permanent magnet is Ampere times square meter per cubic meter, is Ampere per meter.
Magnetic complex reluctance
Magnetic complex reluctance (SI Unit: H) is a measurement of a passive magnetic circuit (or element within that circuit) dependent on sinusoidal magnetomotive force (SI Unit: At·Wb) and sinusoidal magnetic flux (SI Unit: T·m), and this is determined by deriving the ratio of their complex "effective" amplitudes.[Ref. 1-3]
Ultimate tensile strength
Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the International System of Units (SI), the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix "mega"); or, equivalently to pascals, newtons per square metre (N/m²). A United States customary unit is pounds per square inch (lb/in² or psi), or kilo-pounds per square inch (ksi, or sometimes kpsi), which is equal to 1000 psi; kilo-pounds per square inch are commonly used in one country (US), when measuring tensile strengths.
Force
The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of . The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force.
Magnetic diffusivity
The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number. It has SI units of m²/s and is defined as:
while in Gaussian units it can be defined as
In the above, formula_3 is the permeability of free space, formula_4 is the speed of light, and formula_5 is the electrical conductivity of the material in question. In case of a plasma, this is the conductivity due to Coulomb or neutral collisions: formula_6, where
Inertial measurement unit
An inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the magnetic field surroundings the body, using a combination of accelerometers and gyroscopes, sometimes also magnetometers. IMUs are typically used to maneuver aircraft, including unmanned aerial vehicles (UAVs), among many others, and spacecraft, including satellites and landers. Recent developments allow for the production of IMU-enabled GPS devices. An IMU allows a GPS receiver to work when GPS-signals are unavailable, such as in tunnels, inside buildings, or when electronic interference is present. A wireless IMU is known as a WIMU.
Magnetic tension force
The magnetic tension force is a restoring force (SI unit: Pa·m) that acts to straighten bent magnetic field lines. It equals:
Lorentz force velocimetry
The force measurement system is an important part of the Lorentz force velocimetry. With high resolution force measurement system makes the measurement of even lower conductivity possible.Up to date has the force measurement system continually being developed. At first the pendulum-like setups was used (Figure 5). One of the experimental facilities consists of two high power (410 mT) magnets made of NdFeB suspended by thin wires on both side of channel thereby creating magnetic field perpendicular to the fluid flow, here deflection is measured by interferometer system. The second setup consists of state-of-art weighting balance system (Figure 6) from which is being hanged optimized magnets on the base of Halbach array system. While the total mass of both magnet systems are equal (1 kg), this system induces 3 times higher system response due to arrangement of individual elements in the array and it's interaction with predefined fluid profile. Here use of very sensitive force measuring devices is desirable, since flow velocity is being converted from the very tiny detected Lorentz Force. This force in combination with unavoidable dead weight formula_35 of the magnet (formula_36) is around formula_37. After that, the method of differential force measurement was developed. With this method two balance were used, one with magnet and the other is with same-weight-dummy. In this way the influence of environment would be reduced. Recently, it have been reported that the flow measurements by this method is possible for saltwater flows whose electrical conductivity is as small as 0.06 S/m (range of electrical conductivity of the regular water from tap).
Force meter
A force meter is an instrument to measure the magnitude of a force. This is often just a spring contained within a cylinder that has a scale to mark the extension of the spring produced by the force. In the International System of Units, the unit of force is the newton (symbol N). A force meter that measures force in newtons may be referred to as a newtonmeter.
Magnetic reluctance
Magnetic reluctance is a scalar extensive quantity, akin to electrical resistance. The unit for magnetic reluctance is inverse henry, H.
Magnetic field
where formula_32 is the magnetic flux in the circuit, formula_33 is the magnetomotive force applied to the circuit, and is the reluctance of the circuit. Here the reluctance is a quantity similar in nature to resistance for the flux.
Wien filter
Any charged particle in an electric field will feel a force proportional to the charge and field strength such that formula_1, where F is force, q is charge, and E is electric field strength. Similarly, any particle moving in a magnetic field will feel a force proportional to the velocity and charge of the particle. The force felt by any particle is then equal to formula_2, where F is force, q is the charge on the particle, v is the velocity of the particle, B is the strength of the magnetic field, and formula_3 is the cross product. In the case of a velocity selector, the magnetic field is always at 90 degrees to the velocity and the force is simplified to formula_4 in the direction described by the cross product.
Magnetochemistry
The primary measurement in magnetochemistry is magnetic susceptibility. This measures the strength of interaction on placing the substance in a magnetic field. The volume magnetic susceptibility, represented by the symbol formula_1 is defined by the relationship
where, formula_3 is the magnetization of the material (the magnetic dipole moment per unit volume), measured in amperes per meter ( SI units), and formula_4 is the magnetic field strength, also measured in amperes per meter. Susceptibility is a dimensionless quantity. For chemical applications the molar magnetic susceptibility (χ) is the preferred quantity. It is measured in m·mol (SI) or cm·mol (CGS) and is defined as
where ρ is the density in kg·m (SI) or g·cm (CGS) and "M" is molar mass in kg·mol (SI) or g·mol (CGS). 
A variety of methods are available for the measurement of magnetic susceptibility.When an isolated atom is placed in a magnetic field there is an interaction because each electron in the atom behaves like a magnet, that is, the electron has a magnetic moment. There are two types of interaction.
When the atom is present in a chemical compound its magnetic behaviour is modified by its chemical environment. Measurement of the magnetic moment can give useful chemical information.
G-factor (physics)
A g"-factor (also called g" value or dimensionless magnetic moment) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or nucleus. It is essentially a proportionality constant that relates the observed magnetic moment "μ" of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.
Neutron magnetic moment
The nuclear magneton is the spin magnetic moment of a Dirac particle, a charged, spin 1/2 elementary particle, with a proton's mass "m". In SI units, the nuclear magneton is
Proton magnetic moment
The nuclear magneton is the spin magnetic moment of a Dirac particle, a charged, spin 1/2 elementary particle, with a proton's mass "m". In SI units, the nuclear magneton is
Force between magnets
where the direction of m is normal to the area in a direction determined using the current and the right-hand rule. As such, the SI unit of magnetic dipole moment is ampere meter. More precisely, to account for solenoids with many turns the unit of magnetic dipole moment is Ampere-turn meter.
Lorentz force velocimetry
The secondary currents create a magnetic field formula_10, the secondary magnetic field. The interaction of the primary electric current with the secondary magnetic field gives rise to the Lorentz force on the magnet system
formula_11
The reciprocity principle for the Lorentz force velocimetry states that the electromagnetic forces on the fluid and on the magnet system have the same magnitude and act in opposite direction, namely
The general scaling law that relates the measured force to the unknown velocity can be derived with reference to the simplified situation shown in Fig. 2. Here a small permanent magnet with dipole moment formula_13 is located at a distance formula_14 above a semi-infinite fluid moving with uniform velocity formula_4 parallel to its free surface.
The analysis that leads to the scaling relation can be made quantitative by assuming that the magnet is a point dipole with dipole moment formula_16 whose magnetic field is given by
where formula_18 and formula_19. Assuming a velocity field formula_20 for formula_21, the eddy currents can be computed from Ohm's law for a moving electrically conducting fluid
subject to the boundary conditions formula_23 at formula_24 and formula_25 as formula_26. First, the scalar electric potential is obtained as
from which the electric current density is readily calculated. They are indeed horizontal. Once they are known, the Biot–Savart law can be used to compute the secondary magnetic field formula_28. Finally, the force is given by
where the gradient of formula_30 has to be evaluated at the location of the dipole. For the problem at hand all these steps can be carried out analytically without any approximation leading to the result
This provides us with the estimate
Metrication in the United Kingdom
While the politicians were discussing whether or not to adopt the metric system, British scientists were in the forefront in developing the system. In 1845, a paper by James Prescott Joule proved the equivalence of mechanical and thermal energy, a concept that is vital to the metric system – in SI, power is measured in watts and energy in joules regardless of whether it is mechanical, electrical or thermal.
In 1861, a committee of the British Association for Advancement of Science (BAAS) including William Thomson (later Lord Kelvin), James Clerk Maxwell and Joule among its members was tasked with investigating the "Standards of Electrical Resistance". In their first report (1862), they laid the ground rules for their work – the metric system was to be used and measures of electrical energy must have the same units as measures of mechanical energy. 
In the second report (1863), they introduced the concept of a coherent system of units whereby units of length, mass and time were identified as "fundamental units" (now known as "base units"). 
All other units of measure could be derived (hence "derived units") from these base units.
Bryan Kibble
In 1990, the Mark II watt balance was built, with a view to measuring the Planck constant accurately enough to redefine the S.I. unit of the kilogramme from fundamental constants. Such an instrument equalises one force with another, specifically the weight of a [one-kilogramme, typically] test mass and the force produced by an electric current in a moving coil in a magnetic field. The magnitude of the upward force on the coil is controlled by changes to the current. The power of the moving mass is equal to the product of the current and potential difference measured in the coil, hence the term 'watt' balance (as the S.I. unit of power is the watt (W)).
List of electromagnetism equations
Here subscripts "e" and "m" are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by "q"(Wb) = "μ" "q"(Am).
Magnetic field
where the integral sums over the wire length where vector is the vector line element with direction in the same sense as the current , is the magnetic constant, is the distance between the location of and the location where the magnetic field is calculated, and is a unit vector in the direction of . In the case of a sufficiently long wire, this becomes:
Magnetic circuit
Similar to the way that electromotive force (EMF) drives a current of electrical charge in electrical circuits, magnetomotive force (MMF) 'drives' magnetic flux through magnetic circuits. The term 'magnetomotive force', though, is a misnomer since it is not a force nor is anything moving. It is perhaps better to call it simply MMF. In analogy to the definition of EMF, the magnetomotive force formula_1 around a closed loop is defined as:
Force between magnets
where the gradient ∇ is the change of the quantity m · B per unit distance, and the direction is that of maximum increase of m · B. To understand this equation, note that 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). B represents the strength and direction of the magnetic field. This equation 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 having their own m then summing up the forces on each of these regions.
Magnetic field
In SI units, is measured in teslas (symbol: T) and correspondingly (magnetic flux) is measured in webers (symbol: Wb) so that a flux density of 1 Wb/m is 1 tesla. The SI unit of tesla is equivalent to (newton·second)/(coulomb·metre). In Gaussian-cgs units, is measured in gauss (symbol: G). (The conversion is 1 T = 10000 G.) One nanotesla is equivalent to 1 gamma (symbol: γ). The -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units.
Electric field
The Coulomb force on a charge of magnitude formula_25 at any point in space is equal to the product of the charge and the electric field at that point
The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m); in terms of the SI base units they are kg⋅m⋅s⋅A
Kilogram-force
The gram-force and kilogram-force were never well-defined units until the CGPM adopted a "standard acceleration of gravity" of 980.665 cm/s for this purpose in 1901, though they had been used in low-precision measurements of force before that time.
The kilogram-force has never been a part of the International System of Units (SI), which was introduced in 1960. The SI unit of force is the newton.
Centimetre–gram–second system of units
The practical cgs system is a hybrid system that uses the volt and the ampere as the unit of voltage and current respectively. Doing this avoids the inconveniently large and small quantities that arise for electromagnetic units in the esu and emu systems. This system was at one time widely used by electrical engineers because the volt and amp had been adopted as international standard units by the International Electrical Congress of 1881. As well as the volt and amp, the farad (capacitance), ohm (resistance), coulomb (electric charge), and henry are consequently also used in the practical system and are the same as the SI units. However, intensive properties (that is, anything that is per unit length, area, or volume) will not be the same as SI since the cgs unit of distance is the centimetre. For instance electric field strength is in units of volts per centimetre, magnetic field strength is in oersteds and resistivity is in ohm-cm.
Gurley Precision Instruments
The Gurley unit is a measure of the stiffness of a material. Since the measurement device holds a piece of material vertically and tests the force required to deflect the material a given amount. One Gurley unit is equivalent to one milligram of force
, however the Gurley unit also implies measurement with this apparatus. A related unit, the Taber, is highly correlated but uses a different apparatus (manufactured by Taber Industries) for performing measurements.
Electromagnet
which says that the integral of the magnetizing field H around any closed loop of the field is equal to the sum of the current flowing through the loop. Another equation used, that gives the magnetic field due to each small segment of current, is the Biot–Savart law. Computing the magnetic field and force exerted by ferromagnetic materials is difficult for two reasons. First, because the strength of the field varies from point to point in a complicated way, particularly outside the core and in air gaps, where "fringing fields" and "leakage flux" must be considered. Second, because the magnetic field B and force are nonlinear functions of the current, depending on the nonlinear relation between B and H for the particular core material used. For precise calculations, computer programs that can produce a model of the magnetic field using the finite element method are employed.
Planck constant
The gyromagnetic ratio "γ" is the constant of proportionality between the frequency "ν" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field . It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring "B", but the value for protons in water at is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, "γ"′. The gyromagnetic ratio is related to the shielded proton magnetic moment "μ"′, the spin number "I" ( for protons) and the reduced Planck constant.
The ratio of the shielded proton magnetic moment "μ"′ to the electron magnetic moment "μ" can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio. The value of "μ" in Bohr magnetons is also known: it is half the electron g-factor "g". Hence
A further complication is that the measurement of "γ"′ involves the measurement of an electric current: this is invariably measured in "conventional" amperes rather than in SI amperes, so a conversion factor is required. The symbol "Γ"′ is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value "Γ"′(hi) is of interest in determining the Planck constant.
Substitution gives the expression for the Planck constant in terms of "Γ"′(hi):
Magnetic monopole
What are the units in which magnetic charge would be quantized? Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He considered a point-like magnetic charge whose magnetic field behaves as and is directed in the radial direction, located at the origin. Because the divergence of is equal to zero almost everywhere, except for the locus of the magnetic monopole at , one can locally define the vector potential such that the curl of the vector potential equals the magnetic field .
Magnet
A magnet's magnetic moment (also called magnetic dipole moment and usually denoted μ) is a vector that characterizes the magnet's overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet's south pole to its north pole, and the magnitude relates to how strong and how far apart these poles are. In SI units, the magnetic moment is specified in terms of A·m (amperes times meters squared).
Magnetic field
The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols and . In the International System of Units, is measured in units of amperes per meter and is measured in teslas, which are equivalent to newtons per meter per ampere. and differ in how they account for magnetization. In a vacuum, and are the same aside from units; but in a magnetized material, /formula_1 and differ by the magnetization of the material at that point in the material.
Van der Pauw method
When a charged particle—such as an electron—is placed in a magnetic field, it experiences a Lorentz force proportional to the strength of the field and the velocity at which it is traveling through it. This force is strongest when the direction of motion is perpendicular to the direction of the magnetic field; in this case the force
where formula_25 is the charge on the particle in coulombs, formula_26 the velocity it is traveling at (centimeters per second), and formula_27 the strength of the magnetic field (Wb/cm²). Note that centimeters are often used to measure length in the semiconductor industry, which is why they are used here instead of the SI units of meters.
Force between magnets
The force of one magnetic dipole on another is determined by using the magnetic field of the first dipole given above and determining the force due to the magnetic field on the second dipole using the force equation given above. Using vector notation, the force of a magnetic dipole m on the magnetic dipole m is:
where r is the distance-vector from dipole moment m to dipole moment m, with "r"=||r||. The force acting on m is in opposite direction. As an example the magnetic force for two magnets pointing in the z-direction and aligned on the z-axis and separated by the distance z is:
Force gauge
Test units of force measurements are most commonly newtons or pounds. The peak force is the most common result in force testing applications. It is used to determine if a part is good or not. Some examples of force measurement: door latch, quality of spring, wire testing, strength ... but more complicated tests can be performed like peeling, friction, texture.
Magnetomotive force
The term "magnetomotive force" was coined by Henry Augustus Rowland in 1880. Rowland intended this to indicate a direct analogy with electromotive force. The idea of a magnetic analogy to electromotive force can be found much earlier in the work of Michael Faraday (1791-1867) and it is hinted at by James Clerk Maxwell (1831-1879). However, Rowland coined the term and was the first to make explicit an Ohm's law for magnetic circuits in 1873.
Magnetic anomaly
Magnetic anomalies are generally a small fraction of the magnetic field. The total field ranges from 25,000 to 65,000 nanoteslas (nT). To measure anomalies, magnetometers need a sensitivity of 10 nT or less. There are three main types of magnetometer used to measure magnetic anomalies:In ground-based surveys, measurements are made at a series of stations, typically 15 to 60 m apart. Usually a proton precession magnetometer is used and it is often mounted on a pole. Raising the magnetometer reduces the influence of small ferrous objects that were discarded by humans. To further reduce unwanted signals, they do not carry objects such as keys, knives or compasses. In addition, objects such as motor vehicles, railway lines, and barbed wire fences are avoided. If some such contaminant is overlooked, it often shows up as a sharp spike in the anomaly, so such features are treated with suspicion. The main application for ground-based surveys is detailed search for minerals.
Airborne magnetic surveys are often used in oil surveys to provide preliminary information for seismic surveys. In some countries such as Canada, government agencies have made systematic surveys of large areas. The survey generally involves making a series of parallel runs at a constant height and intervals of anywhere from a hundred meters to several kilometers. These are crossed by occasional tie lines, perpendicular to the main survey, to check for errors. The plane is a source of magnetism, so sensors are either mounted on a boom (as in the figure) or towed behind on a cable. Aeromagnetic surveys have a lower spatial resolution of ground surveys, but this can be an advantage for a regional survey of deeper rocks.
Maxwell (unit)
The unit name honours James Clerk Maxwell, who presented a unified theory of electromagnetism. The "maxwell" was recommended as a CGS unit at the International Electrical Congress held in 1900 at Paris. This practical unit was previously called a "line", reflecting Faraday's conception of the magnetic field as curved lines of magnetic force, which he designated as "line of magnetic induction". "Kiloline" (10 line) and "megaline" (10 line) were sometimes used because 1 line was very small relative to the phenomena that it was used to measure.
Magnetic force microscope
Since the tip is magnetized along a specific direction, it will be sensitive to the component of the magnetic stray field of the sample which is aligned to the same direction. The general equation for a magnetic force (formula_15) acting on a ferromagnetic material is
History of electromagnetic theory
Various units of electricity and magnetism have been adopted and named by representatives of the electrical engineering institutes of the world, which units and names have been confirmed and legalized by the governments of the United States and other countries. Thus the volt, from the Italian Volta, has been adopted as the practical unit of electromotive force, the ohm, from the enunciator of Ohm's law, as the practical unit of resistance; the ampere, after the eminent French scientist of that name, as the practical unit of current strength, the henry as the practical unit of inductance, after Joseph Henry and in recognition of his early and important experimental work in mutual induction.
Magnetometer
In 1833, Carl Friedrich Gauss, head of the Geomagnetic Observatory in Göttingen, published a paper on measurement of the Earth's magnetic field. It described a new instrument that consisted of a permanent bar magnet suspended horizontally from a gold fibre. The difference in the oscillations when the bar was magnetised and when it was demagnetised allowed Gauss to calculate an absolute value for the strength of the Earth's magnetic field.
Kibble balance
A conducting wire of length "L" that carries an electric current "I" perpendicular to a magnetic field of strength "B" will experience a Lorentz force equal to "BLI". In the Kibble balance, the current is varied so that this force exactly counteracts the weight "w" of a standard mass "m". This is also the principle behind the ampere balance. "w" is given by the mass "m" multiplied by the local gravitational acceleration "g". Thus
The Kibble balance avoids the problems of measuring "B" and "L" with a second calibration step. The same wire (in practice, a coil of wire) is moved through the same magnetic field at a known speed "v". By Faraday's law of induction, a potential difference "U" is generated across the ends of the wire, which equals "BLv". Thus 
The unknown product "BL" can be eliminated from the equations to give
With "U", "I", "g", and "v" accurately measured, this gives an accurate value for "m". 
Both sides of the equation have the dimensions of power, measured in watts in the International System of Units; hence the original name "watt balance".
Gravitational metric system
In English contexts the unit of force is usually formed by simply appending the suffix "force" to the name of the unit of mass, thus "gram-force" (gf) or "kilogram-force" (kgf, which follows the tradition of pound-force (lbf). In other, international contexts the special name "pond" (p) or "kilopond" (kp) respectively is more frequent.
Magnet
The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denoted M, with units A/m. It is a vector field, rather than just a vector (like the magnetic moment), because different areas in a magnet can be magnetized with different directions and strengths (for example, because of domains, see below). A good bar magnet may have a magnetic moment of magnitude 0.1 A•m and a volume of 1 cm, or 1×10 m, and therefore an average magnetization magnitude is 100,000 A/m. Iron can have a magnetization of around a million amperes per meter. Such a large value explains why iron magnets are so effective at producing magnetic fields.
Electron scattering
The Lorentz force, named after Dutch physicist Hendrik Lorentz, for a charged particle "q" is given (in SI units) by the equation:
where "qE describes the electric force due to a present electric field,E", acting on "q".
And "qv x B describes the magnetic force due to a present magnetic field, B, acting on "q" when "q" is moving with velocity v".
Which can also be written as:
where formula_3 is the electric potential, and A is the magnetic vector potential.
Hall effect
(The units of are usually expressed as m/C, or Ω·cm/G, or other variants.) As a result, the Hall effect is very useful as a means to measure either the carrier density or the magnetic field.
Magnetorotational instability
where we have used the same vector calculus identity. This equation is fully general, and makes no assumptions about the strength or direction of the magnetic field.
The first term on the right is analogous to a pressure gradient. In our problem it may be neglected because it exerts no force in the plane of the disk, perpendicular to formula_78 The second term acts like a magnetic tension force, analogous to a taut string. For a small disturbance formula_79 it exerts an acceleration given by force divided by mass, or equivalently, force per unit volume divided by mass per unit volume:
Magnetometer
Faraday force magnetometry uses the fact that a spatial magnetic field gradient produces force that acts on a magnetized object, F=(M⋅∇)B. In Faraday Force Magnetometry the force on the sample can be measured by a scale (hanging the sample from a sensitive balance), or by detecting the displacement against a spring. Commonly a capacitive load cell or cantilever is used because of its sensitivity, size, and lack of mechanical parts. Faraday Force Magnetometry is approximately one order of magnitude less sensitive than a SQUID. The biggest drawback to Faraday Force Magnetometry is that it requires some means of not only producing a magnetic field, but also producing a magnetic field gradient. While this can be accomplished by using a set of special pole faces, a much better result can be achieved by using set of gradient coils. A major advantage to Faraday Force Magnetometry is that it is small and reasonably tolerant to noise, and thus can be implemented in a wide range of environments, including a dilution refrigerator. Faraday Force Magnetometry can also be complicated by the presence of torque (see previous technique). This can be circumvented by varying the gradient field independently of the applied DC field so the torque and the Faraday Force contribution can be separated, and/or by designing a Faraday Force Magnetometer that prevents the sample from being rotated.
Introduction to electromagnetism
The magnetic field is that which arises from moving charges, currents, and magnetic objects. The field is represented mathematically as a vector-valued function formula_7. The SI unit of the magnetic field is the tesla (T).
Lorentz force
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by Henry Cavendish in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when Charles-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.
Magnetic field
The direction of force on a charge or a current 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 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.
Magnetic susceptibility
The CRC Handbook of Chemistry and Physics has one of the only published magnetic susceptibility tables. Some of the data (e.g., for aluminium, bismuth, and diamond) is listed as cgs, which has caused confusion to some readers. "cgs" is an abbreviation of "centimeters–grams–seconds"; it represents the form of the units, but cgs does not specify units. Correct units of magnetic susceptibility in cgs is cm/mol or cm/g. Molar susceptibility and mass susceptibility are both listed in the CRC. Some table have listed magnetic susceptibility of diamagnets as positives. It is important to check the header of the table for the correct units and sign of magnetic susceptibility readings.
Permeability (electromagnetism)
Permeability is the inductance per unit length. In SI units, permeability is measured in henries per metre (H·m = J/(A·m) = N·A). The auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre (A·m). The product "µ" H thus has dimensions inductance times current per unit area (H·A/m). But inductance is magnetic flux per unit current, so the product has dimensions magnetic flux per unit area, that is, magnetic flux density. This is the magnetic field B, which is measured in webers (volt-seconds) per square-metre (V·s/m), or teslas (T).
Galileo (spacecraft)
The magnetometer (MAG) used two sets of three sensors. The three sensors allowed the three orthogonal components of the magnetic field section to be measured. One set was located at the end of the magnetometer boom and, in that position, was about from the spin axis of the spacecraft. The second set, designed to detect stronger fields, was from the spin axis. The boom was used to remove the MAG from the immediate vicinity of "Galileo" to minimize magnetic effects from the spacecraft. However, not all these effects could be eliminated by distancing the instrument. The rotation of the spacecraft was used to separate natural magnetic fields from engineering-induced fields. Another source of potential error in measurement came from the bending and twisting of the long magnetometer boom. To account for these motions, a calibration coil was mounted rigidly on the spacecraft to generate a reference magnetic field during calibrations. The magnetic field at the surface of the Earth has a strength of about 50,000 nT. At Jupiter, the outboard (11 m) set of sensors could measure magnetic field strengths in the range from ±32 to ±512 nT, while the inboard (6.7 m) set was active in the range from ±512 to ±16,384 nT. The MAG experiment weighed and used 3.9 watts of power.
Work (physics)
The magnetic force on a charged particle is , where "q" is the charge, v is the velocity of the particle, and B is the magnetic field. The result of a cross product is always perpendicular to both of the original vectors, so . The dot product of two perpendicular vectors is always zero, so the work , and the magnetic force does not do work. It can change the direction of motion but never change the speed.
Energy–momentum relation
In particle physics, energy is typically given in units of electron volts (eV), momentum in units of eV·, and mass in units of eV·. In electromagnetism, and because of relativistic invariance, it is useful to have the electric field and the magnetic field in the same unit (Gauss), using the cgs (Gaussian) system of units, where energy is given in units of erg, mass in grams (g), and momentum in g·cm·s.
Electropermanent magnet
Using the formula for force mentioned earlier it is possible to plot the force as a function of the gap distance of the external hiperco bar. Two curves were obtained: one for the EPM in ON state and the other for the EPM in OFF state: If we plot those forces together it is possible to observe the difference of at least 4 orders of magnitude from the EPM when is ON and OFF (This plot is an example of EPM with two cylindrical magnets -one NdFeB and the other AlNiCo- of 1mm diameter and length. The soft magnet material is hiperco with square section bars of side 0.889mm to make the flux area equal to the one in the magnets): 
An example of an EPM of formula_30 by formula_31 is simulation to verify the difference in the magnetic field when the EPM is ON and OFF. This simulation was made using finite element approach by the software COMSOL Multiphysics®. The picture below shows a simulation of the Magnetic Flux density Field (B) for the EPM ON and OFF (with a calculation of the flux in that specific plane) and below shows multiple cross section measurements of the flux density on top of the EPM (ON and OFF as well). The simulations shown that there are at least 4 orders of magnitude of difference in the external magnetic fields between the two operation modes confirming the magnetic circuit model.
Magnetic current
Magnetic current is, nominally, a current composed of fictitious moving magnetic monopoles. It has the dimensions of volts. The usual symbol for magnetic current is formula_1 which is analogous to formula_2 for electric current. Magnetic currents produce an electric field analogously to the production of a magnetic field by electric currents. Magnetic current density, which has the units of V/m² (volts per square meter), is usually represented by the symbols formula_3 and formula_4. The superscripts indicate total and impressed magnetic current density. The impressed currents are the energy sources. In many useful cases, a distribution of electric charge can be mathematically replaced by an equivalent distribution of magnetic current. This artifice can be used to simplify some electromagnetic field problems. It is possible to use both electric current densities and magnetic current densities in the same analysis.
Gyrator–capacitor model
In a magnetic circuit, magnetic inductance (inductive magnetic reactance) is the analogy to inductance in an electrical circuit. In the SI system, it is measured in units of -Ω. This model makes magnetomotive force (mmf) the analog of electromotive force in electrical circuits, and time rate of change of magnetic flux the analog of electric current.
Magnetomotive force
The SI unit of mmf is the ampere, the same as the unit of current (analogously the units of emf and voltage are both the volt). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the MKS system. Occasionally, the cgs system unit of the gilbert may also be encountered.
Pound (force)
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s/ft. In other contexts, the unit "pound" refers to a unit of mass. The international standard symbol for the pound as a unit of mass is lb. 
In the "engineering" systems (middle column), the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit—the use of Newton's Second Law, , requires another factor, "g", usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s).
"Absolute" systems are "coherent" systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.
Torr
The torr is sometimes incorrectly denoted by the symbol "T", which is the SI symbol for the tesla, the unit measuring the strength of a magnetic field. Although frequently encountered, the alternative spelling "Tor" is incorrect.
Magnetic tension force
It is analogous to rubber bands and their restoring force. The force is directed antiradially. Although magnetic tension is referred to as a force, it is actually a pressure gradient (Pa m) which is also a force density (N m).
Magnetohydrodynamic drive
where f is the "force density" (force per unit volume), "ρ" the charge density (charge per unit volume), E the electric field, J the current density (current per unit area) and B the magnetic field.
Conservative force
Many forces (particularly those that depend on velocity) are not force "fields". In these cases, the above three conditions are not mathematically equivalent. For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl). Accordingly, some authors classify the magnetic force as conservative, while others do not. The magnetic force is an unusual case; most velocity-dependent forces, such as friction, do not satisfy any of the three conditions, and therefore are unambiguously nonconservative.
Force between magnets
The magnetic moment of a magnet is therefore a measure of its strength and orientation. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments. More precisely, the term "magnetic moment" normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field.
Electron magnetic moment
In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is approximately .
The electron magnetic moment has been measured to an accuracy of 7.6 parts in 10.
Force
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated; however it still sees use for some purposes as expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque. Other arcane units of force include the sthène, which is equivalent to 1000 N, and the kip, which is equivalent to 1000 lbf.
International System of Units
In 1832, the German mathematician Carl Friedrich Gauss, assisted by Wilhelm Weber, implicitly defined the second as a base unit when he quoted the Earth's magnetic field in terms of millimetres, grams, and seconds. Prior to this, the strength of the Earth's magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a suspended magnet of known mass by the Earth's magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field.
Electromagnetism
Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.
Magnetic moment
All formulae in this article are correct in SI units; they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current and area has magnetic moment (see below), but in Gaussian units the magnetic moment is .
Magnetochemistry
When the Curie law is obeyed, the product of molar susceptibility and temperature is a constant. The effective magnetic moment, μ is then defined as
Where C has CGS units cm mol K, μ is
Magnetic force microscope
In MFM measurements, the magnetic force between the sample and the tip can be expressed as
Van der Pauw method
Note that the strength of the magnetic field "B" needs to be in units of Wb/cm² if n is in cm. For instance, if the strength is given in the commonly used units of teslas, it can be converted by multiplying it by 10.
Weight
In most modern scientific work, physical quantities are measured in SI units. The SI unit of weight is the same as that of force: the newton (N) – a derived unit which can also be expressed in SI base units as kg⋅m/s (kilograms times meters per second squared).
Magnetometer
A magnetometer or magnetic sensor is an instrument that measures magnetism—either the magnetization of a magnetic material like a ferromagnet, or the direction, strength, or relative change of a magnetic field at a particular location. A compass is a simple type of magnetometer, one that measures the direction of an ambient magnetic field.
Coercivity
For ferromagnetic material the coercivity is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero "after" the magnetization of the sample has been driven to saturation. Thus coercivity measures the resistance of a ferromagnetic material to becoming demagnetized. Coercivity is usually measured in oersted or ampere/meter units and is denoted "H". It can be measured using a B-H analyzer or magnetometer.
Magnetic moment
Contributions due to the sources of the first kind can be calculated from knowing the distribution of all the electric currents (or, alternatively, of all the electric charges and their velocities) inside the system, by using the formulas below. On the other hand, the magnitude of each elementary particle's intrinsic magnetic moment is a fixed number, often measured experimentally to a great precision. For example, any electron's magnetic moment is measured to be . The direction of the magnetic moment of any elementary particle is entirely determined by the direction of its spin, with the negative value indicating that any electron's magnetic moment is antiparallel to its spin.
Evans balance
An Evans balance, also known as a Johnson-Matthey balance (after the most prolific producer of the Evans balance) is a device for measuring magnetic susceptibility. Magnetic susceptibility is related to the force experienced by a substance in a magnetic field. Various practical devices are available for the measurement of susceptibility, which differ in the shape of the magnetic field and the way the force is measured.
Magnetic circuit
where formula_1 is the magnetomotive force (MMF) across a magnetic element, formula_11 is the magnetic flux through the magnetic element, and formula_12 is the magnetic reluctance of that element. (It will be shown later that this relationship is due to the empirical relationship between the H-field and the magnetic field B, B="μH", where "μ" is the permeability of the material). Like Ohm's law, Hopkinson's law can be interpreted either as an empirical equation that works for some materials, or it may serve as a definition of reluctance.
Magnetic field
The "magnetization" vector field represents how strongly a region of material is magnetized. It is defined as the net magnetic dipole moment per unit volume of that region. The magnetization of a uniform magnet is therefore a material constant, equal to the magnetic moment of the magnet divided by its volume. Since the SI unit of magnetic moment is A⋅m, the SI unit of magnetization is ampere per meter, identical to that of the -field.
Tonne
Like the gram and the kilogram, the tonne gave rise to a (now obsolete) force unit of the same name, the tonne-force, equivalent to about 9.8 kilonewtons: a unit also often called simply "tonne" or "metric ton" without identifying it as a unit of force. In contrast to the tonne as a mass unit, the tonne-force or metric ton-force is not acceptable for use with SI, partly because it is not an exact multiple of the SI unit of force, the newton.