Instruct: Given a question, retrieve documents that answer the question.
Query: Who first measured magnetic force?
Three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it. Then in 1820, André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions.[7] Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, which correctly predicts the magnetic field around any current-carrying wire.
A Lorentz force velocimetry system is called Lorentz force flowmeter (LFF). A LFF measures the integrated or bulk Lorentz force resulting from the interaction between a liquid metal in motion and an applied magnetic field. In this case the characteristic length of the magnetic field is of the same order of magnitude as the dimensions of the channel. It must be addressed that in the case where localized magnetic fields are used, it is possible to perform local velocity measurements and thus the term Lorentz force velocimeter is used.
Magnetic force microscopy (MFM) is a variety of atomic force microscopy, in which a sharp magnetized tip scans a magnetic sample; the tip-sample magnetic interactions are detected and used to reconstruct the magnetic structure of the sample surface. Many kinds of magnetic interactions are measured by MFM, including magnetic dipole–dipole interaction. MFM scanning often uses non-contact AFM (NC-AFM) mode.
Magnetic tweezers go beyond the capabilities of other single-molecule methods, however, in that interactions between and within complexes can also be observed. This has allowed recent advances in understanding more about DNA-binding proteins, receptor-ligand interactions, and restriction enzyme cleavage. A more recent application of magnetic tweezers is seen in single-complex studies. With the help of DNA as the tethering agent, an entire molecular complex may be attached between the bead and the tethering surface. In exactly the same way as with pulling a DNA hairpin apart by applying a force to the magnetic bead, an entire complex can be pulled apart and force required for the dissociation can be measured. This is also similar to the method of pulling apart receptor-ligand interactions with magnetic tweezers to measure dissociation force.
Magnets exert forces and torques on each other due to the rules of electromagnetism. The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles (such as electrons) that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary force between magnets, therefore, is the magnetic dipole–dipole interaction. If all of the magnetic dipoles that make up two magnets are known then the net force on both magnets can be determined by summing up all these interactions between the dipoles of the first magnet and that of the second.
The neutron magnetic moment is the intrinsic magnetic dipole moment of the neutron, symbol "μ". Protons and neutrons, both nucleons, comprise the nucleus of atoms, and both nucleons behave as small magnets whose strengths are measured by their magnetic moments. The neutron interacts with normal matter through either the nuclear force or its magnetic moment. The neutron's magnetic moment is exploited to probe the atomic structure of materials using scattering methods and to manipulate the properties of neutron beams in particle accelerators. The neutron was determined to have a magnetic moment by indirect methods in the mid 1930s. Luis Alvarez and Felix Bloch made the first accurate, direct measurement of the neutron's magnetic moment in 1940. The existence of the neutron's magnetic moment indicates the neutron is not an elementary particle. For an elementary particle to have an intrinsic magnetic moment, it must have both spin and electric charge. The neutron has spin 1/2 "ħ", but it has no net charge. The existence of the neutron's magnetic moment was puzzling and defied a correct explanation until the quark model for particles was developed in the 1960s. The neutron is composed of three quarks, and the magnetic moments of these elementary particles combine to give the neutron its magnetic moment.
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).
In MFM measurements, the magnetic force between the sample and the tip can be expressed as 
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.
A B-H Analyzer is an instrument that measures the AC magnetic characteristics of soft magnetic materials. It measures residual flux density BR and coercive force HC. It has applications in manufacturing magnetic-related products such as hard disks and magnetic tape, and in analysis of cast irons.
Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied. Early measurements are made using the Gouy balance where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use a superconductive magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the Evans balance. For liquid samples, the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation.
Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner. This method is highly accurate for diamagnetic materials with susceptibilities similar to water.
Lorentz force flowmeters are usually classified in several main conceptual setups. Some of them designed as static flowmeters where the magnet system is at rest and one measures the force acting on it. Alternatively, they can be designed as rotary flowmeters where the magnets are arranged on a rotating wheel and the spinning velocity is a measure of the flow velocity. Obviously, the force acting on a Lorentz force flowmeter depends both on the velocity distribution and on the shape of the magnet system. This classification depends on the relative direction of the magnetic field that is being applied respect to the direction of the flow. In Figure 3 one can distinguish diagrams of the longitudinal and the transverse Lorentz force flowmeters.
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.
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.
At a given location, a full representation of the Earth's magnetic field requires a vector with three coordinates (see figure). These can be Cartesian (North, East and Down) or spherical (declination, inclination and intensity). In the latter system, the declination (the deviation from true north, a horizontal angle) must be measured first to establish the direction of magnetic North; then the dip (a vertical angle) can be measured relative to magnetic North. In China, the horizontal direction was measured as early as the fourth century BC, and the existence of declination first recognized in 1088. In Europe, this was not widely accepted until the middle of the fifteenth century AD. Inclination (also known as "magnetic dip") was first measured in 1544 AD. The intensity was not measured until 1791, after advances in the understanding of electromagnetism.
A Faraday 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.
A Lorentz force velocimetry system is called Lorentz force flowmeter (LFF). A LFF measures the integrated or bulk Lorentz force resulting from the interaction between a liquid metal in motion and an applied magnetic field. In this case the characteristic length of the magnetic field is of the same order of magnitude as the dimensions of the channel. It must be addressed that in the case where localized magnetic fields are used, it is possible to perform local velocity measurements and thus the term Lorentz force velocimeter is used.
A MEMS magnetic field sensor is a small-scale microelectromechanical systems (MEMS) device for detecting and measuring magnetic fields (Magnetometer). Many of these operate by detecting effects of the Lorentz force: a change in voltage or resonant frequency may be measured electronically, or a mechanical displacement may be measured optically. Compensation for temperature effects is necessary. Its use as a miniaturized compass may be one such simple example application.
Time-of-flight Lorentz force velocimetry, is intended for contactless determination of flow rate in conductive fluids. It can be successfully used even in case when such material properties as electrical conductivity or density are not precisely known under specific outer conditions. The last reason makes time-of-flight LFV especially important for industry application. According to time-of-flight LFV (Fig. 9) two coherent measurement systems are mounted on a channel one by one. The measurement is based on getting of cross-correlating function of signals, which are registered by two magnetic measurement's system. Every system consists of permanent magnet and force sensor, so inducing of Lorentz force and measurement of the reaction force are made simultaneously. Any cross-correlation function is useful only in case of qualitative difference between signals and for creating the difference in this case turbulent fluctuations are used. Before reaching of measurement zone of a channel liquid passes artificial vortex generator that induces strong disturbances in it. And when such fluctuation-vortex reaches magnetic field of measurement system we can observe a peak on its force-time characteristic while second system still measures stable flow. Then according to the time between peaks and the distance between measurement system observer can estimate mean velocity and, hence, flow rate of the liquid by equation:
Let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define formula_5 as the measurement time. If formula_6, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero. If formula_7, the magnetization will not flip during the measurement, so the measured magnetization will be what the instantaneous magnetization was at the beginning of the measurement. In the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will appear to be “blocked” in its initial state. 
If the particle is treated as a classical spinning magnetic dipole, it will precess in a magnetic field because of the torque that the magnetic field exerts on the dipole (see torque-induced precession). If it moves through a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the trajectory of the particle is unaffected. However, if the magnetic field is inhomogeneous then the force on one end of the dipole will be slightly greater than the opposing force on the other end, so that there is a net force which deflects the particle's trajectory. If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous. Each particle would be deflected by an amount proportional to its magnetic moment, producing some density distribution on the detector screen. Instead, the particles passing through the Stern–Gerlach apparatus are deflected either up or down by a specific amount. This was a measurement of the quantum observable now known as spin angular momentum, which demonstrated possible outcomes of a measurement where the observable has a discrete set of values or point spectrum.
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.
Magnetic torque magnetometry can be even more sensitive than SQUID magnetometry. However, magnetic torque magnetometry doesn't measure magnetism directly as all the previously mentioned methods do. Magnetic torque magnetometry instead measures the torque τ acting on a sample's magnetic moment μ as a result of a uniform magnetic field B, τ=μ×B.
A torque is thus a measure of the sample's magnetic or shape anisotropy. In some cases the sample's magnetization can be extracted from the measured torque. In other cases, the magnetic torque measurement is used to detect magnetic phase transitions or quantum oscillations. The most common way to measure magnetic torque is to mount the sample on a cantilever and measure the displacement via capacitance measurement between the cantilever and nearby fixed object, or by measuring the piezoelectricity of the cantilever, or by optical interferometry off the surface of the cantilever.
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
Working in this area, and using large magnets, he became interested in the other extreme; this was the measurement of very weak magnetic fields, which for example might be produced by the weak natural currents in the human body. In 1963, he proposed a method using a magnetically shielded room to keep out external magnetic disturbances, as in radiation shielding in nuclear experiments. At that time others reported the first biomagnetic measurement, where the MCG ("magnetocardiogram", the magnetic field due to heart currents) was measured; this was done without shielding, hence showed much external interference. Cohen then built a modest shielded room, and with somewhat clearer signals verified the heart’s magnetic field. He also made the first measurement of the MEG ("magnetoencephalogram", the magnetic field of the brain). However, all these early biomagnetic measurements were generally too noisy, both because of the use of insensitive detectors, and incomplete magnetic shielding.