Tesla (unit)

teslaTteslas
Wb = weber. 10,000 (or 10 4 ) G (Gauss), used in the CGS system. Thus, 10 kG = 1 T (tesla), and 1 G = 10 −4 T = 100 μT (microtesla). 1,000,000,000 (or 10 9 ) γ (gamma), used in geophysics. Thus, 1 γ = 1 nT (nanotesla). 42.6 MHz of the 1 H nucleus frequency, in NMR.

Magnetic flux

fluxfluxes definition of flux used in electromagnetism
If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is :where B is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m 2 (tesla), S is the area of the surface, and θ is the angle between the magnetic field lines and the normal (perpendicular) to S.

International System of Units

SISI unitsSI unit
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.

Electric field

electricelectrostatic fieldelectrical field
The electric field cannot be described independently of the magnetic field in that case. If A is the magnetic vector potential, defined so that, one can still define an electric potential \Phi such that: One can recover Faraday's law of induction by taking the curl of that equation : which justifies, a posteriori, the previous form for E. The total energy per unit volume stored by the electromagnetic field is where ε is the permittivity of the medium in which the field exists, \mu its magnetic permeability, and E and B are the electric and magnetic field vectors. As E and B fields are coupled, it would be misleading to split this expression into "electric" and "magnetic" contributions.

Faraday's law of induction

Faraday's lawMaxwell–Faraday equationelectromagnetic induction
For a loop of wire in a magnetic field, the magnetic flux Φ B is defined for any surface Σ whose boundary is the given loop. Since the wire loop may be moving, we write Σ(t) for the surface. The magnetic flux is the surface integral: where dA is an element of surface area of the moving surface Σ(t), B is the magnetic field, and B·dA is a vector dot product representing the element of flux through dA . In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.

Voltage

potential differenceVvoltages
Under this definition, the voltage difference between two points is not uniquely defined when there are time-varying magnetic fields since the electric force is not a conservative force in such cases. If this definition of voltage is used, any circuit where there are time-varying magnetic fields, such as circuits containing inductors, will not have a well-defined voltage between nodes in the circuit. However, if magnetic fields are suitably contained to each component, then the electric field is conservative in the region exterior to the components, and voltages are well-defined in that region.

Electromotive force

EMFelectromotive force (EMF)
In nature, emf is generated whenever magnetic field fluctuations occur through a surface. The shifting of the Earth's magnetic field during a geomagnetic storm induces currents in the electrical grid as the lines of the magnetic field are shifted about and cut across the conductors. In the case of a battery, the charge separation that gives rise to a voltage difference between the terminals is accomplished by chemical reactions at the electrodes that convert chemical potential energy into electromagnetic potential energy.

Vacuum permeability

magnetic constantpermeability of free spacepermeability of vacuum
The physical constant μ 0, (pronounced "mu nought" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum., the vacuum permeability μ 0 will no longer be a defined constant (per the former definition of the SI ampere), but rather will need to be determined experimentally; The 2018 CODATA value is given below.

Magnetic circuit

Hopkinson's lawMagnetic Circuitsair gap
The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux Φ is defined by a scalar product of the magnetic field and the area element vector. Quantitatively, the magnetic flux through a surface S is defined as the integral of the magnetic field over the area of the surface For a magnetic component the area S used to calculate the magnetic flux Φ is usually chosen to be the cross-sectional area of the component.

Oersted

megagauss oerstedsOeOERSTEDS
In a vacuum, if the magnetizing field strength is 1 Oe, then the magnetic field density is 1 G, whereas, in a medium having permeability μ r (relative to permeability of vacuum), their relation is: Because oersteds are used to measure magnetizing field strength, they are also related to the magnetomotive force (mmf) of current in a single-winding wire-loop: The stored energy in a magnet, called magnet performance or maximum energy product (often abbreviated BH max ), is typically measured in units of megagauss-oersteds (MG⋅Oe). 1 MG⋅Oe is approximately equal to 7957.74715 J/m 3. Centimetre–gram–second system of units. Ampere's model of magnetization.

Electromagnetism

electromagneticelectrodynamicselectromagnetic force
In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, and Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905. Originally, electricity and magnetism were considered to be two separate forces.

SI derived unit

derived unitderived unitsJ/kg
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

Permeability (electromagnetism)

permeabilitymagnetic permeabilityrelative permeability
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 2 ), or teslas (T). B is related to the Lorentz force on a moving charge q: The charge q is given in coulombs (C), the velocity v in meters per second (m/s), so that the force F is in newtons (N): : H is related to the magnetic dipole density. A magnetic dipole is a closed circulation of electric current.

Gauss (unit)

gaussGkG
According to the system of Gaussian units (cgs), the gauss is the unit of magnetic flux density B and the equivalent of Mx/cm 2, while the oersted is the unit of magnetizing field H. One tesla (T) is equal to 10 4 gauss, and one ampere (A) per meter is equal to 4π × 10 −3 oersted. The units for magnetic flux Φ, which is the integral of magnetic field over an area, are the weber (Wb) in the SI and the maxwell (Mx) in the cgs system.

Gaussian units

Gaussiancgs-Gaussian unitsGaussian-cgs units
B and H are the magnetic fields. M is magnetization. \mu is magnetic permeability. \mu_0 is the permeability of vacuum (used in the SI system, but meaningless in Gaussian units). is the magnetic susceptibility. Comprehensive list of Gaussian unit names, and their expressions in base units. The evolution of the Gaussian Units by Dan Petru Danescu.

Gauss's law for magnetism

Gauss' law for magnetismGauss's lawfor magnetism
If magnetic monopoles were discovered, then Gauss's law for magnetism would state the divergence of B would be proportional to the magnetic charge density ρ m, analogous to Gauss's law for electric field. For zero net magnetic charge density ( ρ m = 0 ), the original form of Gauss's magnetism law is the result. The modified formula in SI units is not standard; in one variation, magnetic charge has units of webers, in another it has units of ampere-meters. where μ 0 is the vacuum permeability. So far, no magnetic monopoles have been found, despite extensive search. This idea of the nonexistence of magnetic monopoles originated in 1269 by Petrus Peregrinus de Maricourt.

Magnetic monopole

magnetic monopolesmagnetic chargemonopole
However, in the multipole expansion of a magnetic field, the "monopole" term is always exactly zero (for ordinary matter). A magnetic monopole, if it exists, would have the defining property of producing a magnetic field whose monopole term is non-zero. A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion. The term dipole means two poles, corresponding to the fact that a dipole magnet typically contains a north pole on one side and a south pole on the other side. This is analogous to an electric dipole, which has positive charge on one side and negative charge on the other.

Electromagnetic radiation

electromagnetic waveelectromagnetic waveselectromagnetic
Whereas the magnetic part of the near-field is due to currents in the source, the magnetic field in EMR is due only to the local change in the electric field. In a similar way, while the electric field in the near-field is due directly to the charges and charge-separation in the source, the electric field in EMR is due to a change in the local magnetic field. Both processes for producing electric and magnetic EMR fields have a different dependence on distance than do near-field dipole electric and magnetic fields. That is why the EMR type of EM field becomes dominant in power “far” from sources.

Henry (unit)

henryhenriesH
Expressed in combinations of SI units, the henry is: :in which the following additional derived units occur: coulomb (C), farad (F), joule (J), weber (Wb), tesla (T), volt (V), hertz (Hz), and ohm . The International System of Units (SI) specifies to write the symbol of a unit named for a person with an initial capital letter, while the name is not capitalized in sentence text, except when any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case. The United States National Institute of Standards and Technology recommends users writing in English to use the plural as henries.

Maxwell (unit)

maxwellMx
That is, one maxwell is the total flux across a surface of one square centimetre perpendicular to a magnetic field of strength one gauss. The weber is the related SI unit of magnetic flux, which was defined in 1946. : 1 maxwell = 10 −8 weber Centimetre–gram–second system of units. gauss (unit). Gaussian units. James Clerk Maxwell. Maxwell's equations. Weber (unit).

Centimetre–gram–second system of units

CGScgs unitsCGS unit
Therefore, if the unit of charge is based on the Ampère's force law such that, it is natural to derive the unit of magnetic field by setting. However, if it is not the case, a choice has to be made as to which of the two laws above is a more convenient basis for deriving the unit of magnetic field. Furthermore, if we wish to describe the electric displacement field D and the magnetic field H in a medium other than vacuum, we need to also define the constants ε 0 and μ 0, which are the vacuum permittivity and permeability, respectively. Then we have (generally) and, where P and M are polarization density and magnetization vectors.

Metre

metermmetres
The metre (Commonwealth spelling and BIPM spelling ) or meter (American spelling ) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second.

Ampere

AmAamp
Magnetic constant. Orders of magnitude (current). The NIST Reference on Constants, Units, and Uncertainty. NIST Definition of ampere and μ 0.

Second

ssecmegasecond
The second (symbol: s, abbreviation: sec) is the base unit of time in the International System of Units (SI), commonly understood and historically defined as 1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds (and minutes), and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter.

Coulomb

CPicoCoulomBExacoulomb
The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second: :