magnetic_field_strength

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+ | ====== Magnetic field strength ====== | ||

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+ | | // | ||

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+ | ===== Definition ===== | ||

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+ | **Magnetic field strength** $H$ - a physical quantity used as one of the basic measures of the intensity of [[magnetic field]].[(Mansfield> | ||

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+ | Magnetic field strength $H$ can be thought of as excitation and the [[magnetic flux density]] $B$ as the response of the medium. | ||

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+ | Fig. 1. [[Electric current]] $I$ generates **magnetic field strength** $H$, whose magnitude is independent on the type of the uniform isotropic surrounding medium ([[magnetic]] or [[non-magnetic]]) | ||

+ | [[file/ | ||

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+ | Magnetic field is a [[vector field]] in space, and is a kind of [[energy]] whose full quantification requires the knowledge of the vector fields of both magnetic field strength $H$ and [[flux density]] $B$ (or other values correlated with them, like [[magnetisation]] or [[polarisation]]). In vacuum, at each point the $H$ and $B$ vectors are oriented along the same direction and are directly proportional through [[permeability]] of free space, but in other media they can be misaligned (especially in [[uniform material|non-uniform]] or [[anisotropy|anisotropic]] materials). | ||

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+ | The requirement of two quantities is analogous for example to [[electricity]]. Both [[electric voltage]] $V$ and [[electric current]] $I$ are required to fully quantify the effects of electricity, | ||

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+ | The name // | ||

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+ | ===== Difficulty with definition ===== | ||

+ | It is difficult to give a concise definition of such a basic quantity like [[magnetic field]], but various authors give at least a descriptive version. The same applies to **magnetic field strength**, as well as the other basic quantity - **[[magnetic flux density]]**. | ||

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+ | The table below shows some examples of definitions of $H$ given in the literature (exact quotations are shown). | ||

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+ | <WRAP clear></ | ||

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+ | ^ Publication ^ Definition of // | ||

+ | | Richard M. Bozorth \\ **Ferromagnetism**[([[http:// | ||

+ | | David C. Jiles \\ **Introduction to Magnetism and Magnetic Materials**[(Jiles)] | //One of the most fundamental ideas in magnetism is the concept of the magnetic field. When a field is generated in a volume of space it means that there is a change of energy of that volume, and furthermore that there is an energy gradient so that a force is produced which can be detected by the acceleration of an electric charge moving in the field, by the force on a current-carrying conductor, by the torque on a magnetic dipole such as a bar magnet or even by a reorientation of spins of electrons within certain types of atoms.// | //There are a number of ways in which the magnetic field strength H can be defined. In accordance with the ideas developed here we wish to emphasize the connection between the magnetic field H and the generating electric current. We shall therefore define the unit of magnetic field strength, the ampere per meter, in terms of the generating current. The simplest definition is as follows. The ampere per meter is the field strength produced by an infinitely long solenoid containing //n// turns per metre of coil and carrying a current of 1///n// amperes.// | //When a magnetic field H has been generated in a medium by a current, in accordance with Ampere' | ||

+ | | **Magnetic field**, **Encyclopaedia Britannica**[(Britannica_Field> | ||

+ | | V.A.Bakshi, A.V.Bakshi \\ **Electromagnetic Field Theory**[(Bakshi> | ||

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+ | ===== Analogy to electric circuits ===== | ||

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+ | ==== Electric circuit ==== | ||

+ | [[Electric voltage]] $V$ and [[electric current]] $I$ are both required to fully quantify the effects of [[electricity]] in electric circuits. In [[direct current]] circuits the proportionality between $V$ and $I$ is dictated by [[electrical conductance]] $G$ (or [[resistance]] $R$) of a given medium. | ||

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+ | The product of $V$ and $I$ is a measure of [[power]] and can be expressed in [[watt|watts]] (W), which over [[time]] $t$ gives [[/energy]] $E$ in [[joule|joules]] dissipated or transformed in the circuit. | ||

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+ | If a fixed value of $V$ is applied to a uniform electric circuit then the resulting amplitude of $I$ is dictated by the conductivity of the circuit. For the same voltage, higher values of conductivity will result with higher current. | ||

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+ | If a fixed amplitude of current is forced through a conductor then the [[voltage drop]] will be proportional to the resistance of the conductor. For a [[superconductor]] the resistance is zero, there is no voltage drop and therefore $V · I = 0$. Conversely, if voltage is applied to [[electric insulator]] then very little current flows and thus only small amount of energy is dissipated, so that $V · I \approx 0$. | ||

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+ | ==== Magnetic circuit ==== | ||

+ | By analogy both [[magnetic field strength]] $H$ and [[magnetic flux density]] $B$ (or their representations by other related variables) are required for quantifying the effects of [[magnetism]] in [[magnetic circuit|magnetic circuits]]. The proportionality between $H$ and $B$ is dictated by [[magnetic permeability]] $μ$ of a given medium.[(White)] | ||

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+ | Under [[steady state]] conditions, the product of $H$ and $B$ is a measure of [[specific energy]] in J/ | ||

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+ | If a fixed value of $H$ is applied to a magnetic circuit then the resulting amplitude of $B$ is dictated by permeability $μ$ of the circuit. For the same magnetic field strength, higher values of permeability will result with higher flux density. | ||

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+ | [[Soft ferromagnet|Soft ferromagnets]] have large values of permeability and thus application of small $H$ results with large values of $B$ without storing much energy in the magnetic field, so that $B·H \approx 0$ (e.g. as compared to permanent magnets which can store a lot of energy). | ||

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+ | However, [[superconductor|superconductors]] can completely expel magnetic field from their volume so that they behave as " | ||

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+ | ===== H around electric current | ||

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+ | Fig. 2. Amplitude of **magnetic field strength** $H$ reduces with the distance from a conductor with electric current $I$ | ||

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+ | Fig. 3. Orientation of **magnetic field strength** $H$ vector with respect to the current $I$ follows the [[right-hand rule]] | ||

+ | [[file/ | ||

+ | {{page> | ||

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+ | $H$ is always generated around [[electrical current]] $I$, which can be a solid [[conductor]] with current or just a moving [[electrical charge]] (also in [[free space]]). The direction of the $H$ vector is perpendicular to the direction of the current $I$ generating it, and the senses of the vectors are assumed to follow the [[right-hand rule]].[(Jiles)] | ||

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+ | Without other sources of magnetic field and in a [[uniformity|uniform]] and [[isotropic]] medium the generated magnetic field strength $H$ depends only on the magnitude and direction of the electric current $I$ and the physical sizes involved (e.g. length and diameter of the conductor, etc.) so accordingly to the [[Ampere' | ||

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+ | | (1) | $$ H = \frac{I}{l} $$ | (A/m) | | ||

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+ | For the simplest case of a round, straight and infinitely long conductor with current (Fig. 2) the value of $H$ for a given circle with a radius $r$ can be calculated from the magnetic path length of the circle: | ||

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+ | | (2) | $$ H = \frac{I}{2⋅π⋅r} $$ | (A/m) | | ||

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+ | In a linear isotropic medium the values from various sources combine and can be calculated from the superposition of the sources. For simple geometrical cases the value of $H$ can be calculated analytically, | ||

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+ | The relationship between $H$ and $I$ is often shown by employing the [[Biot-Savart law|Biot-Savart' | ||

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+ | In many examples given in the literature there is an implicit assumption (typically not stated) that the derivation is carried out for vacuum and not for an arbitrary medium with a different permeability[(MIT)]. When the $μ_0$ permeability is reduced in the equations on both sides then $H$ is proportional only to $I$ and this is true for any uniform isotropic medium with any permeability, | ||

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+ | The situation is slightly different for [[anisotropic]] or discontinuous medium. They can give rise to additional sources of magnetic field because new [[magnetic pole|magnetic poles]] can be generated by the excited medium, and these poles must be taken into account in order to accurately describe distribution of $H$. For instance, pole pieces in an [[electromagnet]] affect $H$, whose distribution is no longer dictated by just the coils with electric current. | ||

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+ | ===== Defining H with force ===== | ||

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+ | It is shown in the literature that magnetic field strength at a given point in space can be defined as the mechanical [[force]] acting on [[unit pole]] at the given point.[(Mansfield)][(Bakshi)] However, calculation of force requires $B$, which depends on the properties of medium. Indeed, the original experiment performed by Biot and Savart involved physical forces acting on wires.[(Biot> | ||

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+ | Therefore, the forces acting on two magnetised bodies will be different if they are placed in oxygen (which is [[paramagnetic]]) or in water (which is [[diamagnetic]]). This difference will be directly proportional to the relative permeabilities of the involved media. However, the $H$ produced around the wire (Fig. 2) will be the same (as long as the medium is uniform and isotropic). | ||

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+ | ===== See also ===== | ||

+ | *[[Magnetic field]] | ||

+ | *[[Magnetic flux density]] | ||

+ | *[[Confusion between B and H]] | ||

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+ | ===== References ===== | ||

+ | ~~REFNOTES~~ | ||

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+ | {{tag> Magnetic_field Counter}} |