Magnetic Flux Density

When a current I flows steadily through a magnetic field, a force proportional to the current acts in a direction perpendicular to the current. The force d F acting on an infinitesimal portion of the current I d r is expressed by the vector field B defined by the following equation. This vector field is called the magnetic flux density.

dF = Idr × B

Magnetic flux density B is a fundamental quantity corresponding to the electric field E. The force acting on a charge q moving at speed v through an electric field E and magnetic flux density B is expressed by the following equation.

F = q ( E + v × B )

This approach to electromagnetism, which establishes a correspondence between electric fields and magnetic flux density, is called the E - B correspondence. In this correspondence, the relationship between magnetic flux density B , magnetic field strength H , and magnetization M is expressed as follows:

B = μ ₀ ( H + M )

Here, μ ₀ is the magnetic permeability of a vacuum. On the other hand, there is a view that constructs electromagnetism by corresponding the electric field E and the magnetic field H. Starting from this view, the relationship between the magnetic flux density B and the magnetization M is defined as follows:

B = μ ₀ H + M

Therefore, the unit of magnetization differs by μ ₀ between E - H correspondence and E - B correspondence. The unit of magnetic flux density in the International System of Units (SI units) is Tesla (T), which is different from the unit of Gaussian unit, Gauss (G).

1 G = 10 ⁴ T
These are related as follows.

Source: Morikita Publishing "Chemical Dictionary (2nd Edition)" Information about the Chemical Dictionary 2nd Edition

磁場中を定常的に電流Iが流れていると，電流に対して垂直な方向に電流に比例した力がはたらく．電流の微小部分Idrにはたらく力dFは，次の式で定義されるベクトル場Bによって表される．このベクトル場を磁束密度という．

dF ＝ Idr × B

磁束密度Bは電場Eに対応する基本的な量である．電場E，磁束密度Bのなかを速度vで移動する電荷qにはたらく力は次式で表される．

F ＝ q(E ＋ v × B)

このように，電場と磁束密度を対応させて電磁気学を構成する立場をE-B対応という．この対応では，磁束密度Bと磁場の強さHおよび磁化Mとの関係は次のように表される．

B ＝ μ₀(H ＋ M)

ここで，μ₀ は真空の透磁率である．一方，電場Eと磁場Hを対応させて電磁気学を組み立てる立場がある．この立場からはじめると，磁束密度Bと磁化Mとの関係は次のように定義される．

B ＝ μ₀H ＋ M

そのため，E-H対応とE-B対応では磁化の単位が μ₀ の分だけ違ってくる．国際単位系(SI単位)による磁束密度の単位はテスラ(T)であり，ガウス単位系の単位であるガウス(G)とは

1 G ＝ 10⁴ T
の関係にある．

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