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cgs Gauss単位系 |
E-H対応 MKSA単位系 |
E-B対応 SI単位系 |
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磁荷が磁場を作る |
磁荷が磁場を作る |
電流が磁場を作る |
Faradayの法則 |
$\nabla\times\mathbf{E}=-\dfrac{1}{c}\dfrac{\partial\mathbf{B}}{\partial t}$ |
$\nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t}$ |
$\nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t}$ |
Maxwell-Ampereの法則 |
$\nabla\times\mathbf{H}=\dfrac{1}{c}\dfrac{\partial \mathbf{D}}{\partial t}+\dfrac{4\pi}{c}\mathbf{I}$ |
$\nabla\times\mathbf{H}=\dfrac{\partial\mathbf{D}}{\partial t}+\mathbf{I}$ |
$\nabla\times\mathbf{H}=\dfrac{\partial\mathbf{D}}{\partial t}+\mathbf{I}$ |
Poisson方程式 |
$\nabla\cdot\mathbf{D}=4\pi\rho$ |
$\nabla\cdot\mathbf{D}=\rho$ |
$\nabla\cdot\mathbf{D}=\rho$ |
磁場 |
$\nabla\cdot\mathbf{B}=0$ |
$\nabla\cdot\mathbf{B}=0$ |
$\nabla\cdot\mathbf{B}=0$ |
Biot-Savartの法則 |
$d\mathbf{H} = \dfrac{1}{cr^2} \mathbf{I}\cdot d\mathbf{\ell}\times\hat{\mathbf{u}}$ |
$d\mathbf{H}=\dfrac{1}{4\pi r^2}\mathbf{I}\cdot d\mathbf{\ell}\times\hat{\mathbf{u}}$ |
$d\mathbf{H}=\dfrac{1}{4\pi r^2}\mathbf{I}\cdot d\mathbf{\ell}\times\hat{\mathbf{u}}$ |
Lorentz力 |
$q^{\mathrm{e}}(\mathbf{E}+\dfrac{1}{c}\mathbf{v}\times\mathbf{B})$ |
$q^{\mathrm{e}}(\mathbf{E}+\mathbf{v}\times\mathbf{B})$ |
$q^{\mathrm{e}}(\mathbf{E}+\mathbf{v}\times\mathbf{B})$ |
constitutive relation |
$\mathbf{D}=\varepsilon \mathbf{E}=\mathbf{E}+4\pi\mathbf{P}$ |
$\mathbf{D}=\varepsilon \mathbf{E}=\varepsilon_0 \mathbf{E}+ \mathbf{P}$ |
$\mathbf{D}=\varepsilon \mathbf{E}=\varepsilon_0 \mathbf{E}+ \mathbf{P}$ |
電気感受率 |
$\mathbf{P}=\chi^{\mathrm{e}} \mathbf{E},~ \varepsilon = 1+4\pi\chi^{\mathrm{e}}$ |
$\mathbf{P}=\varepsilon_0 \chi^{\mathrm{e}} \mathbf{E},~ \dfrac{\varepsilon}{\varepsilon_0}=1+\chi^{\mathrm{e}}$ |
$\mathbf{P}=\varepsilon_0 \chi^{\mathrm{e}} \mathbf{E},~ \dfrac{\varepsilon}{\varepsilon_0}=1+\chi^{\mathrm{e}}$ |
constitutive relation |
$\mathbf{B}~[\mathrm{G}] = \mu \mathbf{H} = \mathbf{H}~[\mathrm{Oe}] +4\pi\mathbf{M}~\left[\mathrm{\dfrac{emu}{cm^3}}\right]$ |
$\mathbf{B}~[\mathrm{T}] = \mu \mathbf{H} = \mu_0 \mathbf{H}+\mathbf{M}~\left[\mathrm{\dfrac{N}{A\cdot m}}=\mathrm{\dfrac{Wb}{m^2}}\right]$ |
$\mathbf{B}~[\mathrm{T}] = \mu \mathbf{H} = \mu_0(\mathbf{H}+\mathbf{M})= \mu_0\mathbf{H}+\mathbf{J}~\left[\mathrm{\dfrac{N}{A\cdot m}}=\mathrm{\dfrac{Wb}{m^2}}\right]$ |
磁気感受率 |
$\mathbf{M}=\chi^{\mathrm{m}} \mathbf{H}, ~ \mu = 1+4\pi \chi^{\mathrm{m}}$ |
$\mathbf{M}=\mu_0\chi^{\mathrm{m}} \mathbf{H}, ~ \dfrac{\mu}{\mu_0} = 1 + \chi^{\mathrm{m}}$ |
$\mathbf{M}=\chi^{\mathrm{m}} \mathbf{H}, ~ \dfrac{\mu}{\mu_0} = 1 + \chi^{\mathrm{m}}$ |
誘電率 |
$\varepsilon_0=1$ |
$\varepsilon_0\simeq 8.854\times{10^{-12}}~\left[\mathrm{\dfrac{C^2}{N\cdot m^2}}=\mathrm{\dfrac{F}{m}}\right]$ |
$\varepsilon_0\simeq 8.854\times{10^{-12}}~\left[\mathrm{\dfrac{C^2}{N\cdot m^2}}=\mathrm{\dfrac{F}{m}}\right]$ |
透磁率 |
$\mu_0=1$ |
$\mu_0 = 4\pi\times{10^{-7}}~\left[\mathrm{\dfrac{Wb}{A\cdot{m}}}=\mathrm{\dfrac{N}{A^2}}=\mathrm{\dfrac{H}{m}}\right]$ |
$\mu_0 = 4\pi\times{10^{-7}}~\left[\mathrm{\dfrac{Wb}{A\cdot{m}}}=\mathrm{\dfrac{N}{A^2}}=\mathrm{\dfrac{H}{m}}\right]$ |
電荷 |
$q^{\mathrm{e}}~[\mathrm{esu}=\mathrm{statC}]$ |
$q^{\mathrm{e}}~[\mathrm{C}]$ |
$q^{\mathrm{e}}~[\mathrm{C}]$ |
磁荷 |
$q^{\mathrm{m}}~[\mathrm{emu}]$ |
$q^{\mathrm{m}}~\left[\mathrm{Wb}=\mathrm{\dfrac{N\cdot m}{A}}\right]$ |
$\left(q^{\mathrm{m}}~[\mathrm{A\cdot m}]\right)$ |
電場 |
$E=\dfrac{q_1^e}{r^2}~\left[\mathrm{\dfrac{statV}{cm}}\right]$ |
$E=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1^e}{r^2}~\left[\mathrm{\dfrac{N}{C}}=\mathrm{\dfrac{V}{m}}\right]$ |
$E=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1^e}{r^2}~\left[\mathrm{\dfrac{N}{C}}=\mathrm{\dfrac{V}{m}}\right]$ |
磁場 |
$H=\dfrac{q_1^{\mathrm{m}}}{r^2}~[\mathrm{Oe}]$ |
$H=\dfrac{1}{4\pi\mu_0}\dfrac{q_1^{\mathrm{m}}}{r^2}~\left[\mathrm{\dfrac{A}{m}}=\mathrm{\dfrac{N}{Wb}}\right]$ |
$\left(H=\dfrac{1}{4\pi}\dfrac{q_1^{\mathrm{m}}}{r^2}~\left[\mathrm{\dfrac{A}{m}}\right]\right)$ |
電荷によるCoulomb力 |
$\dfrac{q_1^{\mathrm{e}}q_2^{\mathrm{e}}}{r^2}=Eq_2^{\mathrm{e}}~[\mathrm{dyne}]$ |
$\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1^{\mathrm{e}}q_2^{\mathrm{e}}}{r^2} = Eq_2^{\mathrm{e}}~[\mathrm{N}]$ |
$\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1^{\mathrm{e}}q_2^{\mathrm{e}}}{r^2} = Eq_2^{\mathrm{e}}~[\mathrm{N}]$ |
磁荷によるCoulomb力 |
$\dfrac{q_1^{\mathrm{m}}q_2^{\mathrm{m}}}{r^2}=Hq_2^{\mathrm{m}}~[\mathrm{dyne}]$ |
$\dfrac{1}{4\pi\mu_0}\dfrac{q_1^{\mathrm{m}}q_2^{\mathrm{m}}}{r^2}=Hq_2^{\mathrm{m}}~[\mathrm{N}]$ |
$\dfrac{\mu_0}{4\pi}\dfrac{q_1^{\mathrm{m}}q_2^{\mathrm{m}}}{r^2}=\mu_0 Hq_2^{\mathrm{m}}~[\mathrm{N}]$ |
磁気モーメント |
$\mathbf{m}=\dfrac{1}{c}I\mathbf{S}~\mathrm{or}~q^{\mathrm{m}}\mathbf{r} ~ \left[\mathrm{emu}=\mathrm{\dfrac{erg}{Oe}} \right]$ |
$\mathbf{m}=\mu_0 I\mathbf{S}~\mathrm{or}~q^{\mathrm{m}}\mathbf{r} ~ [\mathrm{Wb \cdot m}]$ |
$\mathbf{m}=I\mathbf{S}~(\mathrm{or}~q^{\mathrm{m}}\mathbf{r}) ~ \left[\mathrm{A\cdot m^2}=\mathrm{\dfrac{J}{T}} \right]$ |
磁化 |
$\mathbf{M}=\dfrac{\mathbf{m}}{V}~\left[\mathrm{\dfrac{emu}{cm^3}}\right]$ |
$\mathbf{M}=\dfrac{\mathbf{m}}{V}~\left[\mathrm{\dfrac{Wb}{m^2}}\right]$ |
$\mathbf{M}=\dfrac{\mathbf{m}}{V}~\left[\mathrm{\dfrac{A}{m}}\right],~\mathbf{J}=\mu_0 \mathbf{M}~[\mathrm{T}]$ |
Zeemanエネルギー |
$-\mathbf{m}\cdot\mathbf{H}~[\mathrm{erg}]$ |
$-\mathbf{m}\cdot\mathbf{H}~[\mathrm{J}]$ |
$-\mathbf{m}\cdot\mathbf{B}~[\mathrm{J}]$ |
磁束 |
$\Phi=HS~[\mathrm{Oe \cdot cm^2}=\mathrm{Mx}]$ |
$\Phi=\mu_0 HS~[\mathrm{Wb}=\mathrm{V\cdot s}=\mathrm{H\cdot A}]$ |
$\Phi=\mu_0 HS~[\mathrm{Wb}=\mathrm{V\cdot s}=\mathrm{H\cdot A}]$ |
誘導起電力 |
$-\dfrac{1}{c} \dfrac{\partial\Phi}{\partial t}~\left[\mathrm{\dfrac{Mx}{cm}} = \mathrm{V}\right]$ |
$-\dfrac{\partial\Phi}{\partial t}~\left[\mathrm{\dfrac{Wb}{s}} = \mathrm{V}\right]$ |
$-\dfrac{\partial\Phi}{\partial t}~\left[\mathrm{\dfrac{Wb}{s}} = \mathrm{V}\right]$ |
Poyntingベクトル |
$\dfrac{c}{4\pi}(\mathbf{E}\times\mathbf{H})~\left[\mathrm{\dfrac{erg}{s \cdot cm^2}}\right]$ |
$\mathbf{E}\times\mathbf{H}~\left[\mathrm{\dfrac{J}{s \cdot m^2}}\right]$ |
$\mathbf{E}\times\mathbf{H}~\left[\mathrm{\dfrac{J}{s \cdot m^2}}\right]$ |
電磁場エネルギー密度 |
$\dfrac{1}{8\pi}(E^2+B^2)$ |
$\dfrac{1}{2}\left(\varepsilon_0 E^2+\dfrac{B^2}{\mu_0}\right)~\left[\mathrm{\dfrac{J}{m^3}}\right]$ |
$\dfrac{1}{2}\left(\varepsilon_0 E^2+\dfrac{B^2}{\mu_0}\right)~\left[\mathrm{\dfrac{J}{m^3}}\right]$ |
電子の電荷量 |
$e=4.803\times10^{-10}~[\mathrm{statC}]$ |
$e=1.602\times 10^{-19}~[\mathrm{C}]$ |
$e=1.602\times 10^{-19}~[\mathrm{C}]$ |
Bohr磁子 |
$\mu_{\mathrm{B}}=\dfrac{e \hbar}{2mc}=9.274\times 10^{-21}~\left[\mathrm{emu}=\mathrm{Oe \cdot cm^3}=\mathrm{\dfrac{erg}{Oe}}\right]$ |
$\mu_{\mathrm{B}}=\dfrac{\mu_0 e \hbar}{2m}=1.165\times 10^{-29}~\left[\mathrm{Wb \cdot m}\right]$ |
$\mu_{\mathrm{B}}=\dfrac{e \hbar}{2m}=9.274\times 10^{-24}\,\left[\mathrm{A \cdot m^2}=\mathrm{\dfrac{J}{T}}\right]$ |