Производные электромагнитные поля

Last modified by Alexey Popov on 2019/05/24 10:53

$\mathbf E = \nabla (\mathbf v \cdot (-\mathbf v))-\frac{\partial \mathbf v}{\partial t}$

$\mathbf B = \nabla \times \mathbf v$

$\nabla \times \mathbf B = \nabla \times (\nabla \times \mathbf v)=\mathbf J$

$\varphi = \frac{\rho^2}{\rho_n^2} (\mathbf B)\cdot ( - \mathbf B)= \frac{\rho^2}{\rho_n^2} (\nabla \times \mathbf v)\cdot ( - \nabla \times \mathbf v) + \nabla \cdot (\nabla (\mathbf v \cdot (- \mathbf v)))$

$\rho_S = \square \varphi$

$\mathbf J_S = \square \varphi \mathbf v$

$\mathbf S = \varphi\mathbf v$

$\mathbf B_S = \nabla \times \mathbf S$

$\mathbf E_S = -\nabla\varphi-\frac{\partial \mathbf S}{\partial t} + 2\mathbf S \times (\nabla \times \mathbf S)$

$\nabla \times \mathbf B_S = \mathbf J_S +\frac{\partial \mathbf E_S}{\partial t}$

$\nabla \cdot \mathbf s = (\mathbf B_S)\cdot (-\mathbf B_S) = (\nabla \times \mathbf S)\cdot (-\nabla \times \mathbf S)=(\nabla \times \varphi\mathbf v)\cdot (-\nabla \times \varphi\mathbf v)$

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Created by Alexey Popov on 2019/05/16 12:15

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