Потенциалы электромагнитного поля второго порядка

Last modified by Alexey Popov on 2019/12/12 17:15

$\mathbf E = - \mathbf \nabla \varphi - \frac{\partial \mathbf A}{\partial t}$

$\mathbf B = \mathbf \nabla \times \mathbf A$

$\nabla \cdot \mathbf A + \frac{1}{c^2}\frac{\partial \varphi }{\partial t} = 0$

$\square\mathbf A = -\mu_0 \mathbf J$

$\square \varphi = - \frac{1}{\varepsilon_0} \rho$

$\mathbf E = - \nabla\varphi - \frac{\partial \mathbf A}{\partial t} + \nabla \times \nabla \times \mathbf E_q - \nabla (\nabla \cdot \mathbf E_q) + \frac{1}{v^2}\frac{\partial^2 \mathbf E_q}{\partial t^2}$

$\mathbf B = \nabla \times \mathbf A + \nabla \times \nabla \times \mathbf B_q + \frac{1}{v^2}\frac{\partial^2 \mathbf B_q}{\partial t^2}$

$\nabla \cdot \mathbf E_q = \varphi$

$\nabla \cdot \mathbf B_q = 0$

$\nabla \times \mathbf E_q = - \frac{\partial \mathbf B_q}{\partial t}$

$\nabla \times \mathbf B_q = \mathbf A + \frac{1}{v^2}\frac{\partial \mathbf E_q}{\partial t}$

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Created by Alexey Popov on 2019/12/11 16:45

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