Воздействие векторного потенциала A на плотность заряда

Last modified by Alexey Popov on 2019/07/23 16:29

$\rho \frac{D \mathbf A}{D t} = \rho \frac{\partial \mathbf A}{\partial t} + (\mathbf J \cdot \nabla) \mathbf A =$

$= \frac{1}{2} (\rho \frac{\partial \mathbf A}{\partial t} + \frac{\partial \rho\mathbf A}{\partial t} - \frac{D \rho}{D t}\mathbf A + \nabla \left(\mathbf {A} \cdot \mathbf {J} \right)\,+\,\mathbf {J} \left(\nabla \cdot \mathbf {A} \right) \,+\,\nabla \times \left(\mathbf {A} \times \mathbf {J} \right) - \mathbf {A} \times \left(\nabla \times \mathbf {J} \right)-\mathbf {J} \times \mathbf {B})$

$(\mathbf A \cdot \nabla)\mathbf B = \nabla (\mathbf A \cdot \mathbf B) - \mathbf A \times (\nabla \times \mathbf B)$

$\rho \frac{D \mathbf A}{D t} = \rho \frac{\partial \mathbf A}{\partial t} + \nabla (\mathbf J \cdot \mathbf A) - \mathbf J \times (\nabla \times \mathbf A)$

$\frac{D \mathbf A}{D t} = \frac{\partial \mathbf A}{\partial t} + \nabla (\mathbf v \cdot \mathbf A) - \mathbf v \times (\nabla \times \mathbf A)$

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Created by Alexey Popov on 2019/07/23 16:00