Maxwell's Equations

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Revision as of 18:24, 8 March 2020 by 76.28.40.176 (talk)
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$$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$
$$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
$$\nabla \cdot \mathbf{B} = 0$$
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$

In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:

$$\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
$$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
$$\nabla \cdot \mathbf{B} = 0$$
$$\nabla \cdot \mathbf{E} = 0$$

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