Maxwell's Equations: Difference between revisions

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: $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \cdot \mathbf{B} = 0$$
: $$\nabla \cdot \mathbf{B} = 0$$
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In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:


: $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{B} = + \mu_0 \epsilon_0  \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \cdot \mathbf{B} = 0$$
: $$\nabla \cdot \mathbf{B} = 0$$
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