Maxwell's Equations: Difference between revisions
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: $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | : $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | ||
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$J=0$$), these equations reduce to: | In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathvf{J}=0$$), these equations reduce to: | ||
: $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$ | : $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$ | ||
Revision as of 18:20, 8 March 2020
Joe Schmoe (b. xxxx)
Title xxxx
- $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathvf{J}=0$$), these equations reduce to:
- $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = 0$$