Difference between revisions of "Maxwell's Equations"
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In general, Maxwell's equations take the form: | |||
: $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$ | : $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$ | ||
| Line 4: | Line 6: | ||
: $$\nabla \cdot \mathbf{B} = 0$$ | : $$\nabla \cdot \mathbf{B} = 0$$ | ||
: $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | : $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | ||
where $$\epsilon_0$$ is the permittivity of free space and $$\mu_0$$ is the permeability of free space. \\ | |||
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: | ||
Revision as of 18:26, 8 March 2020
In general, Maxwell's equations take the form:
- $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
where $$\epsilon_0$$ is the permittivity of free space and $$\mu_0$$ is the permeability of free space. \\
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:
- $$\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = 0$$