Maxwell's Equations: Difference between revisions
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: $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \ | : $$\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} = +\ | : $$\nabla \times \mathbf{B} = + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$ | ||
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$ | : $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$ | ||
: $$\nabla \cdot \mathbf{B} = 0$$ | : $$\nabla \cdot \mathbf{B} = 0$$ | ||
Revision as of 18:23, 8 March 2020
- $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:
- $$\nabla \times \mathbf{B} = + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = 0$$