Maxwell's Equations: Difference between revisions
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: $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$ | : $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$ | ||
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$ | : $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$ | ||
: $$\nabla \cdot \mathbf{B} = 0$$ | : $$\nabla \cdot \mathbf{B} = 0$$ | ||
: $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | : $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ | ||
This formulation assumes no charge $$\rho=0$$ and $$J=0$$. One common example of these conditions is a vacuum. | |||
: $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$ | |||
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$ | |||
: $$\nabla \cdot \mathbf{B} = 0$$ | |||
: $$\nabla \cdot \mathbf{E} = 0$$ | |||
== Resources: == | == Resources: == | ||
*[https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's Equations] | *[https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's Equations] | ||
== Discussion: == | == Discussion: == | ||
Revision as of 18:19, 8 March 2020
Joe Schmoe (b. xxxx)
Title xxxx
- $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
This formulation assumes no charge $$\rho=0$$ and $$J=0$$. One common example of these conditions is a vacuum.
- $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
- $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
- $$\nabla \cdot \mathbf{B} = 0$$
- $$\nabla \cdot \mathbf{E} = 0$$