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| '''James Clerk Maxwell''' (b. 1831) | | '''Joe Schmoe''' (b. xxxx) |
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| '''''Maxwell's Equations''''' 1861 | | '''''Title''''' xxxx |
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| In general, Maxwell's equations take the form:
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| : <math>\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)</math>
| | This formulation assumes no charge $$\rho=0$$ and $$J=0$$. One common example of these conditions is a vacuum. |
| : <math>\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}</math>
| | : $$\nabla \times \mathbf{B} = +\frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}$$ |
| : <math>\nabla \cdot \mathbf{B} = 0</math>
| | : $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}$$ |
| : <math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}</math>
| | : $$\nabla \cdot \mathbf{B} = 0$$ |
| Β | | : $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ |
| where <math>\epsilon_0</math> is the permittivity of free space and <math>\mu_0</math> is the permeability of free space.
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| Β | |
| In the example of an ideal vacuum with no charge or current, (i.e., <math>\rho=0</math> and <math>\mathbf{J}=0</math>), these equations reduce to:
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| Β | |
| : <math>\nabla \times \mathbf{B} = \mu_0 \epsilon_0Β \frac{\partial \mathbf{E}}{\partial t}</math> | |
| : <math>\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}</math> | |
| : <math>\nabla \cdot \mathbf{B} = 0</math> | |
| : <math>\nabla \cdot \mathbf{E} = 0</math> | |
| Β | |
| Note that the speed of light is:
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| Β | |
| : <math>c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}</math>
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| == 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: == |