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mLine 21:
Line 21: − <math>\nabla \cdot \mathbf{D} = \rho</math> + − <math>\nabla \cdot \mathbf{B} = 0</math> + − <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math> + − <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>+ − <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>+ − <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>+ − <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A} </math>+ − <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} ++
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One the the most important applications of the concepts you have learned are the equations which describe classical electricity and magnetism. These equations, called the [[Maxwell equations]] after [[James Clerk Maxwell]], are
One the the most important applications of the concepts you have learned are the equations which describe classical electricity and magnetism. These equations, called the [[Maxwell equations]] after [[James Clerk Maxwell]], are
<math>\nabla \cdot \mathbf{D} = \rho</math>
<math>\nabla \cdot \mathbf{B} = 0</math>
<math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
<math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
We can integrate all these equations to get the '''integral forms''':
We can integrate all these equations to get the '''integral forms''':
<math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
<math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
<math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A} </math>
<math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>