Automoderated users, edit
3,552
edits
Changes
Jump to navigation
Jump to search
Line 17:
Line 17: − + + + + + + + + + + + + + + + +
a start
-->
-->
=The Maxwell Equations=
=The Maxwell Equations=
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''':
<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>
The four laws are called, respectively, Coulombs/Gauss' Law, absence of magnetic monopoles, Faraday's/Induction Law, and Ampère's Law.
{{MVCalc}}
{{MVCalc}}