Electromagnetic Theory

(1294) | ||

(1295) | ||

(1296) | ||

(1297) | ||

(1298) | ||

(1299) |

(Fitzpatrick 2008). Here, is the electric field-strength, the magnetic intensity, the current density (i.e., the current per unit area), the electric permittivity of free space, and the magnetic permeability of free space.

For the case of a vacuum,

(1300) |

Hence, the previous equations simplify to give

(1301) | ||

(1302) | ||

(1303) | ||

(1304) | ||

(1305) | ||

(1306) |

For the case of a dielectric medium,

(1307) |

where is the electric dipole moment per unit volume (Fitzpatrick 2008). Hence, we obtain

(1308) | ||

(1309) | ||

(1310) | ||

(1311) | ||

(1312) | ||

(1313) |

In a linear dielectric medium,

(1314) |

where is the relative dielectric constant (Fitzpatrick 2008). In this case, defining the electric displacement,

(1315) |

we get

(1316) | ||

(1317) | ||

(1318) | ||

(1319) | ||

(1320) | ||

(1321) |

where is the characteristic wave speed, and the velocity of light in vacuum.

In an Ohmic conductor,

(1322) |

where is the electrical conductivity (Fitzpatrick 2008). Thus, the equations governing electromagnetic wave propagation in such a medium become

(1323) | ||

(1324) | ||

(1325) | ||

(1326) | ||

(1327) | ||

(1328) |

The energy flux associated with an electromagnetic wave has the components

(1329) | ||

(1330) | ||

(1331) |

irrespective of the medium (as long as it is non-magnetic) (Fitzpatrick 2008).

If is the interface between two different (non-magnetic) media then the general matching conditions for the components of the electric and magnetic fields across the interface are

(1332) | ||

(1333) | ||

(1334) | ||

(1335) | ||

(1336) | ||

(1337) |

(Fitzpatrick 2008).

The equation of motion of a particle of mass and charge situated in electric and magnetic fields is

(1338) | ||

(1339) | ||

(1340) |

where are the particle's Cartesian coordinates, and is the magnetic field-strength (Fitzpatrick 2008).