3.9.3 Current Density

where has been assumed. By taking the limit ( and ) and assuming that the right-hand-side of (3.85) approaches zero in this limit, one obtains

(3.86) |

By multiplying both sides by and recalling the definition of the charge density, one recovers the continuity equation

where the current density is defined as

Under steady-state condition the current density takes the form [60]