where

Using , we can write
.....................................(7.2)

By solving equation (7.2) electric field can be determined for a specified current density and can be computed from by using (7.1b). However, as mentioned such direct computations are often difficult. Simplification can be obtained by introducing potential functions.

Since , we can write

.....................................................(7.3)

because and A is the vector potential.

From (7.1) and (7.3)

   
or,