As a scalar quantity the current density J is defined by the following formula:
∆idi
(22) J = lim ----=---
∆sn →0 ∆sn dsn
where sn is the cross section of the current flux ΦJ . It is useful to note that
usually with i is denoted the flow of positive charges. The flow of negative
charges could be easily replaced with positive current with equal magnitude but
opposite direction. Sometimes however we would like to underline the nature of
the charges in the current and use vectors with indices i+ or i- where the
direction of the vectors coincides with the direction of motion.
If we have cable and current flowing through it, according to the Ohm’s law the
current i is proportional to the voltage V and conductance G and inversely
proportional to the resistance R:
|
(23) |
V i = — = V .G |
|
(24) |
R = ρS s |
|
(25) |
G = γ η- |
where ρ is the specific resistance for the media, γ is the specific conductance, l is
the length of the cable and s is its cross section.
22