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where - conductor length; S - cross-sectional area;  - specific
resistance of the conductor. It is stated from (37.2) that at = 1 m and
2
S = 1 m the specific resistance is numerically equal to R, that is:
the specific resistance of the conductor is numerically equal to
the resistance of the conductor from this material of unit length and
the unit area of the cross section.

In the SI system, the specific resistance of the conductor is
measured in Ohm. The value, inversely proportional to the specific
resistance, is called specific conductivity and is denoted by  (sigma).

1
  . (37.3)


For an infinitely small element of a conductor, within which the

specific conductivity is the same, Ohm law is written in the
differential form:

 
j  E (37.4)

This form of recording links the differential values, that is, the
quantities related to the infinitely small volume, that is got to the point.

1
The current density vector j at this point of the conductor is

proportional to the vector strength E of the electric field at the same
point of the conductor. The coefficient of proportionality is the
specific conductivity of the conductor at this point.
The electric current in metals is caused by free movement of

electrons. According to the ideas of classical physics, the free
electrons in metal can be considered as an ideal gas. In an external
electric field, the chaotic (thermal) movement of electrons is

superimposed by the ordered one, as a result there is an electric
current. The classical electronic theory of conductivity of metals gives
the derivation of the Ohm's law in a differential form (37.5)

1
The current density j – is the ratio of the current strength in the
conductor to its cross-sectional area j=І/S. The direction of the current density
vector has the direction of positive charge movement in a conductor under the
action of an electric field.

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