Current Density

Current density ‘’ defined as current flowing per unit cross-section area, is a vector quantity. Its direction is the same as that of current and it has following relation with current.

Alt txt : current-density

Integration is carried over the whole cross-section. Hence current may also be defined as the flux of current density vector through a cross-sectional area.

Illustration:

 If in the above figure, angle between , current density vector and , the are vector of cross section is 60^o, current i is 10A and area of given cross section is 2 × 10^–6 m². What is magnitude of current density.

        I = |||| cos q (as  is constant over the cross-section,  = A) 

        Þ || = 1 × 10⁷ A/m²