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Define the term current density of a metallic conductor. Deduce the relation connecting current density (J) and the conductivity σ of the conductor, when an electric field E, is applied to it.

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In a conductor, current density at particular point is the current flowing per unit area in conductor provided the area is in direction normal to current. 

Current density is a vector quantity. Its direction is the direction of motion of positive charge. The unit of current density is ampere/meter2, or [Am-2]

Relation between J and E :

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