What is the relation between current density and electric field?

Current density J is a vector quantity which is defined as the current flowing per unit area measured in a direction normal to the direction of flow of charge.

|J| = |I|/ A

Substituting the value of I and Vd in this equation |J| = |I|/ A ;

|J|= nAqVd / A

= nq. (qt|E|/ m)

|J| = (nq2t/ m).|E|

 The vector J is parallel to the electric field vector.

In the above equation the quantity nq2t/ m is called conductivity σ.

|J| = (nq2t/ m).|E| = σ |E|

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