Electric current density

 

1)

 


 


2) Suppose a conductor with area of cross-section A.


3) Suppose I current is applied across the conductor.


4) for a time period the charge passing through the conductor is




5) Now suppose

n = is the number of free electrons per unit volume.

Vd = is the drift velocity of electron

A = area of cross-section



Therefore distance travelled by electrons at time is



6) Volume of the conductor is





7) No of free electrons in that volume




8) then charge of these electrons






Now this charge is equal to 

 

 

9) therefore




10) this quantity



or current passing through per unit area of cross-section is also called the current density denoted as J.


or J = n e Vd 



11) we also know that drift velocity Vd is




12) therefore the current density J is