Question

write the expression for current density in terms of drift velocity.

Answer 1

I-- nAev is the right answer

Answer 2

Answer: The current density will be in terms of drift velocity $I = A\ n\ e\ vd$.

Explanation:  

Let us consider, we have a conductor having length of l and A is area of cross section.

Therefore, the volume of the conductor is

$V = Al$

The total number of free electron in the conductor = $An$

The total charge on all the free electron in the  conductor

$Q = A\ l\ n\ e$

Now, the time taken by the free electron cross to the conductor

$t = \dfrac{l}{v_d}$

Where,

v =  drift velocity

l = length

Now, the current is

$I = \dfrac{Q}{t}$

Put the value of Q and t in equation (I)

$I = \dfrac{A\ l\ n\ e\ v_d}{l}$

$I = A\ n\ e\ v_d$

Hence, the current density will be in terms of drift velocity $I = A\ n\ e\ v_d$.