Question

Define current density (j)and write expression for current density in terms of drift velocity.

Answer 1

Current density is the electric current per unit area of cross section.

Consider a conductor of length l and area of cross section A. Let the number of free electrons per unit volume be n. When a pd V is applied, let the drift velocity of electrons be v.

The total no. of free electrons in the piece of conductor = nAl (no. of free electrons per unit volume x volume)

Total charge due to free electrons; q  = nAle

The time taken by this charge to completely traverse the conductor, t =l/v

Therefore, the current in the conductor, I=q/t = nAle/(l/v) = nAev

i.e; I=nAev

Answer 2

The amount of electric current flowing per unit cross-sectional area of a material.
Consider a conductor of length l and area of cross section A. Let the number of free electrons per unit volume be n. When a pd V is applied, let the drift velocity of electrons be v.

The total no. of free electrons in the piece of conductor = nAl (no. of free electrons per unit volume x volume)

Total charge due to free electrons; q = nAle

The time taken by this charge to completely traverse the conductor, t =l/v

Therefore, the current in the conductor, I=q/t = nAle/(l/v) = nAev

i.e; I=nAev

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