Using the concept of free electrons in a conductior , derive the expression for the conductivity of a wire in terms of number density and relaxation time . Hence obtain the relation between current density and the applied electric field E.

Explanation

Derivation of the expression for conductivity Relation between density and electric field
The acceleration ` overset to ( a) = - ( in )/( m ) oversetto E `
The average drift velocity , vd , is given by
` vd = - ( eE) /( m ) `
` ( tau `=average time between collisions / relaxtion time )
If n is the number of free electrons per unit volumes , the current I is given by
` I= neA | vd|
` = ( e^(2) A)/( m ) tau n |E| `
But I= |j| A ( j = current density )
we . therefore . get