The relation between current density j, drift velocity v_d, number density n and charge e for a metallic conductor is

1. The number of free electrons crossing area A in time Δt is n A v_d Δt. 2. Each electron carries charge e, so total charge is n e A v_d Δt. 3. Current I = charge / time = n e A v_d, giving current density j = I / A = n e v_d. 4. So current density is the product of number density, charge and drift velocity. _Source: syllabus Physics, Ch 3 "Current Electricity", §3.5_