The relation between current density j, drift velocity v_d, number density n and charge e for a metallic conductor is
A{'text': 'j = n e / v_d', 'label': 'A'}
B{'text': 'j = e v_d / n', 'label': 'B'}
C{'text': 'j = n v_d / e', 'label': 'C'}
D{'text': 'j = n e v_d', 'label': 'D'}
Answer & Solution
Correct answer: D. {'text': 'j = n e v_d', 'label': 'D'}
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: NCERT Class 12 Physics, Ch 3 "Current Electricity", §3.5_
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