Choose the correct relation between drift velocity (\( v_d \)) and current density (J) from the following:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( v_d = \displaystyle\frac{J}{ne} \)
Current density is the current per unit area of cross-section, \( J = I/A \). The current in a conductor with \( n \) free electrons per unit volume, each of charge \( e \), moving with drift velocity \( v_d \), is \( I = n e A v_d \).
\( \displaystyle J = \frac{I}{A} = n e v_d \;\Rightarrow\; v_d = \frac{J}{ne} \)
NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “… If n is the number of free electrons per unit volume in the metal, then there are n Δt |vd|A such electrons. … The amount of charge crossing the area A in time Δt is by definition [Eq. (3.2)] I Δt, where I is the magnitude of the current. Hence,
\( \displaystyle I\,\Delta t = +\,n e A \left|v_d\right| \Delta t \qquad (3.18) \)
… By definition I is related to the magnitude |j| of the current density by
\( \displaystyle I = |j| A \qquad (3.20) \)”