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Physics · 2025 · 3 marks
CBSE 2025 · Region 6 · Set 2 · Q22
(a) Define the term'drift velocity'of conduction electrons in a conductor. (b) A conductor of length l and area of cross-section A is connected…
(a)
Define the term'drift velocity'of conduction electrons in a conductor.
(b)
A conductor of length $\displaystyle l$ and area of cross-section A is connected across an ideal battery of emf V. Derive the formula for the current density in terms of relaxation time $\displaystyle \tau$.
Marking-scheme solution
(a)
Drift velocity is the average velocity with which the free electrons move under external electric field in a conductor.
(b)
Current density
\[j = \frac{I}{A} \]
\[\because I = neA\mathrm{v}_d \]
\[\therefore j = ne\mathrm{v}_d \]
But $\displaystyle \mathrm{v}_d = \dfrac{eE\tau}{m}$
\[\therefore j = \frac{ne^{2}\tau E}{m} = \frac{ne^{2}\tau}{m}\left(\frac{V}{l}\right) \]
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