Appeared in: 2024 (3 sets)
Assertion (A) : When electrons drift in a conductor, it does not mean that all free electrons in the conductor are moving in the same direction.
Reason (R) : The drift velocity is superposed over large random velocities of electrons.
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Official Evaluation Steps & EL10 Insight
Step 1 (Formula / Governing Law & Given Data): [0.5 Marks]
In a conductor, the total velocity $\vec{v}_i$ of the $i^{\text{th}}$ free electron in the presence of an external electric field $\vec{E}$ is given by the superposition of its random thermal velocity $\vec{u}_i$ and the acquired drift velocity $\vec{v}_d$:
$$\vec{v}_i = \vec{u}_i + \vec{v}_d$$Where:
- $\vec{u}_i$ = Thermal velocity due to temperature ($\sim 10^5 \text{ m/s}$ to $10^6 \text{ m/s}$, randomly oriented such that $\sum \vec{u}_i = 0$).
- $\vec{v}_d = -\frac{e\vec{E}}{m}\tau$ = Drift velocity ($\sim 10^{-4} \text{ m/s}$, directed opposite to $\vec{E}$).
- $\tau$ = Relaxation time between successive collisions.
Step 2 (Step-by-Step Mathematical Working): [0.5 Marks]