Discussion
When the electric field applied across a conductor is doubled without changing its temperature, the drift velocity
Answer: A
The drift velocity doubles.
Drift velocity is \(v_{d} = \frac{eE\tau}{m} = \mu E\), where the relaxation time \(\tau\) (and so the mobility \(\mu\)) depends on temperature. With the temperature unchanged, \(\tau\) stays the same, so \(v_{d}\) is directly proportional to \(E\): doubling the field doubles the drift velocity.
Tripling or quadrupling would need \(v_{d}\) to depend on a higher power of \(E\), and halving or no change would contradict the direct proportionality. This proportionality is the microscopic basis of Ohm's law.
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