If Ohm's law is presumed to be valid, then drift velocity $V_{d}$ and electric field E are related as

v_{d} \propto E^{2}

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v_{d} \propto \sqrt{E}

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v_{d} \propto E

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v_{d} \propto E_{0}

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Solution

The correct option is B $v_{d} \propto E$
The force on electron due to applied electric field is: $F = e E$ .
If $m$ is the mass of electron, then acceleration produced is given by: $a = \frac{F}{m} = \frac{e E}{m}$ .
If $t$ is the average time interval then drift velocity of electron is: $v_{d} = a t = \frac{e E}{m} t$
Thus, $v_{d} \propto E$

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