A) \[{{v}_{\text{P}}}={{v}_{\text{Q}}}\]
B) \[{{v}_{\text{P}}}={{v}_{\text{Q}}}\]
C) \[{{v}_{\text{P}}}=\frac{1}{4}{{v}_{\text{Q}}}\]
D) \[{{v}_{\text{P}}}=\text{ 2}{{v}_{\text{Q}}}\]
Correct Answer: C
Solution :
Drift velocity \[{{v}_{d}}=\frac{i}{neA}\Rightarrow {{v}_{d}}\propto \frac{1}{A}\text{ or}\,{{v}_{d}}\propto \frac{1}{{{d}^{2}}}\] \[\Rightarrow \,\frac{{{v}_{P}}}{{{v}_{Q}}}={{\left( \frac{{{d}_{Q}}}{{{d}_{P}}} \right)}^{2}}={{\left( \frac{d/2}{d} \right)}^{2}}=\frac{1}{4}\Rightarrow {{v}_{P}}=\frac{1}{4}{{v}_{Q}}\].
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