The drift velocity of electrons in a conductor is 'v' when a current 'i' flows through it. If the area of the cross-section of the conductor is reduced to half of its initial value, then the drift velocity will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( v \)
Note: The given answer is as per the official NTA Answer Key. However, according to us the correct answer should be Option (3) \( 2v \), because it seems that NTA has assumed that the drift velocity does not depend on the area of cross-section, whereas for a fixed current it does, as explained below.
Working as per the NTA key
The drift velocity is set by the electric field inside the conductor; the area of cross-section does not appear, so for the same field it stays \( v \). This gives Option (2).
\( \displaystyle v_{d} = \mu E \)
Working as per the standard method
The question keeps the same current, and \( n \) and \( e \) do not change:
\( \displaystyle I = n\,e\,A\,v_{d} \;\Rightarrow\; v_{d} = \frac{I}{n e A} \propto \frac{1}{A} \)
\( \displaystyle v' = \frac{I}{n e (A/2)} = 2\,\frac{I}{n e A} = 2v \)
Hence, as per the standard method, the correct answer is Option (3).