Solution:
Since \(I = n e A v_d = n e \pi r^2 v\), the new current is \(I' = n e \pi \left(\frac{r}{2}\right)^2 (2v) = \frac{1}{2} n e \pi r^2 v = I/2\).
In a wire of cross-section radius \(r\), free electrons travel with drift velocity \(v\) when a current \(I\) flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is \(2v\)?
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