A uniform wire of diameter d carries a current of 100 mA when the mean drift velocity of electrons in the wire is v. For a wire of diameter d/2 ​

Question

A uniform wire of diameter d carries a current of 100 mA when the mean drift velocity of electrons in the wire is v. For a wire of diameter \(\frac{d}{2}\)of the same material to carry a current of 200 mA, the mean drift velocity of electrons in the wire is

(1) 4v

(2) 8v

(3) v

(4) 2v

Answer 1

Correct option is : (2) 8v

current \(i=n A v_{d} e\)  \( \left(v_{d}=\text { mean drift velocity}\right) \)

\(=n\left(\frac{\pi D^{2}}{4}\right) v_{d} e\) 

\(\therefore\ i \propto D^{2} v_{d} \) 

\(\frac{100}{200}=\frac{(d)^{2}}{\left(\frac{d}{2}\right)^{2}} \times \frac{v}{v^{\prime}} \) 

\( \Rightarrow v^{\prime}=2 \times 2^{2} v=8 v\)