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Current Density Vector

A current i...

Question

A current $i$ is flowing through the wire of diameter $d$ having drift velocity of electrons $v_{d}$ in it. What will be new drift velocity when diameter of wire is made $\frac{d}{4}$ ?

A

4 V_{d}

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B

\frac{V_{d}}{4}

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C

16 V_{d}

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D

\frac{V_{d}}{16}

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Solution

The correct option is C $16 V_{d}$
$I = n A e V_{d}$
Now $I$ is constant
$V_{d} α \frac{1}{A}$
If diameter of wire is $\frac{d}{4}$ than area is $\frac{1}{16}$ times so $V_{d}$ new drift velocity $= 16 V_{d}$ .

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