A current flowing in a copper wire is passed through another copper wire of the same length but of double the radius of the first one. How would the drift velocity of free electrons change?

Solution

Drift velocity is given by,

$v_{d} = \frac{1}{n Ae} = \frac{1}{n π r^{2} e} i . e ., v_{d} \propto \frac{1}{r^{2}}$

$∴$ $\frac{v_{d_{2}}}{v_{d_{1}}} = \frac{r^{2}}{(2 r)^{2}} = \frac{1}{4}$
$v_{d_{2}} = \frac{1}{4} v_{d_{1}}$

So, the drift velocity becomes one-fourth of it's initial value when radius of the conductor is doubled.

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Current Electricity

A current flowing in a copper wire is passed through another copper wire of the same length but of double the radius of the first one. How would the drift velocity of free electrons change?

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