The drift velocity of free electrons in a con | vedclass

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(B) The drift velocity $v_d$ of free electrons in a conductor is given by the formula: $v_d = \frac{i}{neA}$,where $i$ is the current,$n$ is the numbe

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$\frac{v}{2}$

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(B) The drift velocity $v_d$ of free electrons in a conductor is given by the formula: $v_d = \frac{i}{neA}$,where $i$ is the current,$n$ is the number density of electrons,$e$ is the charge of an electron,and $A$ is the cross-sectional area of the conductor.Since the conductor is a wire,the cross-sectional area $A = \pi r^2$,where $r$ is the radius.Thus,$v_d = \frac{i}{ne\pi r^2}$.From this,we can see that $v_d \propto \frac{i}{r^2}$.Let the initial drift velocity be $v_1 = v$,initial current be $i_1 = i$,and initial radius be $r_1 = r$.Let the new drift velocity be $v_2$,new current be $i_2 = 2i$,and new radius be $r_2 = 2r$.Using the proportionality $v_d \propto \frac{i}{r^2}$,we get:$\frac{v_2}{v_1} = \frac{i_2}{i_1} 	imes \left( \frac{r_1}{r_2} ight)^2$$\frac{v_2}{v} = \frac{2i}{i} 	imes \left( \frac{r}{2r} ight)^2$$\frac{v_2}{v} = 2 	imes \left( \frac{1}{2} ight)^2 = 2 	imes \frac{1}{4} = \frac{1}{2}$Therefore,$v_2 = \frac{v}{2}$.

The drift velocity of free electrons in a conductor is $v$ when a current $i$ is flowing in it. If both the radius and current are doubled,then the drift velocity will be

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