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Question

When a current I is set up in a wire of radius r, the drift velocity is vd. If the same current is set up through a wire of radius 2r of same material, the drift velocity will be

A
4vd
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B
vd2
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C
2vd
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D
vd4
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Solution

The correct option is D vd4
We know the relation between current and drift velocity given by,
I=neAvd
where n= number of electrons per unit volume.
e= charge on electron
A= Area
vd=IneA(1)
For wire with radius 2r, area Af=π(2r)2=4πr2=4A
Hence for wire of radius 2r drift velocity, vdfIneAf=Ine(4A)=vd4

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