A current .I. flows through a metallic wire of radius .r. and the free electrons in it drift with a velocity `v_(d)`. Calculate the drift velocity of the free electrons through the wire of the same material, having double the radius, when same current flows through it.

Explanation

We know that, `I="ne"Av_(d)`
Drift velocity, `v_(d)=(I)/("ne"A)=(I)/("ne"pir^(2))" "......(1)`
When the radius is doubled,
Drift velocity, `v._(d)=(I)/("ne"pi(2r)^(2))" "......(2)`
Now, `(v_(d))/(v._(d))=((I)/("ne"pir^(2)))/((I)/("ne"pir^(2)(4)))`
[Using equation (1) and (2)]
`(v_(d))/(v._(d))=4`
`v._(d)=(v_(d))/(4)=(1)/(4)` th of the original