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

Options

A. v
B. `(v)/(2)`
C. `(v)/(4)`
D. `(v)/(8)`

Answer

B

Explanation

Given initial drift velocity `(v_(d_(1)))=v`, initial current `(I_(1))=I`, initial radius `(r_(1))=r`, final radius `(r_(2))=2r` and final current `(I_(2))=2I`. The drift velocity is given by
`v_(d)=(I)/(n eA)=(I)/(n exxpir^(2))i.e., v_(d)prop(I)/(r^(2))`
Therefore, `(v_(d_(1)))/(v_(d_(2)))=(I_(1))/(I_(2))xx(r_(2)^(2))/(r_(1)^(2))=(I)/(2I)xx((2r)^(2))/(r^(2))=2 therefore v_(d_(2))=(v_(d_(1)))/(2)=(v)/(2)`