Two long parallel conducting wires carrying currents are seperated by a distance 'x' . Work done per unit length in changing the distance between the wires is proportional to

Options

A. `(1)/(log_(e)x)`
B. `(1)/(x)`
C. `log_(e)x`
D. x

Answer

C

Explanation

We know that
`(F)/(l) = (mu_(0)I_(1)I_(2))/(2pi x) " ". . . (i)`
When conducting wire is displaced by (x) dx distance, then work done per unit length is
dW = f . dx
`dE = (mu_(0) I_(1)I_(2))/(2 pi x) dx " "["From Eq" . (i) ] `
`int dw= int (mu_(0)I_(1)I_(2))/(2pi x) dx `
` W = (mu_(0) I_(1)I_(2))/(2pi) int (dx)/(x)`
`W = ((mu_(0) I_(1)I_(2))/(2pi)) log_(e)x`
`rArr Wprop log _(e)x`