Two long straight parallel conductors are carrying currents `i_(1)andi_(2)` in the same direction. Work done per unit length, when the distance between them is doubled is

Options

A. `2xx(mu_(0))/(2pi)i_(1)i_(2)`
B. `(mu_(0))/(2pi)i_(1)i_(2)ln[2]`
C. `(mu_(0))/(2pi)i_(1)i_(2)ln[4]`
D. 0

Answer

B

Explanation

Work done = `int_(d)^(2d)F*dx=int_(d)^(2d)(mu_(0)i_(1)i_(2))/(2pix)*dx`
= `(mu_(0)i_(1)i_(2))/(2pi)[log_(e)x]_(d)^(2d)=(mu_(0)i_(1)i_(2))/(2pi)(log_(e)2)`