An arrangment of three parallel staright wires placed perpendcular to plane of paper carrying same current `I` along the same direction is shown in figure. Magnitude of force per unit length on the middle wire `'B'` is given by

Options

A. `(mu_(0)i^(2))/(2pid)`
B. `(2mu_(0)i^(2))/(pid)``(mu_(0)i^(2))/(2pid)`
C. `(sqrt(2mu)_(0)i^(2))/(pid)`
D. `(mu_(0)i^(2))/(sqrt(2)(pid))`

Answer

D

Explanation

As ,force on wire B due to A and c are attractive so we have following condition
Resultant force on B
`=sqrt(F_(1)^(2)+F_(2)^(2))`
`=sqrt(2)F=sqrt(2)xx(mu_(0)I^(2))/(2pid)=(mu_(0)I^(2))/(sqrt(2pid))`