An arrangement of three parallel straight wires placed perpendicular 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. `(2mu_(0) i^(2))/(pi d)`
B. `(sqrt(2) mu_(0) i^(2))/(pi d)`
C. `(mu_(0) i^(2))/(sqrt(2) pi d)`
D. `(mu_(0) i^(2))/(2pi d)`

Answer

C

Explanation

`F = (mu_(0) i_(1) i_(2))/(2pi d)` = force per unit length
`F_(1) = ((mu_(0)i)i)/(2pi d) = (mu_(0) i^(2))/(2pi d) = F_(2)`

`F_(net) = sqrt(F_(1)^(2) + F_(2)^(2)) = (mu_(0) i^(2))/(sqrt(2pi d))`