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. `(mu_(0) i^(2))/(2pi d)`
B. `(2 mu_(0) i^(2))/(pi d)`
C. `(sqrt2 mu_(0) i^(2))/(pi d)`
D. `(mu_(0) i^(2))/(sqrt2 pi d)`

Answer

D

Explanation

So , `vecF_("net") = sqrt(F^(2) + F^(2)) = sqrt2F = (sqrt2 mu_(0) I^(2))/(2pi d) = (mu_0 i^2)/(sqrt2 pi d)`