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

Options

A. `(2mu_0I^2)/(pid)`
B. `(sqrt(2))mu_0 I^2)/(pid)`
C. `(mu_0I^2)/(sqrt(2)pid)`
D. `(mu_0I^2)/(2pid)`

Answer

C

Explanation

Force between sires A and B = force between wires B and CC
`therefore F_(BC) = F_(AB) = (mu_0I^2l)/(2pi d)`
As `vecF_(AB) _|_ vecF_(BC),` net force on wire B,
`F_("net")= sqrt(2)F_(BC) = (sqrt(2)mu_0 I^2l)/(2pid)`
`F_("net") = (mu_0I^2l)/(sqrt(2)pi d) or (F_("net"))/(l) = (mu_0I^2)/(sqrt(2)pid)`