An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I'

Question

31. An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire ' \( B \) ' is given by [NEET 2017] 

(A) \( \frac{\mu_{0} I^{2}}{2 \pi d} \) (B) \( \frac{2 \mu_{0} I^{2}}{\pi d} \) (C) \( \frac{\sqrt{2} \mu_{0} I^{2}}{\pi d} \) (D) \( \frac{\mu_{0} I^{2}}{\sqrt{2} \pi d} \)

Answer 1

Correct option is (D) \(\frac {\mu _ 0 i^2}{\sqrt 2 \pi d}\)

Magnetic force per unit length on one wire due to another wire is given by,

\(F_{net} =\sqrt {F^2_1 + F^2 _2} = \frac {\mu _0 i^2}{\sqrt {2} \pi d}\)