A square wire frame of side a is placed a distance b away from a long straight conductor carrying current I. The frame has resistance R and self-inductance L. The frame is rotated by $180^{o}$ about OO' as shown in Fig. Find the electric charge flown through the frame -

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i = 1 R d ϕ d t + L d i d t q = ∫ i d t = 1 R ∆ ϕ + 0 = ∆ ϕ R = 1 R ∫ b - a b + a B a d x = 1 R ∫ b - a b + a μ 0 i a 2 π x d x = μ 0 i a 2 π R log e ⁡ b + a b - a

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