A rectangular frame of negligible resistance with capacitor of capacitance C is placed nearby an infinitely long wire carrying current $I = I_{0} sin (ω t + \frac{π}{6})$ , wire and frame being in same plane. Select correct alternative (s):

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Flux through frame = 2 π μ 0 ​ ​ ∫ 2 4 ​ x 4 d x ​ ∴ ϕ = ( π 2 μ 0 ​ ℓ n 2 ​ ) i ∴ ε = ​ d t d ϕ ​ ​ = ( π 2 μ 0 ​ ℓ n 2 ​ ) d t d i ​ = π 2 μ 0 ​ i 0 ​ ω ℓ n 2 ​ cos ( ω t + 6 π ​ ) ⇒ Q = ξ c = ( π 2 μ 0 ​ i 0 ​ ω ℓ n 2 ​ ) cos ( ω t + 6 π ​ ) ∴ Q max ​ = ε max ​ C = ( π 2 μ 0 ​ i 0 ​ ω ℓ n 2 ​ ) C and i frame ​ = ​ d t d q ​ ​ = ( π 2 μ 0 ​ i 0 ​ ω 2 ℓ n 2 ​ ) ( ω t + 6 π ​ )

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