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A rectangular coil $C$ having $N$ turns, length $2 l$ , width $l$ and resistance per unit length $λ$ is placed in a uniform magnetic field of magnitude $B$ . The plane of the coil is initially perpendicular to $B$ . When the coil is rotated by an angle $θ$ about the axis $X Y$ , a charge $Q$ flows through it

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$Q = \frac{N B l}{3 λ},$ for $θ = \frac{π}{2}$

$Q = \frac{2 N B l}{3 λ},$ for $θ = π$

$Q = \frac{2 N B l}{3 λ},$ for $θ = \frac{3 π}{2}$

$Q = \frac{N B l}{6 λ},$ for $θ = 2 π$

answer is A, B.

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Detailed Solution

$Q = \frac{1}{R} [∆ ϕ] ϕ_{i} = N B A \cos 0 = N B A = 2 N B l^{2} ϕ_{t} = N B A \cos θ = 2 N B l^{2} \cos θ R = 2 λ (2 l + l) = 6 λ l \Rightarrow Q = \frac{2 N B l^{2}}{6 λ l} |1 - \cos θ|$

For $θ = 90 °, Q = \frac{N B l}{3 λ}$

For $θ = 180 °, Q = \frac{2 N B l}{3 λ}$

For $θ = 270 °, Q = \frac{N B l}{3 λ}$

For $θ = 360 °, Q = \frac{N B l}{3 λ}$

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