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In the given figure two concentric cylindrical region in which time varying magnetic field is present as shown. From the center to radius R magnetic field is perpendicular
into the plane varying as dB/dt = 2k₀ and in a region from R to 2R magnetic field is perpendicular out of the plane varying as dB/dt = 4k₀.Find the induced emf across an arc AB of radius 3R.

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$6 R^{2} k θ$

none of these

$5 R^{2} k θ$

$7 R^{2} k θ$

answer is B.

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Detailed Solution

$\begin{array}{l} \begin{array}{l} ∮ \vec{E} \cdot d \vec{l} = 10 π R^{2} k \\ E (6 π R) = 10 π R^{2} k \\ E = \frac{10}{6} R k = \frac{5}{3} R k \end{array} \\ Induced emf across A B = \frac{5}{3} R k (3 R θ) = 5 R^{2} k θ \end{array} \to$

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