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A square loop \( A B C D \) of side \( \ell \) is moving in \( x y \) plane with velocity \( \vec{v}=\beta t \hat{j} \). There exists a non-uniform magnetic field \( \vec{B}=-B_{0}\left(1+\alpha y^{2}\right) \hat{k} \quad(y0) \), where \( B_{0} \) and \( \alpha \) are positive constants. Initially, the upper wire of the loop is at \( y=0 \). Find the induced voltage across the resistance \( R \) as a function of time. Neglect the magnetic force due to induced current.
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