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A circular loop wire of radius \( r \) rotates about the \( z \)-axis with angular velocity \( \omega \). The normal to the loop is always perpendicular to the \( z \)-axis. At time \( t=0 \), the normal is parallel to the \( y \)-axis. An external magnetic field \( \vec{B}=B_{y} \hat{j}+B_{z} \hat{k} \) is applied. The EMF \( \varepsilon(t) \) induced in the loop is :
(a) \( \pi r^{2} \omega B_{y} \sin \omega t \)
(b) \( \pi r^{2} \omega B_{z} \cos \omega t \)
(c) \( \pi r^{2} \omega B_{z} \sin \omega t \)
(d) \( \pi r^{2} \omega B_{y} \cos \omega t \)
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